// Numbas version: exam_results_page_options
{"name": "Chapter 7 Exercises", "metadata": {"description": "<p>End of chapter exercises for <a href=\"http://engineeringstatics.org\"><em>Engineering Statics: Open and Interactive</em></a>&nbsp;</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": true, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Centroids by Composite Area", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "Shape with Hole", "Rectangles and Triangles"], "variable_overrides": [[], [], []], "questions": [{"name": "Centroid of parts", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [["question-resources/centroids.png", "/srv/numbas/media/question-resources/centroids.png"], ["question-resources/centroids_3A0rXlj.png", "/srv/numbas/media/question-resources/centroids_3A0rXlj.png"], ["question-resources/centroids_zSOgoBb.png", "/srv/numbas/media/question-resources/centroids_zSOgoBb.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": [], "metadata": {"description": "<p>Locate the centroid of a rectangle, triangle, and semi-circle on a coordinate grid.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Determine the coordinates of the centroids of the three shapes. &nbsp;Grid units are [<em>{units}</em>].</p>\n<p>{geogebra_applet('xjjm7qqr',[['R_1',R1],['R_2',R2],['T_1',T1],['T_2',T2],['C_1',C1],['C_2',C2]])}</p>\n<p></p>\n<p></p>", "advice": "<p>For a rectangle, the centroid is at the geometric center.</p>\n<p>For a right triangle, divide the base and height into thirds. &nbsp;The centroid is located at the intersection point nearest to the right angle.</p>\n<p>For a semicircle, the centroid is located on the axis of symmetry, a distance of $\\frac{4r}{3\\pi}$ from the straight edge.</p>\n<p></p>\n<p><img src=\"resources/question-resources/centroids_zSOgoBb.png\" width=\"778\" height=\"250\"/></p>", "rulesets": {}, "variables": {"CC": {"name": "CC", "group": "Ungrouped variables", "definition": "C1 + (C2-C1) 4 / 3 / 3.14159", "description": "", "templateType": "anything"}, "C2": {"name": "C2", "group": "inputs", "definition": "random(\n  vector(C1[0],c1[1]+random(-6..6)),\n  vector(C1[0]+random(-6..6),C1[1]))\n  \n  \n  \n  ", "description": "", "templateType": "anything"}, "TC": {"name": "TC", "group": "Ungrouped variables", "definition": "T1 + (T2-T1)/3", "description": "", "templateType": "anything"}, "T1": {"name": "T1", "group": "inputs", "definition": "vector(random(-10..10),random(-8..8))", "description": "", "templateType": "anything"}, "T2": {"name": "T2", "group": "inputs", "definition": "vector(random(-10..10),random(-8..8))", "description": "", "templateType": "anything"}, "C1": {"name": "C1", "group": "inputs", "definition": "vector(random(-10..10),random(-8..8))\n", "description": "", "templateType": "anything"}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything"}, "R1": {"name": "R1", "group": "inputs", "definition": "vector(random(-10..10),random(-8..8))", "description": "", "templateType": "anything"}, "R2": {"name": "R2", "group": "inputs", "definition": "vector(random(-10..10),random(-8..8))", "description": "", "templateType": "anything"}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "random('in','cm','mm','ft')", "description": "", "templateType": "anything"}, "RC": {"name": "RC", "group": "Ungrouped variables", "definition": "R1 + (R2-R1)/2", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "(R1-R2)[0] >= 2 and (R1-R2)[1] >= 2 and  \n(T1-T2)[0] >= 2 and (T1-T2)[1] >= 2 and \nC1<>C2 and abs(C1-C2) > 2\n\n", "maxRuns": "200"}, "ungrouped_variables": ["units", "RC", "TC", "CC", "debug"], "variable_groups": [{"name": "inputs", "variables": ["R1", "R2", "T1", "T2", "C1", "C2"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<table border=\"1\" style=\"float: left;\">\n<tbody>\n<tr>\n<th>Part</th>\n<td style=\"text-align: center;\">$\\bar{x}$</td>\n<td style=\"text-align: center;\">$\\bar{y}$</td>\n</tr>\n<tr>\n<th span=\"\" style=\"color: blue;\">Rectangle</th>\n<td>[[0]]</td>\n<td>[[1]]</td>\n</tr>\n<tr>\n<th span=\"\" style=\"color: red;\">Triangle</th>\n<td>[[2]]</td>\n<td>[[3]]</td>\n</tr>\n<tr>\n<th style=\"color: green;\">Semicircle:</th>\n<td>[[4]]</td>\n<td>[[5]]</td>\n</tr>\n</tbody>\n</table>\n<p><span data-jme-visible=\"debug\"> {RC} {units}</span></p>\n<p><span data-jme-visible=\"debug\">{TC} {units}</span></p>\n<p><span data-jme-visible=\"debug\">{CC} {units}</span></p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$R_x$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(rc[0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$R_y$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(rc[1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$T_x$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(tc[0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$T_y$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(tc[1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$C_x$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(cc[0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$C_y$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(cc[1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Centroid of a composite area: shape with hole", "extensions": ["geogebra"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["centroids", "composite area method", "Mechanics", "mechanics", "Statics", "statics"], "metadata": {"description": "<p>Find the centroid of&nbsp;a shape made from&nbsp;a rectangle, triangle, and circle.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{geogebra_applet('fcfsjuv9',[ ['A',A],['b_1',b1],['h_1',h1],['h_t',ht],['n',n],['Center',center],['radius',radius]])}</p>\n<p><strong></strong>Complete the table below and detemine the coordinates of the centroid of the composite shape.</p>\n<p>Consider the shape to be made up of a {if (m=1,'large','')} rectangle {if (m=0,'and a triangle with a circle','with a triangle and circle')} removed.&nbsp;The circular hole has a {if(random(true,false), 'radius of '+ radius , 'diameter of '+ 2*radius)} {units}, centered at ({(center+A)[0]}, {(center+A)[1]}).</p>", "advice": "<p>{geogebra_applet('fcfsjuv9',[ ['A',A],['b_1',b1],['h_1',h1],['h_t',ht],['n',n],['Center',center],['radius',radius],['visibility',m]])}</p>\n<p></p>\n<p>1. Divide the shape into three subshapes as described in the problem statement.&nbsp;</p>\n<p>2. You should be able to set up a table to gather the required information like the one provided in this problem.</p>\n<p>3. Determine and enter&nbsp;the area and centroidal coordinates for each subshape into the table</p>\n<p style=\"padding-left: 30px;\">$\\qquad A_i, \\bar{x}_i,\\bar{y}_i$</p>\n<p>4. Multiply area by the centroidal coordinates to&nbsp;get the moment of areas for the pieces.</p>\n<p style=\"padding-left: 30px;\">$\\qquad (Q_x)_i = A_i\\bar{y}_i ,\\quad(Q_y)_i=A_i\\bar{x}_i$.</p>\n<p>5. Sum columns 1, 4, and 5&nbsp;to find the total area and moments of area.</p>\n<p style=\"padding-left: 30px;\">$\\qquad A, Q_x, Q_y$</p>\n<p></p>\n<table class=\"centroid\">\n<tbody>\n<tr class=\"underline\">\n<td><strong> Part </strong></td>\n<td>$A_i$ [{units}<sup>2</sup>]</td>\n<td>$\\bar{x}_i$ [{units}]</td>\n<td>$\\bar{y}_i$ [{units}]</td>\n<td>$A_i\\bar{x}_i$ [{units}<sup>3</sup>]</td>\n<td>$A_i\\bar{y}_i$ [{units}<sup>3</sup>]</td>\n</tr>\n<tr>\n<td><strong> rectangle </strong></td>\n<td>{area_rect[m]}</td>\n<td>{C_rect[m][0]}</td>\n<td>{C_rect[m][1]}</td>\n<td>{Q_rect[1]}</td>\n<td>{Q_rect[0]}</td>\n</tr>\n<tr>\n<td><strong> triangle </strong></td>\n<td>{area_tri[m]}</td>\n<td>{siground(C_tri[m][0],3)}</td>\n<td>{siground(C_tri[m][1],3)}</td>\n<td>{Q_tri[1]}</td>\n<td>{Q_tri[0]}</td>\n</tr>\n<tr>\n<td><strong> circle </strong></td>\n<td class=\"underline\">{siground(area_circ[m],3)}</td>\n<td>{C_circ[m][0]}</td>\n<td>{C_circ[m][1]}</td>\n<td class=\"underline\">{siground(Q_circ[1],3)}</td>\n<td class=\"underline\">{siground(Q_circ[0],3)}</td>\n</tr>\n<tr>\n<td><strong> $\\Sigma$ </strong></td>\n<td>{siground(area_total,3)}</td>\n<td></td>\n<td></td>\n<td>{siground(Q_total[1],3)}</td>\n<td>{siground(Q_total[0],3)}</td>\n</tr>\n</tbody>\n</table>\n<p>6. Find answers&nbsp;with&nbsp;&nbsp;</p>\n<p></p>\n<p style=\"padding-left: 30px;\">$\\qquad &nbsp;\\bar{x} = \\dfrac{Q_y}{A} =\\dfrac{\\Sigma A_i \\bar{x}_i}{\\Sigma A_i} = \\dfrac{\\var{siground(Q_total[1],3)}}{\\var{siground(area_total,3)}} = &nbsp;\\var{siground(centroid[0],3)}\\, \\var{units}$</p>\n<p style=\"padding-left: 30px;\">$\\qquad &nbsp;\\bar{y} &nbsp;= \\dfrac{Q_x}{A} = \\dfrac{\\Sigma A_i \\bar{y}_i}{\\Sigma A_i}= \\dfrac{\\var{siground(Q_total[0],3)}}{\\var{siground(area_total,3)}}= \\var{siground(centroid[1],3)}\\, \\var{units} $</p>", "rulesets": {}, "variables": {"ht": {"name": "ht", "group": "Input values", "definition": "random(3..9#3)", "description": "<p>\"height\" of triangle &nbsp;</p>\n<p>horizontal for n = 4,5,6,10,11,12</p>\n<p>vertical for n = 1,2,3,7,8,9</p>", "templateType": "anything"}, "C_rect": {"name": "C_rect", "group": "centroids", "definition": "[vector(b1/2,h1/2) + A,\n if(n in [1,2,3], vector(b1/2,(h1-ht)/2)+A,\n if(n in [4,5,6], vector((b1+ht)/2,h1/2)+A,\n if(n in [7,8,9], vector(b1/2,(h1+ht)/2)+A,\n vector((b1-ht)/2,h1/2)+A)))] ", "description": "", "templateType": "anything"}, "C_circ": {"name": "C_circ", "group": "centroids", "definition": "[center +A ,center +A]", "description": "", "templateType": "anything"}, "units": {"name": "units", "group": "Input values", "definition": "random('in', 'cm', 'ft' )", "description": "<p>Offset of bottom right corner from originl</p>", "templateType": "anything"}, "area_circ": {"name": "area_circ", "group": "Calculated areas", "definition": "[- pi * radius^2, - pi* radius^2]", "description": "", "templateType": "anything"}, "area_total": {"name": "area_total", "group": "Calculated areas", "definition": "area_rect[0]+area_tri[0]+area_circ[0]", "description": "", "templateType": "anything"}, "area_tri": {"name": "area_tri", "group": "Calculated areas", "definition": "[if(n in [1,2,3,7,8,9], b1*ht/2,h1*ht/2),\n-if(n in [1,2,3,7,8,9], b1*ht/2,h1*ht/2)]", "description": "", "templateType": "anything"}, "center": {"name": "center", "group": "Input values", "definition": "vector(b1/2,h1/2) + random(0..3) *\nvector(if(n<=3,[0,-1],\nif(n<=6,[1,0],\nif(n<=9,[0,1],\n[-1,0]))))\n\n\n\n\n", "description": "<p>center of the circle measured from bottom left of the rectangle</p>", "templateType": "anything"}, "Q_circ": {"name": "Q_circ", "group": "moments of area", "definition": "area_circ[m] * vector(C_circ[m][1],C_circ[m][0])", "description": "", "templateType": "anything"}, "radius": {"name": "radius", "group": "Input values", "definition": "random(1..(min(h1-1,b1-1)/2)#0.5)", "description": "<p>radius of the circle</p>", "templateType": "anything"}, "A": {"name": "A", "group": "Input values", "definition": "-vector(random([0,0],[b1,0],[b1,h1],[0,h1],[b1/2,h1/2],[0,h1/2],[center[0],center[1]]))", "description": "<p>This offsets the shape to one of the corners of the rect, the center of the rect, or the center of the circle.</p>", "templateType": "anything"}, "h1": {"name": "h1", "group": "Input values", "definition": "random(4..12#2)", "description": "<p>vertical height of rectangle</p>", "templateType": "anything"}, "b1": {"name": "b1", "group": "Input values", "definition": "random(4..12#2)", "description": "<p>horizontal base of rectangle</p>", "templateType": "anything"}, "n": {"name": "n", "group": "Input values", "definition": "random(1 .. 12#1)", "description": "<p>Selects the position of the triangle, index gives vertex location</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">9</td>\n<td style=\"text-align: center;\">8</td>\n<td style=\"text-align: center;\">7</td>\n<td style=\"text-align: center;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">10</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">6</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">11</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">rectangle</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">5</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">12</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">4</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">1</td>\n<td style=\"text-align: center;\">2</td>\n<td style=\"text-align: center;\">3</td>\n<td style=\"text-align: center;\"></td>\n</tr>\n</tbody>\n</table>", "templateType": "randrange"}, "C_tri": {"name": "C_tri", "group": "centroids", "definition": "// determines location of centroid\n// returns array of centroid coordinates, first term for m=0 \n[\nswitch(\n  n=1, vector(b1/3,-ht/3),\n  n=2, vector(b1/2,-ht/3),\n  n=3, vector(2*b1/3,-ht/3),\n  n=4, vector(b1+ht/3,h1/3),\n  n=5, vector(b1+ht/3,h1/2),\n  n=6, vector(b1+ht/3,2*h1/3),\n  n=7, vector(2 * b1/3, h1+ht/3),\n  n=8, vector(b1/2, h1+ht/3),\n  n=9, vector(b1/3, h1+ht/3),\n  n=10, vector(-ht/3,2*h1/3),\n  n=11, vector(-ht/3,h1/2),\n  n=12, vector(-ht/3,h1/3)\n  ) + A\n  ,\n  switch(\n  n=3, vector(b1/3,-2*ht/3),\n  n=2, vector(b1/2,-2*ht/3),\n  n=1, vector(2*b1/3,-2*ht/3),\n  n=6, vector(b1+2*ht/3,h1/3),\n  n=5, vector(b1+2*ht/3,h1/2),\n  n=4, vector(b1+2*ht/3,2*h1/3),\n  n=9, vector(2 * b1/3, h1+2*ht/3),\n  n=8, vector(b1/2, h1+2*ht/3),\n  n=7, vector(b1/3, h1+2*ht/3),\n  n=12, vector(-2*ht/3,2*h1/3),\n  n=11, vector(-2*ht/3,h1/2),\n  n=10, vector(-2*ht/3,h1/3)\n  ) + A\n  ]", "description": "<p>determines location of centroid of triangle based on location and method<br />returns array of centroid coordinates, first term for m=0 <br /><br /></p>", "templateType": "anything"}, "m": {"name": "m", "group": "Input values", "definition": "if(n in [2,5,8,11],0,random(0..1))\n", "description": "<p>This is the method used to solve the problem:&nbsp;</p>\n<p>m=0: small rectangle + triangle - circle</p>\n<p>m=1: big rectangle - triangle - circle</p>\n<p>when n is in [2,5,8,11], use method 0, becauses otherwise it would require 2 negative triangles.</p>", "templateType": "anything"}, "Q_rect": {"name": "Q_rect", "group": "moments of area", "definition": "area_rect[m] * vector(C_rect[m][1],C_rect[m][0])", "description": "<p>[Q_x,Q_y]</p>", "templateType": "anything"}, "area_rect": {"name": "area_rect", "group": "Calculated areas", "definition": "[b1*h1,if(n in [1,2,3,7,8,9],b1*(h1+ht),h1*(b1+ht))]", "description": "", "templateType": "anything"}, "centroid": {"name": "centroid", "group": "moments of area", "definition": "vector(Q_total[1]/area_total,Q_total[0]/area_total)", "description": "", "templateType": "anything"}, "Q_tri": {"name": "Q_tri", "group": "moments of area", "definition": "area_tri[m] * vector(C_tri[m][1],C_tri[m][0])", "description": "", "templateType": "anything"}, "Q_total": {"name": "Q_total", "group": "moments of area", "definition": "Q_rect+Q_tri+Q_circ", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "// tries to prevent the circle from extending beyond the perimiter.\n\nif (n<=3,  center[1]-2*radius   > -(h1+ht/2),\nif (n<=6, (center[0]+2*radius) <  (b1+ht/2),\nif (n<=9, (center[1]+2*radius) <  (h1+ht/2),\n          (center[0]-2*radius) > -(b1-ht/2))))\n", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Input values", "variables": ["A", "b1", "h1", "ht", "center", "units", "radius", "n", "m"]}, {"name": "Calculated areas", "variables": ["area_rect", "area_tri", "area_circ", "area_total"]}, {"name": "centroids", "variables": ["C_rect", "C_circ", "C_tri"]}, {"name": "moments of area", "variables": ["Q_rect", "Q_tri", "Q_circ", "Q_total", "centroid"]}], "functions": {}, "preamble": {"js": "\n", "css": "table.centroid{margin-left:0;}\n\ntable.centroid td {\n  width:6em; \n  vertical-align:center; \n  text-align:center;}\ntable.centroid *.underline {border-bottom: 2px solid black;}\n\n"}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Table", "marks": 0, "scripts": {"mark": {"script": "//var method = Numbas.jme.unwrapValue(this.scope.variables.m);\n//numbasGGBApplet0.setValue('visibility',method)\n", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<table class=\"centroid &lt;/button&gt;\" tbody=\"\">\n<tbody>\n<tr class=\"underline\">\n<td><strong> Part </strong></td>\n<td>\n<p>$A_i$&nbsp;</p>\n</td>\n<td class=\"underline\">\n<p>$\\bar{x}_i$&nbsp;</p>\n</td>\n<td>\n<p>$\\bar{y}_i$&nbsp;</p>\n</td>\n<td>\n<p>$A_i\\bar{x}_i$&nbsp;</p>\n</td>\n<td>\n<p>$A_i\\bar{y}_i$&nbsp;</p>\n</td>\n</tr>\n<tr>\n<td><strong> rectangle </strong></td>\n<td>[[0]]</td>\n<td>[[4]]</td>\n<td>[[7]]</td>\n<td>[[10]]</td>\n<td>[[14]]</td>\n</tr>\n<tr>\n<td><strong> triangle </strong></td>\n<td>[[1]]</td>\n<td>[[5]]</td>\n<td>[[8]]</td>\n<td>[[11]]</td>\n<td>[[15]]</td>\n</tr>\n<tr>\n<td><strong> circle </strong></td>\n<td class=\"underline\">[[2]]</td>\n<td>[[6]]</td>\n<td>[[9]]</td>\n<td class=\"underline\">[[12]]</td>\n<td class=\"underline\">[[16]]</td>\n</tr>\n<tr>\n<td><strong> $\\Sigma$ </strong></td>\n<td>[[3]]</td>\n<td></td>\n<td></td>\n<td>[[13]]</td>\n<td>[[17]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Ar", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(area_rect[m],units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "At", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(area_tri[m],units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Ac", 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"C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "xr", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(C_rect[m][0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "xt", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(C_tri[m][0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "xc", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(C_circ[m][0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "yr", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(C_rect[m][1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "yt", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(C_tri[m][1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "yc", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(C_circ[m][1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qyr", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_rect[1],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qyt", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_tri[1],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qyc", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_circ[1],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qy", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_total[1],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qxr", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_rect[0],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qxt", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_tri[0],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qxr", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_circ[0],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qx", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_total[0],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Centroid", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\bar{x} =\\dfrac{Q_y}{A} =$ [[0]]&nbsp;$\\qquad \\bar{y} =\\dfrac{Q_x}{A} = $ [[1]]<br/><br/></p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "xbar", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "quantity(centroid[0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "ybar", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "quantity(centroid[1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Centroid of a composite area: rectangles and triangles", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [["question-resources/centroid-t-r.ggb", "/srv/numbas/media/question-resources/centroid-t-r.ggb"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["centroids", "first moment of area", "mechanics", "Mechanics", "statics", "Statics"], "metadata": {"description": "<p>Find the centroid of a shape made up of a rectangle and two triangles.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{applet()}</p>\n<p>Determine the coordinates of the centroid of the polygon shown. &nbsp;Grid units are [{units}].</p>\n<p>Consider the polygon to be made up of a ({b0} $\\times$&nbsp;{h0}) rectangle {sign1} a ({b1} $\\times$&nbsp;{h1}) triangle {sign2} a ({b2} $\\times$&nbsp;{h2}) triangle.</p>", "advice": "<div>\n<table border=\"1px\" style=\"float: left;\">\n<tbody>\n<tr>\n<td>Part</td>\n<td>$A_i$</td>\n<td>$\\bar{x}_i$</td>\n<td>$\\bar{y}_i$</td>\n<td>$A_i\\bar{x}_i$</td>\n<td>$A_i\\bar{y}_i$</td>\n</tr>\n<tr>\n<td>Rectangle</td>\n<td>{A0}</td>\n<td>{bar(C0[0])}</td>\n<td>{bar(C0[1])}</td>\n<td>{Q(a0, c0[0])}</td>\n<td>{Q(a0, c0[1])}</td>\n</tr>\n<tr>\n<td>Triangle 1</td>\n<td>{A1}</td>\n<td>{bar(C1[0])}</td>\n<td>{bar(C1[1])}</td>\n<td>{Q(a1, c1[0])}</td>\n<td>{Q(a1, c1[1])}</td>\n</tr>\n<tr>\n<td>Triangle 2</td>\n<td>{A2}</td>\n<td>{bar(C2[0])}</td>\n<td>{bar(C2[1])}</td>\n<td>{Q(a2, c2[0])}</td>\n<td>{Q(a2, c2[1])}</td>\n</tr>\n<tr>\n<td>$\\Sigma$</td>\n<td>{AT}</td>\n<td></td>\n<td></td>\n<td>{display(xbar AT)}</td>\n<td>{display(ybar AT)}</td>\n</tr>\n</tbody>\n</table>\n</div>\n<div>\n<p>$\\qquad\\bar{x} = \\dfrac{\\Sigma A_i\\bar{x}_i}{\\Sigma A_i} = &nbsp;\\var{display(xbar)}$</p>\n<p>$\\qquad \\bar{y} = &nbsp;\\dfrac{\\Sigma A_i\\bar{y}_i}{\\Sigma A_i} &nbsp;=\\var{display(ybar)}$</p>\n</div>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"A": {"name": "A", "group": "Ungrouped variables", "definition": "vector(0,random(2..12))", "description": "", "templateType": "anything", "can_override": false}, "C2": {"name": "C2", "group": "geometry", "definition": "vector(A[0],B[1])+(vector(B[0],A[1])-vector(A[0],B[1]))/3  ", "description": "", "templateType": "anything", "can_override": false}, "A0": {"name": "A0", "group": "geometry", "definition": "b0 h0", "description": "", "templateType": "anything", "can_override": false}, "A2": {"name": "A2", "group": "geometry", "definition": "b2 h2/2 if(sign2='+',1,-1)", "description": "", "templateType": "anything", "can_override": false}, "b0": {"name": "b0", "group": "geometry", "definition": "qty(B[0\n  ],units)", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "vector(random(2..12),0)", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "geometry", "definition": "b0", "description": "", "templateType": "anything", "can_override": false}, "C1": {"name": "C1", "group": "geometry", "definition": "vector(B[0],C[1])+(vector(C[0],B[1])-vector(B[0],C[1]))/3  ", "description": "", "templateType": "anything", "can_override": false}, "A1": {"name": "A1", "group": "geometry", "definition": "b1 h1 /2 if(sign1='+',1,-1)", "description": "", "templateType": "anything", "can_override": false}, "ybar": {"name": "ybar", "group": "Unnamed group", "definition": "(a0 c0[1] + a1 c1[1] + a2 c2[1])/AT qty(1,units)", "description": "", "templateType": "anything", "can_override": false}, "h1": {"name": "h1", "group": "geometry", "definition": "h0", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "vector(random(2..12),random(2..12))", "description": "", "templateType": "anything", "can_override": false}, "h0": {"name": "h0", "group": "geometry", "definition": "qty(B[1],units)", "description": "", "templateType": "anything", "can_override": false}, "sign2": {"name": "sign2", "group": "geometry", "definition": "if(b[1]<a[1],'+','\u2013')", "description": "", "templateType": "anything", "can_override": false}, "C0": {"name": "C0", "group": "geometry", "definition": "(B/2)", "description": "", "templateType": "anything", "can_override": false}, "AT": {"name": "AT", "group": "geometry", "definition": "A0+A1+A2", "description": "", "templateType": "anything", "can_override": false}, "h2": {"name": "h2", "group": "geometry", "definition": "qty(abs(b[1]-A[1]),units)", "description": "", "templateType": "anything", "can_override": false}, "xbar": {"name": "xbar", "group": "Unnamed group", "definition": "(a0 c0[0] + a1 c1[0] + a2 c2[0])/AT qty(1,units)", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "geometry", "definition": "qty(abs(b[0]-c[0]),units)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "random('in','cm','ft','m')", "description": "", "templateType": "anything", "can_override": false}, "sign1": {"name": "sign1", "group": "geometry", "definition": "if(b[0]<c[0],'+','\u2013')", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "D": {"name": "D", "group": "Ungrouped variables", "definition": "vector(0,0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "B[1]<>A[1] and B[0]<>C[0]", "maxRuns": "100"}, "ungrouped_variables": ["A", "B", "C", "D", "units", "debug"], "variable_groups": [{"name": "geometry", "variables": ["b0", "h0", "b2", "h1", "b1", "h2", "sign1", "sign2", "A0", "A1", "A2", "AT", "C0", "C2", "C1"]}, {"name": "Unnamed group", "variables": ["xbar", "ybar"]}], "functions": {"Q": {"parameters": [["area", "quantity"], ["distance", "number"]], "type": "quantity", "language": "jme", "definition": "display(area*distance*qty(1,units))"}, "display": {"parameters": [["q", "quantity"]], "type": "quantity", "language": "jme", "definition": "string(siground(q,4))"}, "bar": {"parameters": [["coord", "number"]], "type": "quantity", "language": "jme", "definition": "display(quantity(coord,units))"}, "applet": {"parameters": [], "type": "ggbapplet", "language": "javascript", "definition": "\n// Create the worksheet. \n// This function returns an object with a container `element` and a `promise` resolving to a GeoGebra applet.\nvar params = {\n  material_id: 'ftkm8mfx',\n  //alternate method, load from file.\n  //filename: \"resources/question-resources/centroid-t-r.ggb\",\n  //width:400,\n  //height:300\n  // was geogebra_applet('ftkm8mfx',[['A',A],['B',B],['C',C]])\n}\n\nvar result = Numbas.extensions.geogebra.createGeogebraApplet(params);\n\n// Once the applet has loaded, run some commands to manipulate the worksheet.\nresult.promise.then(function(d) {\n  var app = d.app;\n  question.applet = d;\n  \n  \nfunction setGGBPoint(name) {\n    // moves point in GGB to location of Numbas Vector Variable\n    var pt = question.scope.evaluate(name).value\n    app.setFixed(name,false,false);\n    app.setCoords(name, pt[0], pt[1]);\n    app.setFixed(name,true,true);\n  }\n\n  setGGBPoint(\"A\");\n  setGGBPoint(\"B\");\n  setGGBPoint(\"C\");\n  setGGBPoint(\"D\");\n  app.setVisible(\"Centroid\",false);\n  \n});\n\n// This function returns the result of `createGeogebraApplet` as an object \n// with the JME data type 'ggbapplet', which can be substituted into the question's content.\nreturn new Numbas.jme.types.ggbapplet(result);"}}, "preamble": {"js": "question.signals.on('adviceDisplayed',function() {\n   try{\n    var app = question.applet.app;\n \n  app.setVisible(\"Centroid\",true);\n  \n  }\n  catch(err){}  \n})\n\n\n\n", "css": "table.centroid{margin-left:0;}\n\ntable.centroid td {\n  width:6em; \n  vertical-align:center; \n  text-align:center;}\ntable.centroid *.underline {border-bottom: 2px solid black;}\n\n"}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Info Table", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<table style=\"float: left; width: 625px;\" class=\"centroid\">\n<tbody>\n<tr class=\"underline\">\n<th style=\"width: 120px;\">Part</th>\n<td style=\"width: 120px; text-align: center;\">$A_i$</td>\n<td style=\"width: 120px; text-align: center;\">$\\bar{x}_i$</td>\n<td style=\"width: 120px; text-align: center;\">$\\bar{y}_i$</td>\n<td style=\"width: 120px; text-align: center;\">$A_i\\bar{x}_i$</td>\n<td style=\"width: 120px; text-align: center;\">$A_i\\bar{y}_i$</td>\n</tr>\n<tr>\n<th>Rectangle</th>\n<td>[[0]]</td>\n<td>[[4]]</td>\n<td>[[7]]</td>\n<td>[[10]]</td>\n<td>[[13]]</td>\n</tr>\n<tr>\n<th>Triangle 1</th>\n<td>[[1]]</td>\n<td>[[5]]</td>\n<td>[[8]]</td>\n<td>[[11]]</td>\n<td>[[14]]</td>\n</tr>\n<tr style=\"border-bottom: 2px;\">\n<th>Triangle 2</th>\n<td class=\"underline\">[[2]]</td>\n<td>[[6]]</td>\n<td>[[9]]</td>\n<td class=\"underline\">[[12]]</td>\n<td class=\"underline\">[[15]]</td>\n</tr>\n<tr>\n<th>$\\Sigma$</th>\n<td>[[3]]</td>\n<td></td>\n<td></td>\n<td>[[16]]</td>\n<td>\n<p>[[17]]</p>\n</td>\n</tr>\n</tbody>\n</table>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "A_0", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "A0", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "A_1", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "A1", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "A_2", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "A2", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$A$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "AT", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "x_0", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(c0[0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "x_1", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(c1[0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "x_2", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(c2[0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "y_0", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(c0[1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "y_1", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(c1[1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "y_2", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(c2[1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Q_{y_0}", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "a0 * c0[0] * qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Q_{y_1}+", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "a1 * c1[0] * qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Q_{y_2}", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "a2 * c2[0] * qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Q_{x_0}", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "a0 * c0[1] * qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Q_{x_1}", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "a1 * c1[1] * qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Q_{x_2}", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "a2 * c2[1] * qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$Q_y$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "xbar * AT", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$Q_x$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "ybar * AT", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Results", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\bar{x} =\\dfrac{Q_y}{A} = $&nbsp;[[0]] &nbsp;$\\qquad \\bar{y} =\\dfrac{Q_x}{A} =$&nbsp;[[1]]</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$\\bar{x}$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "xbar", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$\\bar{y}$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "ybar", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Centroids by Integration", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "Area under a curve", "", "Upper and lower bounds are functions"], "variable_overrides": [[], [], [], []], "questions": [{"name": "Differential Elements", "extensions": ["geogebra", "weh"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["centroids", "centroids by integration", "Mechanics", "mechanics", "statics", "Statics"], "metadata": {"description": "<p>Given a random spandrel, find the expressions for the differential elements of area and the coordinates of its centroid needed to determine the location of the&nbsp;centroid by integration.&nbsp;</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{geogebra_applet('tpndhsyt',[['version',version]])}</p>", "advice": "<p>The area of the strip, dA is the width times the height of the strip.</p>\n<p>The narrow width of the element is either $dx$ or $dy$&nbsp;</p>\n<p>The coordinates of the centroid are found by averaging the coordinates of the top and bottom of the strip.</p>", "rulesets": {}, "variables": {"dA": {"name": "dA", "group": "Ungrouped variables", "definition": "expression(['y*dx',\"(y'-y)*dx\",\"(b-y)*dx\", \"(x-x')*dy\",\"x*dy\",\"(a-x)*dy\"][version-1\n])", "description": "", "templateType": "anything"}, "ybar": {"name": "ybar", "group": "Ungrouped variables", "definition": "expression([\"y/2\",\"(y+y')/2\",\"(y+b)/2\",\"y\",\"y\",\"y\"][version-1])", "description": "", "templateType": "anything"}, "xbar": {"name": "xbar", "group": "Ungrouped variables", "definition": "expression([\"x\",\"x\",\"x\",\"(x+x')/2\",\"x/2\",\"(x+a)/2\"][version-1])", "description": "", "templateType": "anything"}, "version": {"name": "version", "group": "Ungrouped variables", "definition": "random(1..6)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["version", "dA", "xbar", "ybar"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the properties of the differential strip in terms of the known coordinates.</p>\n<p>$dA$ =&nbsp;[[0]]</p>\n<p>$\\bar{x}_{el}$ =&nbsp;[[1]]&nbsp;</p>\n<p>$\\bar{y}_{el}$ =[[2]]&nbsp;&nbsp;</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "da", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{dA}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "xbar", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{xbar}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "ybar", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ybar}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Area under a curve by integration", "extensions": ["geogebra", "quantities", "weh"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [["question-resources/centroid-integration.ggb", "/srv/numbas/media/question-resources/centroid-integration.ggb"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["area", "Area", "definite integral", "Mechanics", "mechanics", "Statics", "statics"], "metadata": {"description": "<p>Find roots and the area under a parabola</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p style=\"float: right; padding: 3px;\">{applet()}</p>\n<p>Given the function $\\color{red}{y=\\simplify[!noleadingminus,unitfactor]{{A} x^2 + {B} x + {C}}}$, determine the area under the curve from the <em>y</em>-axis to the point where the curve crosses the positive <em>x</em>-axis. &nbsp;The x- and y- coordinates are in&nbsp;[{units}].&nbsp;You may not use a graphing calculator to solve this problem.</p>\n<p></p>\n<p></p>\n<p></p>", "advice": "<ol>\n<li>To find the point where the curve crosses the <em>y</em>-axis, set <em>x</em> = 0 and solve for <em>y</em>.</li>\n<li>To find the point where the curve crosses the positive <em>x</em>-axis, set <em>y</em> to zero and solve for <em>x</em> using the quadratic formula. Take the positive root.</li>\n<li>To find the area under the curve, divide the shaded area into vertical differential strips where&nbsp;$dA = y\\, dx$ then integrate between the horizontal limits to find the area.</li>\n</ol>\n<p style=\"padding-left: 30px;\">$\\begin{align}A &amp;= \\int dA \\\\&amp;= \\int_0^a y\\,dx \\\\&amp;= \\int_0^a(\\simplify[!noleadingminus,unitfactor]{{A} x^2 + {B} x + {C}})\\, dx\\\\&amp; = \\left[&nbsp;\\simplify[unitfactor,collectnumbers]{{A}&nbsp;x^3/3&nbsp;+ {B} x^2/2 + {C}x}\\right]_0^\\var{scalar(siground(root1,4))}\\\\&amp;=\\var{siground(area,4)}\\end{align}$</p>", "rulesets": {}, "variables": {"area": {"name": "area", "group": "Ungrouped variables", "definition": "let(x,scalar(root1), qty(A x^3/3 + B x^2/2 + C x,units)) qty(units)", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "random(-0.5..-2#0.5)", "description": "", "templateType": "anything"}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything"}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "random(0..3)+0.5", "description": "", "templateType": "anything"}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "templateType": "anything"}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "random('in','ft','mm','cm')", "description": "", "templateType": "anything"}, "root1": {"name": "root1", "group": "Ungrouped variables", "definition": "qty((-b - sqrt(b^2-4 a c))/(2 a),units)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["A", "B", "C", "root1", "area", "units", "debug"], "variable_groups": [], "functions": {"applet": {"parameters": [], "type": "ggbapplet", "language": "javascript", "definition": "\n// Create the worksheet. \n// This function returns an object with a container `element` and a `promise` resolving to a GeoGebra applet.\nvar params = {\n  filename: 'resources/question-resources/centroid-integration.ggb',\n  width: 300,\n  height: 300\n  // was {geogebra_applet('nuhzkzqp',[['a',A],['b',B],['c',C]])}\n}\n\nvar result = Numbas.extensions.geogebra.createGeogebraApplet(params);\n\n// Once the applet has loaded, run some commands to manipulate the worksheet.\nresult.promise.then(function(d) {\n  var app = d.app;\n  question.applet = d;\n  \n function setGGBNumber(name) {\n    // Sets number in GGB to a Numbas Variable\n    var n = question.scope.evaluate(name).value;\n    app.setValue(name,n);\n  }\n  \nfunction setGGBPoint(name) {\n    // moves point in GGB to location of Numbas Vector Variable\n    var pt = question.scope.evaluate(name).value\n    app.setFixed(name,false,false);\n    app.setCoords(name, pt[0], pt[1]);\n    app.setFixed(name,true,true);\n  }\n\n  setGGBPoint(\"a\");\n  setGGBPoint(\"b\");\n  setGGBPoint(\"c\");\n  app.setGridVisible(false);\n  app.recalculateEnvironments();\n\n  \n});\n\n// This function returns the result of `createGeogebraApplet` as an object \n// with the JME data type 'ggbapplet', which can be substituted into the question's content.\nreturn new Numbas.jme.types.ggbapplet(result);"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the points where the curve crosses the axes.</p>\n<p>$h$ =&nbsp;[[0]] <span data-jme-visible=\"debug\">{qty(C,units)}</span></p>\n<p>$a$ =&nbsp;[[1]] <span data-jme-visible=\"debug\">{siground(root1,4)}</span></p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "h", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(C,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "a", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "root1", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "A", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Set up and evaluate&nbsp;the integral equation below to find the area under the curve.</p>\n<p>$\\begin{align} A &amp;= \\int{dA}\\\\&amp;=\\int_0^a y\\, dx \\\\ \\vdots\\end{align}$</p>\n<p>$A$ = [[0]] <span data-jme-visible=\"debug\">&nbsp;{siground(area,4)}</span></p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "area", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "area", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Centroids by integration ", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["area under curve", "centroidal coordinates", "centroids by integration", "first moment of area", "integration", "mechanics", "Mechanics", "Statics", "statics"], "metadata": {"description": "<p>Find the area, first moment of area, and coordinates of a general spandrel. &nbsp;The area&nbsp;may be above or below the function.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{geogebra_applet('bqnqgpfp',[['n',n],['h',random(1,1.5)],['b',random(0.8,1.3)],['Above', above],['Vertical',vertical]])}</p>\n<p>Use integration with {if(Vertical=1,'vertical','horizontal')} strips to determine the area&nbsp;of the spandrel bounded by the function $\\color{red}{y = f(x) = h - k \\simplify[all,fractionnumbers]{x^{n}}}$ and $\\var{if(Above=1, 'the lines $y=h$ and $x=b$','the $x$- and $y$-axes')}$,&nbsp;and also find the coordinates of its centroid. Note:&nbsp;<em>b</em>&nbsp;and <em>h</em> are constants.</p>", "advice": "<div data-jme-visible=\"vertical = 0\" style=\"background: yellow; border: 1px solid black; padding: 1em; margin: 1em;\">\n<p>Note: The solutions below is&nbsp;for Vertical Strips. &nbsp;</p>\n<p>The procedure&nbsp;for horizontal strips is similar, but with these strip properties and limits:</p>\n<p>Strip properties: &nbsp;<span data-jme-visible=\"Above = 1\">$dA = (b-x)\\,dy$, $\\bar{x}_{el} = \\dfrac{x+b}{y}$, $\\bar{y}_{el} = y&nbsp;$</span><span>&nbsp;</span><span data-jme-visible=\"above = 0\">$dA = x&nbsp;\\,dy$, $\\bar{x}_{el} = x/2$, $\\bar{y}_{el} =y$</span></p>\n<p>Limits: &nbsp;$x= 0 \\text{ to } h$</p>\n<p>You will get the same results for $A, Q_x, Q_y, \\bar{x} \\text{ and } \\bar{y}$, which ever strips you choose.</p>\n</div>\n<p>1. Bounding function: $y = f(x) = h - k \\simplify[all,fractionnumbers]{x^{n}}$</p>\n<p>2. Constant&nbsp;$k$ in terms of $b$:&nbsp;at $x=b, y=0&nbsp;\\therefore&nbsp;h - k&nbsp;\\simplify[all,fractionnumbers]{b^{n}} &nbsp;= 0 \\therefore k = \\dfrac{h}{\\simplify[all,fractionnumbers]{b^{n}}}$</p>\n<p>3. Strip properties: &nbsp;<span data-jme-visible=\"Above = 0\">$dA = y\\,dx$, $\\bar{x}_{el} = x$, $\\bar{y}_{el} = y/2$</span><span>&nbsp;</span><span data-jme-visible=\"above = 1\">$dA = (h-y)\\,dx$, $\\bar{x}_{el} = x$, $\\bar{y}_{el} = (h+y)/2$</span></p>\n<p>4. Limits: &nbsp;$x= 0 \\text{ to } b$</p>\n<p>5. Area under the curve:</p>\n<p><span data-jme-visible=\"above=0\">$\\begin{align} A &amp;= \\int dA\\\\&amp;= \\int_0^b y\\, dx\\\\&amp;= \\int_0^b &nbsp;(h - k \\simplify[all,fractionnumbers]{x^{n}})\\, dx\\\\&amp;= \\left[ hx - k \\dfrac{\\simplify[all,fractionnumbers]{x^{n+1}}}{\\simplify[all,fractionnumbers]{{n+1}}}\\right]_0^b\\\\&amp;= \\left[ hb - \\left(\\dfrac{h}{\\simplify[all,fractionnumbers]{b^{n}}}\\right)&nbsp;\\dfrac{\\simplify[all,fractionnumbers]{b^{n+1}}}{\\simplify[all,fractionnumbers]{{n+1}}}\\right]\\\\&amp;=hb-\\dfrac{hb}{\\simplify[all,fractionnumbers]{{n}+1}}\\\\&amp;=\\var[all,fractionnumbers]{{n}/({n}+1)} h b\\end{align}$</span></p>\n<p><span data-jme-visible=\"above=1\">$\\begin{align} A &amp;= \\int dA\\\\&amp;= \\int_0^b (h-y)\\, dx\\\\&amp;= \\int_0^b &nbsp;h - (h - k \\simplify[all,fractionnumbers]{x^{n}})\\, dx\\\\&amp;=\\int_0^bk \\simplify[all,fractionnumbers]{x^{n}}dx\\\\&amp;= \\left[k \\dfrac{\\simplify[all,fractionnumbers]{x^{n+1}}}{\\simplify[all,fractionnumbers]{{n+1}}}\\right]_0^b\\\\&amp;= \\left[ \\left(\\dfrac{h}{\\simplify[all,fractionnumbers]{b^{n}}}\\right)&nbsp;\\dfrac{\\simplify[all,fractionnumbers]{b^{n+1}}}{\\simplify[all,fractionnumbers]{{n+1}}}\\right]\\\\&amp;=\\dfrac{hb}{\\simplify[all,fractionnumbers]{{n}+1}}\\\\&amp;=\\var[all,fractionnumbers]{1/({n}+1)} h b\\end{align}$</span></p>\n<p>6. $Q_x$ and $Q_y$ &nbsp;Perform similar integrations to get:&nbsp;</p>\n<p><span data-jme-visible=\"above=0\">$Q_x = \\int \\bar{y}_{el}\\,dA &nbsp;= \\simplify[all,simplifyfractions,fractionnumbers]{{n}^2&nbsp;/(2{n}^2+3{n}+1) h^2b} &nbsp;\\qquad&nbsp;Q_y = \\int \\bar{x}_{el}\\,dA &nbsp;= \\simplify[all,fractionnumbers,simplifyfractions]{{n}/(2{n}+4)} hb^2$</span></p>\n<p><span data-jme-visible=\"above=1\">$Q_x = \\int \\bar{y}_{el}\\,dA &nbsp;= \\simplify[all,simplifyfractions,fractionnumbers]{(3{n}+1)/(2({n}+1)(2{n}+1))}h^2b&nbsp;\\qquad&nbsp;Q_y = \\int \\bar{x}_{el}\\,dA &nbsp;= \\simplify[all,fractionnumbers,simplifyfractions]{1/({n}+2)} hb^2$</span></p>\n<p>7. Centroid:</p>\n<p><span data-jme-visible=\"above=0\">$\\bar{x} = \\dfrac{Q_y}{A} = \\dfrac{\\simplify[all,fractionnumbers,simplifyfractions]{{n}/(2{n}+4)} hb^2}{\\var[all,fractionnumbers]{{n}/({n}+1)} h b} = \\simplify[all,collectnumbers]{({n}+1)/(2{n}+4)}b&nbsp;\\qquad&nbsp;\\bar{y} = \\dfrac{Q_x}{A} = \\dfrac{\\simplify[all,fractionnumbers,simplifyfractions]{{n^2}/(({n}+1)(2{n}+1))} h^2b}{\\var[all,fractionnumbers]{{n}/({n}+1)} h b}&nbsp;= \\simplify[all,collectnumbers,simplifyfractions]{{n}/(2{n}+1)}h&nbsp;$</span></p>\n<p><span data-jme-visible=\"above=1\">$\\bar{x} = \\dfrac{Q_y}{A} = \\dfrac{\\simplify[all,fractionnumbers,simplifyfractions]{1/({n}+2)} hb^2}{\\var[all,fractionnumbers]{1/({n}+1)} h b} = \\simplify[all,collectnumbers]{({n}+1)/({n}+2)}b&nbsp;\\qquad&nbsp;\\bar{y} = \\dfrac{Q_x}{A} = \\dfrac{\\simplify[all,simplifyfractions,fractionnumbers]{(3{n}+1)/(2({n}+1)(2{n}+1))}h^2b}{\\var[all,fractionnumbers]{1/({n}+1)} h b}&nbsp;= \\simplify[all,collectnumbers,simplifyfractions]{(3{n}+1)/(4{n}+2)}h&nbsp;$</span></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Qy": {"name": "Qy", "group": "answers", "definition": " simplify(substitute([\"n\" :n],\n if(Above=1, \n    expression('h b^2/(n+2)'),\n    expression('h b^2 n / (2 n + 4 )'))),\"basic,collectNumbers,simplifyFractions\")", "description": "", "templateType": "anything", "can_override": false}, "ybar_el": {"name": "ybar_el", "group": "answers", "definition": "expression(['y','y/2','y','(h+y)/2'][version])", "description": "", "templateType": "anything", "can_override": false}, "xbar": {"name": "xbar", "group": "answers", "definition": " simplify(substitute([\"n\" :n],\n  if(Above=1,\n    expression('b* (n+1)/(n+2)'),\n    expression('b * (n+1)/(2n+4)'))),\"basic,collectNumbers,simplifyFractions,cancelTerms\")", "description": "<p>expression(\"(\"+ string(Qy) +\")/(\"+ string(area) +\")\")</p>", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "inputs", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "inputs", "definition": "expression(if(vertical=1,'h/b^n','b/h^(1/n)'))", "description": "", "templateType": "anything", "can_override": false}, "Qx": {"name": "Qx", "group": "answers", "definition": " simplify(substitute([\"n\" :n],\n  if(Above=1,\n    expression('(b h^2 /2)(3n+1)/((n+1) (2n+1))'),\n    expression('h^2 b n^2/((n+1)(2n+1))'))),\"basic,collectNumbers,simplifyFractions\")", "description": "", "templateType": "anything", "can_override": false}, "Above": {"name": "Above", "group": "inputs", "definition": "random(0,1)", "description": "<p>area above or below the curve?</p>", "templateType": "anything", "can_override": false}, "version": {"name": "version", "group": "inputs", "definition": "2 above + vertical\n", "description": "<p>0 = below horizontal</p>\n<p>1 = below vertical</p>\n<p>2 = above horizontal</p>\n<p>3 = above vertical</p>\n<p>horizontal strips not implemented</p>", "templateType": "anything", "can_override": false}, "Vertical": {"name": "Vertical", "group": "inputs", "definition": "random(0,1)", "description": "<p>0 = horizontal strips</p>\n<p>1 = vertical strips? &nbsp;Horizontal strips not currently implemented.</p>\n<p></p>\n<p>&nbsp;Can't figure out how to pass a boolean to geogebra, so using {0,1} instead. Only exponents &lt; 2 can be horizontal &nbsp;</p>", "templateType": "anything", "can_override": false}, "ybar": {"name": "ybar", "group": "answers", "definition": " simplify(substitute([\"n\" :n],if(Above=1,\n    expression('h * (3 n +1)/(4 n+2)'),\n    expression('h n / (2 n+1)'))),\"basic,collectNumbers,simplifyFractions\")", "description": "<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p>", "templateType": "anything", "can_override": false}, "area": {"name": "area", "group": "answers", "definition": "simplify(substitute([\"n\" :n], if(Above=1,\n    expression('b h / (n+1)'),\n    expression('b h n /(n +1)'))),\"basic,collectNumbers,simplifyFractions,cancelTerms\")", "description": "<p>ok</p>", "templateType": "anything", "can_override": false}, "lower_limit": {"name": "lower_limit", "group": "answers", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "inputs", "definition": "random(1/3,1/2,1,3/2,2,3)", "description": "<p>the exponent of the function (1-kx^n) (0.5 .. 5#0.5)</p>", "templateType": "anything", "can_override": false}, "upper_limit": {"name": "upper_limit", "group": "answers", "definition": "if(Vertical=1,'b','h')", "description": "", "templateType": "anything", "can_override": false}, "xbar_el": {"name": "xbar_el", "group": "answers", "definition": "expression(['x/2','x','(b+x)/2','x'][version])", "description": "", "templateType": "anything", "can_override": false}, "dA": {"name": "dA", "group": "answers", "definition": "expression(['x dy','y dx','(b-x) dy','(h-y) dx'][version])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "inputs", "variables": ["n", "version", "Vertical", "Above", "k", "debug"]}, {"name": "answers", "variables": ["dA", "xbar_el", "ybar_el", "upper_limit", "lower_limit", "area", "Qy", "xbar", "ybar", "Qx"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Bounding function", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The bounding funtion&nbsp;contains a constant $k$ which can be expressed in terms of&nbsp;$b$ and $h$. &nbsp;Determine the value of $k$ in terms of <em>b</em> and <em>h&nbsp;</em>by substituting in the coordinates of a point which is on the curve into the bounding function.</p>\n<p>$k$ =&nbsp;[[0]] <span data-jme-visible=\"debug\">{k}</span></p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "k", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "h/b^{n}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "b", "value": ""}, {"name": "h", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Strip", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the area of the rectangular differential strip.</p>\n<p>$dA$ =&nbsp;[[0]] <span data-jme-visible=\"debug\">{da}</span></p>\n<p>Determine expressions for the coordinates of the centroid of the strip.</p>\n<p>$\\bar{x}_{el} = $ [[1]]&nbsp;$\\qquad\\bar{y}_{el} = $&nbsp;[[2]]&nbsp;&nbsp;<span data-jme-visible=\"debug\">xbar= {xbar_el} &nbsp;ybar = {ybar_el}</span></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "$dA$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{dA}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "$\\bar{x}$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{xbar_el}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "$\\bar{y}$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ybar_el}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Limits", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the limits of integration for these strips.</p>\n<p>Lower limit is:&nbsp;[[0]] <span data-jme-visible=\"debug\">{0}</span>&nbsp;$\\qquad$ Upper limit is:&nbsp;[[1]] <span data-jme-visible=\"debug\">{upper_limit}</span></p>", "gaps": [{"type": "patternmatch", "useCustomName": true, "customName": "lower", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "0", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "upper", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{upper_limit}", "displayAnswer": "", "matchMode": "exact"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Area", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>With the information determined above, evaluate this integral to find the area of the spandrel in terms of constants <em>b</em> and <em>h</em>.</p>\n<p>$A = &nbsp;\\int dA &nbsp;= $&nbsp;[[0]]&nbsp; &nbsp;</p>\n<p><span data-jme-visible=\"debug\">area = {area}</span></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "area", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{area}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "First Moments", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Perform the following integrals to determine the first moments of area with respect to the x- and y-axis.</p>\n<p></p>\n<p>$Q_x = \\int \\bar{y}_{el} dA =$ [[0]] <span data-jme-visible=\"debug\">{Qx}</span> $\\qquad Q_y = \\int \\bar{x}_{el} dA =$&nbsp;[[1]]&nbsp;<span data-jme-visible=\"debug\">{Qy}</span></p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "qx", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{Qx}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "qy", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{Qy}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Centroid", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Use the information you found above to determine the coordinates of the centroid of the shaded spandrel.</p>\n<p>$\\bar{x}&nbsp;= \\dfrac{Q_y}{A} = $ &nbsp;[[0]]&nbsp;&nbsp;<span data-jme-visible=\"debug\">{xbar} &nbsp;</span>$\\qquad\\bar{y}&nbsp;= \\dfrac{Q_x}{A} = $ &nbsp;[[1]]&nbsp;&nbsp;<span data-jme-visible=\"debug\">{ybar} &nbsp;</span></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "xbar", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{xbar}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "ybar", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ybar}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Centroid by integration: upper and lower bounds are functions", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["centroid", "integration", "Mechanics", "mechanics", "Statics", "statics"], "metadata": {"description": "<p>Use integration to find the centroid of an area bounded by a parabola, a sloping line, and the y-axis. &nbsp;</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>{applet()}</p>\n<p>Determine the coordinates of the centroid of the shaded area bounded by the $y$-axis, a parabola passing throught the origin and point $A$, and a straight line passing through points $A$ and $B$.</p>\n<p>Given: &nbsp;$A = ( \\var{A[0]}, \\var{A[1]} ),&nbsp;B = (0, \\var{b}) $</p>", "advice": "<p style=\"clear: both;\"><strong>Bounding Functions</strong></p>\n<p style=\"padding-left: 30px;\">Parabola: $f(x) = k x^2$</p>\n<p style=\"padding-left: 60px;\">at $x=\\var{A[0]},&nbsp;f(x)=\\var{A[1]}$ , so $k = \\dfrac{\\var{A[1]}}{\\var{A[0]}^2}$</p>\n<p style=\"padding-left: 60px;\">so, $f(x) = \\var[fractionNumbers]{A[1]/A[0]^2} x^2$</p>\n<p style=\"padding-left: 30px;\">Line: $g(x) = m x + b$</p>\n<p style=\"padding-left: 60px;\">where $m = \\dfrac{(\\var{A[1]}-\\var{b})}{\\var{x}}$, and $b = \\var{b}$</p>\n<p style=\"padding-left: 60px;\">so, g(x) = $\\var[fractionNumbers]{(A[1]-b)&nbsp;/x} x + \\var{b}$</p>\n<p><strong>Strip Properties for Vertical strips</strong></p>\n<p style=\"padding-left: 30px;\">$dA = [g(x) - f(x)]\\; dx =\\left(\\simplify[all]{- {A[1]}/{A[0]}^2} x^2 +\\simplify{({A[1]}-{b}) /{x}} x + \\simplify{{b}} \\right )\\; dx $</p>\n<p style=\"padding-left: 30px;\">$\\bar{x}_{el} = x$</p>\n<p style=\"padding-left: 30px;\">$\\bar{y}_{el} = \\dfrac{g(x) + f(x)}{2}&nbsp;$</p>\n<p><strong>Integrals</strong></p>\n<p style=\"padding-left: 30px;\">$A = \\int_0^\\var{x}\\; dA =&nbsp;\\var{siground(area,4)} \\text{ units}^2$</p>\n<p style=\"padding-left: 30px;\">$Q_y = \\int_0^\\var{x} \\bar{x}_{el} \\; dA = \\var{siground(Qy,4)} \\text{ units}^3$</p>\n<p style=\"padding-left: 30px;\">$Q_x = \\int_0^\\var{x}&nbsp;\\bar{y}_{el} \\; dA = \\var{siground(Qx,4)}\\text{ units}^3$</p>\n<p><strong>Centroid</strong></p>\n<p style=\"padding-left: 30px;\">&nbsp;$\\bar{x} = \\dfrac{Q_y}{A} = \\var{siground(xbar,4)}$&nbsp;&nbsp;units</p>\n<p style=\"padding-left: 30px;\"><strong></strong>&nbsp;$\\bar{y} = \\dfrac{Q_x}{A} = \\var{siground(ybar,4)}$&nbsp;&nbsp;units</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"A": {"name": "A", "group": "Ungrouped variables", "definition": "vector(random(1..10),random(3..12))", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(0..10)", "description": "<p>y&nbsp;component of point B</p>", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "A[1]/A[0]^2", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "(A[1]-b)/A[0]", "description": "<p>slope</p>", "templateType": "anything", "can_override": false}, "area": {"name": "area", "group": "Unnamed group", "definition": "- k x^3/3 + m x^2/2 + b x", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "A[0]", "description": "", "templateType": "anything", "can_override": false}, "Qy": {"name": "Qy", "group": "Unnamed group", "definition": "- k x^4/4 + m x^3/3 + b x^2/2", "description": "", "templateType": "anything", "can_override": false}, "xbar": {"name": "xbar", "group": "Unnamed group", "definition": "Qy/area", "description": "", "templateType": "anything", "can_override": false}, "Qx": {"name": "Qx", "group": "Unnamed group", "definition": "(-k^2 x^5/5 + m^2 x^3/3 +  m b x^2 + b^2 x)/2", "description": "", "templateType": "anything", "can_override": false}, "ybar": {"name": "ybar", "group": "Unnamed group", "definition": "Qx/area", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "m <> 0 // don't want the line to be horizontal", "maxRuns": 100}, "ungrouped_variables": ["A", "b", "k", "m", "x"], "variable_groups": [{"name": "Unnamed group", "variables": ["area", "Qy", "xbar", "Qx", "ybar"]}], "functions": {"g": {"parameters": [["x", "number"]], "type": "number", "language": "jme", "definition": " m x + by"}, "applet": {"parameters": [], "type": "ggbapplet", "language": "javascript", "definition": "//{geogebra_applet('cpf7gyej',['A': A, 'by': b,  \"C\": [visible: false, label_style: 3]])}\n// Create the worksheet. \n// This function returns an object with a container `element` and a `promise` resolving to a GeoGebra applet.\nvar params = {\n  material_id: 'cpf7gyej'\n}\n\nvar result = Numbas.extensions.geogebra.createGeogebraApplet(params);\n\n// Once the applet has loaded, run some commands to manipulate the worksheet.\nresult.promise.then(function(d) {\n  var app = d.app;\n  question.applet = d;\n   \n  //initialize the dimensions and forces\n  \n   function setGGBPoint(g_name, n_name = g_name) {\n    // moves point in GGB to location of Numbas Vector Variable\n    // g_name = geogebra point, n_name = numbas vector\n    \n    //var pt = question.scope.evaluate(n_name).value\n    var pt = scope.getVariable(n_name).value\n    app.setFixed(g_name,false,false);\n    app.setCoords(g_name, pt[0], pt[1]);\n    app.setFixed(g_name,true,true);\n  }\n  \n  function setGGBNumber(gname, nname=gname) {\n    // Sets number in GGB to a Numbas Variable\n    var n = question.scope.evaluate(nname).value;\n    app.setValue(gname,n);\n  }\n    \n  setGGBPoint(\"A\");\n  setGGBNumber(\"by\", \"b\");\n  app.setVisible(\"C\",false);// centroid\n\n  \n});\n\n// This function returns the result of `createGeogebraApplet` as an object \n// with the JME data type 'ggbapplet', which can be substituted into the question's content.\nreturn new Numbas.jme.types.ggbapplet(result);\n"}}, "preamble": {"js": "question.signals.on('adviceDisplayed',function() {\n   try{\n    var app = question.applet.app;\n    app.setVisible(\"C\", true,false);\n  }\n  catch(err){} \n    \n})\n\n\n\n", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "centroid", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p style=\"padding-left: 30px;\">$\\bar{x} = $ [[0]]&nbsp; units&nbsp;</p>\n<p style=\"padding-left: 30px;\">$\\bar{y} = $&nbsp; [[1]]&nbsp;units</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "xbar", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(xbar,'')", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "ybar", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(ybar,'')", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Distributed Loads", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["Uniformly distributed load", "Uniformly varying load", "Trapezoidal loading"], "variable_overrides": [[], [], []], "questions": [{"name": "Reactions for beam with uniformly distributed load", "extensions": ["geogebra", "quantities", "weh"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": [], "metadata": {"description": "<p>Find the reactions for a beam with a uniformly distributed load.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{geogebra_applet('kuhdcgxv',[ 'a': scalar(A),'b':&nbsp;scalar(B),'c':&nbsp;scalar(C),'d':&nbsp;scalar(D),'l':&nbsp;scalar(L)])}</p>\n<p>A&nbsp;{L} long beam is subjected to a {loading} uniformly distributed load.&nbsp;Assume the weight of the beam is negligible.</p>\n<p><span data-jme-visible=\"debug\">w: {loading} W: {w} &nbsp;$F_A$: {FA} &nbsp;$F_B$ {FB}</span></p>", "advice": "<p>To solve, replace the distributed load with an equivalent concentrated load. &nbsp;The equivalent concentrated load acts at the centroid of the rectangle, and its magnitude is the \"area\" of the rectangle.</p>\n<p>Once replaced, draw a free body diagram; then take moments at <em>A</em> to find<em> B</em> and vice-versa. &nbsp;Check your work by applying $\\Sigma F_y = 0$.</p>", "rulesets": {}, "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "(C+D)/2", "description": "<p>midpoint of load</p>", "templateType": "anything"}, "loading": {"name": "loading", "group": "inputs", "definition": "qty(random(1,2,3,4,5,6)* random(10, 20, 50, 100),units[0]+\"/\"+units[1])", "description": "<p>magnitude of distributed loading [force/length]</p>", "templateType": "anything"}, "D": {"name": "D", "group": "inputs", "definition": "qty(random(scalar(C)..scalar(L)),units[1])", "description": "<p>distributed load ends here</p>\n<p>D-C &gt; 3 and B-A &gt; L/2 and A&lt;&gt;C and B&lt;&gt;D</p>", "templateType": "anything"}, "C": {"name": "C", "group": "inputs", "definition": "qty(random(0..scalar(L)),units[1])", "description": "<p>distributed load starts here</p>", "templateType": "anything"}, "FA": {"name": "FA", "group": "Ungrouped variables", "definition": "W-FB", "description": "<p>reaction at A</p>", "templateType": "anything"}, "B": {"name": "B", "group": "inputs", "definition": "qty(random(scalar(A)..scalar(L)),units[1])", "description": "<p>location of right hand support</p>", "templateType": "anything"}, "W": {"name": "W", "group": "Ungrouped variables", "definition": "loading * (D-C)", "description": "<p>Downward force</p>", "templateType": "anything"}, "L": {"name": "L", "group": "inputs", "definition": "qty(random(8,10,12,14,16),units[1])", "description": "<p>length of beam</p>", "templateType": "anything"}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything"}, "FB": {"name": "FB", "group": "Ungrouped variables", "definition": "(x-A) * W / (B-A)\n", "description": "<p>reaction at B</p>", "templateType": "anything"}, "units": {"name": "units", "group": "inputs", "definition": "random(['lb','ft'],['N','m'])", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "inputs", "definition": "qty(random(0..scalar(L)/2),units[1])", "description": "<p>location of left hand support</p>", "templateType": "anything"}}, "variablesTest": {"condition": "D-C > qty(3,units[1]) and B-A > L/2 and A<>C and B<>D", "maxRuns": 100}, "ungrouped_variables": ["W", "FB", "x", "FA", "debug"], "variable_groups": [{"name": "inputs", "variables": ["A", "B", "C", "D", "loading", "units", "L"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Reactions", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the reactions at $A$ and $B$.</p>\n<p>$A$ =&nbsp;[[0]]&nbsp;&nbsp;$B$ =&nbsp;[[1]]&nbsp;</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "A", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "FA", "right": "0.1", "close": "1.0", "C1": "80", "C2": "80", "C3": "60"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "B", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "FB", "right": "0.1", "close": "1.0", "C1": "80", "C2": "80", "C3": "60"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Reactions for beam with uniformly varying load", "extensions": ["geogebra", "quantities", "weh"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [["question-resources/dist-load.ggb", "/srv/numbas/media/question-resources/dist-load.ggb"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["mechanics, statics, reactions, distributed load, uniformly varying load"], "metadata": {"description": "<p>Find the reactions for a beam with a uniformly varying distributed load.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{applet}</p>\n<p>A {qty(L, units[1]) } long beam is subjected to a load which varies uniformly from {qty(wc * loading,units[0])} at $C$ to {qty(wd * loading,units[0])} at $D$. The beam itself weighs {qty(w_b,units[0] + \"/\" + units[1])}.</p>\n<p><span data-jme-visible=\"debug\">W: {w} &nbsp;beam: {wb} xbar: {x} check: {check}</span></p>\n<p><span data-jme-visible=\"debug\">$F_A$: {precround(FA,4)} &nbsp;$F_B$ {precround(FB,4)}</span></p>", "advice": "<ol>\n<li>To solve, divide the trapazoid into a rectangle and a triangle or two triangles, then replace each&nbsp;with an equivalent concentrated load. &nbsp;The equivalent concentrated load acts at the centroid of each&nbsp;shape, and its magnitude is the \"area\" of the shape. &nbsp;</li>\n<li>Treat the beam as a uniformly distributed load, and place the weight of the beam at the&nbsp;center.</li>\n<li>Once replaced, draw a free body diagram; then take moments at <em>A</em> to find<em> B</em> and vice-versa. &nbsp;Check your work by applying $\\Sigma F_y = 0$.</li>\n</ol>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"D": {"name": "D", "group": "inputs", "definition": "random(C+3..L except B)", "description": "<p>distributed load ends here</p>", "templateType": "anything", "can_override": false}, "L": {"name": "L", "group": "inputs", "definition": "random(8,10,12,14)", "description": "<p>length of beam</p>\n<p></p>", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "inputs", "definition": "random(['lb','ft'],['kN','m'])", "description": "", "templateType": "anything", "can_override": false}, "loading": {"name": "loading", "group": "inputs", "definition": "random(10..50#10)", "description": "<p>distributed loading [force/length]</p>", "templateType": "anything", "can_override": false}, "FA": {"name": "FA", "group": "Ungrouped variables", "definition": "(W + WB)-FB", "description": "<p>reaction at A</p>", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "wc": {"name": "wc", "group": "inputs", "definition": "random(0..2#0.5 except 0.5)", "description": "<p>load at c (scaled)</p>", "templateType": "anything", "can_override": false}, "W": {"name": "W", "group": "Ungrouped variables", "definition": "precround(loading * (wc+wd)/2 * (D-C),5)", "description": "<p>Downward force due to load</p>", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "inputs", "definition": "random(L-3..L)", "description": "<p>location of right hand support</p>", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "inputs", "definition": "random(0..5 except A)", "description": "<p>distributed load starts here</p>", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "inputs", "definition": "0", "description": "<p>location of left hand support</p>", "templateType": "anything", "can_override": false}, "wd": {"name": "wd", "group": "inputs", "definition": "random(0..2#0.5 except 0.5)", "description": "<p>loading at d scaled</p>", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "C + (wc / 6 + wd/ 3)(D-C) * 2/(wc+wd)", "description": "<p>midpoint of load</p>", "templateType": "anything", "can_override": false}, "FB": {"name": "FB", "group": "Ungrouped variables", "definition": "precround(((x-A) * W + (CG-A) *  WB) / (B-A),5)\n", "description": "<p>reaction at B</p>", "templateType": "anything", "can_override": false}, "w_b": {"name": "w_b", "group": "inputs", "definition": "siground(random(0.1..1 #0.1) loading,3)", "description": "<p>Weight of the beam in W/L units</p>", "templateType": "anything", "can_override": false}, "CG": {"name": "CG", "group": "Ungrouped variables", "definition": "L/2", "description": "<p>center of the beam</p>", "templateType": "anything", "can_override": false}, "WB": {"name": "WB", "group": "Ungrouped variables", "definition": "w_b L ", "description": "<p>Weight of the beam itself</p>", "templateType": "anything", "can_override": false}, "check": {"name": "check", "group": "Ungrouped variables", "definition": "(W + WB)= (FA+FB)", "description": "", "templateType": "anything", "can_override": false}, "params": {"name": "params", "group": "ggb", "definition": "[ a: A, b: B, c: C, d: D, l: L, w_c: wc, w_d: wd ]", "description": "", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "ggb", "definition": "geogebra_file('dist-load.ggb',params)", "description": "", "templateType": "anything", "can_override": false}, "points": {"name": "points", "group": "inputs", "definition": "sort(deal(L)[0..2])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "D-C > L/3 and \nwc<>wd", "maxRuns": 100}, "ungrouped_variables": ["W", "FB", "x", "FA", "debug", "CG", "WB", "check"], "variable_groups": [{"name": "inputs", "variables": ["A", "B", "C", "D", "loading", "units", "L", "wc", "wd", "w_b", "points"]}, {"name": "ggb", "variables": ["params", "applet"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Find Reactions", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the reactions at $A$ and $B$.</p>\n<p>$A$ =&nbsp;[[0]]&nbsp;&nbsp;$B$ =&nbsp;[[1]]&nbsp;&nbsp;</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "A", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(precround(FA,4),units[0])", "right": "0.1", "close": "1.0", "C1": "80", "C2": "80", "C3": "60"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "B", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(siground(FB,4),units[0])", "right": "0.1", "close": "1.0", "C1": "80", "C2": "80", "C3": "60"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Distributed Loads: trapezoidal loading", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["beam", "distributed load", "Equilibrium", "equilibrium", "Mechanics", "mechanics", "Statics", "statics"], "metadata": {"description": "<p>Find the reactions of a simply-supported beam with a trapazoidal distributed load.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>{geogebra_applet('xgjx2s8s',[['a', a 10/L], ['b', b&nbsp;10/L],['c',&nbsp;c&nbsp;10/L],['showfbd','false']])} &nbsp;</p>\n<p>$\\var{qty(L,unit[0])}$ long beam $AB$ is subjected to a distributed load which</p>\n<ul>\n<li data-jme-visible=\"a&lt;b\">varies uniformly from $\\var{Q0}$ &nbsp;at &nbsp;$x=\\var{QA}$ to $\\var{QW}$ &nbsp;at &nbsp;$x=\\var{QB}$, and</li>\n<li>is&nbsp;constant &nbsp;$\\var{QW}$ between $x=\\var{if(c&lt;b,QC,QB)}$ and $x=\\var{if(c&lt;b,QB,QC)}$.</li>\n<li data-jme-visible=\"a&gt;b\">varies uniformly from $\\var{QW}$ &nbsp;at &nbsp;$x=\\var{QB}$ to &nbsp;$\\var{Q0}$ &nbsp;at $x=\\var{QA}$. &nbsp; &nbsp;</li>\n</ul>\n<p>Determine the reactions at $A$ and $B$.</p>", "advice": "<p>{geogebra_applet('xgjx2s8s',[['a', a 10/L], ['b', b 10/L],['c', c 10/L],['showfbd','true']])}</p>\n<ol>\n<li>Draw a free body diagram of the beam, replacing the distributed loads with equivalent concentrated loads at the centroids of the triangle and rectangle.</li>\n<li>Determine locations of the centroids and the 'area' under the loading curve for each part.\n<p>$\\begin{align}\\\\ W_R &amp;= \\var{QWR} &amp; x_R &amp;= \\var{QxR} \\\\ &nbsp;W_T &amp;= \\var{QWT}&nbsp;&amp;x_T &amp;= \\var{QxT}\\end{align}$</p>\n</li>\n<li>Find the reactions\n<p>$\\begin{align}\\\\ \\Sigma M_A &amp;= 0 &nbsp;\\\\W_R x_r + W_T x_T &amp;=&nbsp;&nbsp;B L \\\\ B &amp;= \\frac{W_R x_r + W_T x_T}{L} &nbsp;\\\\&amp;= \\var{QRB} \\\\ \\\\ \\Sigma F_y &amp;= 0 \\\\ A + B &amp;= W_T + W_R \\\\ A &amp;= W_T + W_R - B \\\\ &amp;= \\var{QRA} \\end{align}$</p>\n</li>\n<li>You may check your answer by finding $A$ using $\\Sigma M_B = 0$. &nbsp;You should get the same result either way.</li>\n</ol>", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(0..L)", "description": "<p>horizontal location of the starts of the triangular&nbsp;load.</p>\n<p>could be on the left or right of point&nbsp;B</p>", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(0..L)", "description": "<p>horizontal position of point between triangle and rectangle. &nbsp;l</p>", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(0..L)", "description": "<p>horizontal location of the end&nbsp;of the rectangular&nbsp;load.</p>\n<p>could be on the left or right of point B</p>", "templateType": "anything"}, "w": {"name": "w", "group": "Ungrouped variables", "definition": "random(50..150#10)", "description": "<p>Max value of loading &nbsp;in &nbsp;[force/distance]</p>", "templateType": "anything"}, "WT": {"name": "WT", "group": "solution", "definition": "abs(a-b) w /2", "description": "<p>weight of the triangular load</p>", "templateType": "anything"}, "WR": {"name": "WR", "group": "solution", "definition": "abs(b-c) w", "description": "<p>weight of the rectangular load</p>", "templateType": "anything"}, "WTot": {"name": "WTot", "group": "solution", "definition": "WT+WR", "description": "<p>Total weight of load</p>", "templateType": "anything"}, "xR": {"name": "xR", "group": "solution", "definition": "(b+c)/2", "description": "<p>location of centroid of rect</p>", "templateType": "anything"}, "xT": {"name": "xT", "group": "solution", "definition": "b + (a-b)/3", "description": "<p>Centroid of triangle</p>", "templateType": "anything"}, "L": {"name": "L", "group": "Ungrouped variables", "definition": "random([10,12,16,20])", "description": "<p>length of beam</p>", "templateType": "anything"}, "unit": {"name": "unit", "group": "Ungrouped variables", "definition": "random([['ft','lb'],['m','kN']])", "description": "", "templateType": "anything"}, "RB": {"name": "RB", "group": "solution", "definition": "(WR xR + WT xT)/ L", "description": "", "templateType": "anything"}, "RA": {"name": "RA", "group": "solution", "definition": "(WT * (L-xT) + WR * (L-xR ))/ L", "description": "", "templateType": "anything"}, "check": {"name": "check", "group": "solution", "definition": "RA + RB = Wtot", "description": "", "templateType": "anything"}, "QxR": {"name": "QxR", "group": "quantities", "definition": "quantity(xR,unit[0])", "description": "", "templateType": "anything"}, "QxT": {"name": "QxT", "group": "quantities", "definition": "qty(precround(xT,2),unit[0])", "description": "", "templateType": "anything"}, "Qw": {"name": "Qw", "group": "quantities", "definition": "qty(w,unit[1] + \"/\" + unit[0])", "description": "", "templateType": "anything"}, "QWr": {"name": "QWr", "group": "quantities", "definition": "qty(Wr,unit[1])", "description": "", "templateType": "anything"}, "QWt": {"name": "QWt", "group": "quantities", "definition": "qty(Wt,unit[1])", "description": "", "templateType": "anything"}, "QRA": {"name": "QRA", "group": "quantities", "definition": "qty(precround(RA,2),unit[1])", "description": "", "templateType": "anything"}, "QRB": {"name": "QRB", "group": "quantities", "definition": "qty(precround(RB,2),unit[1])", "description": "", "templateType": "anything"}, "QA": {"name": "QA", "group": "quantities", "definition": "qty(A,unit[0])", "description": "", "templateType": "anything"}, "QB": {"name": "QB", "group": "quantities", "definition": "qty(B,unit[0])", "description": "", "templateType": "anything"}, "QC": {"name": "QC", "group": "quantities", "definition": "qty(C,unit[0])", "description": "", "templateType": "anything"}, "Q0": {"name": "Q0", "group": "quantities", "definition": "qty(0,unit[1] + \"/\" + unit[0])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "b > min(a,c) and b < max(a,c) and abs(a-b) L/10 > 1 and abs(b-c) L/10 > 1", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "w", "L", "unit"], "variable_groups": [{"name": "solution", "variables": ["WT", "WR", "WTot", "xR", "xT", "RB", "RA", "check"]}, {"name": "quantities", "variables": ["QxR", "QxT", "Qw", "QWr", "QWt", "QRA", "QRB", "QA", "QB", "QC", "Q0"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Find Reactions", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$A = $&nbsp;[[0]]&nbsp; &nbsp;$B = $&nbsp;[[1]]&nbsp;&nbsp;</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "A", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "{QRA}", "right": "0.2", "close": "1.0", "C1": "80", "C2": "80", "C3": "65"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "B", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "{QRB}", "right": "0.2", "close": "1.0", "C1": "80", "C2": "80", "C3": "65"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "menu", "onleave": {"action": "none", "message": ""}, "preventleave": false, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "extensions": ["geogebra", "quantities", "weh"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [["question-resources/centroids.png", "/srv/numbas/media/question-resources/centroids.png"], ["question-resources/centroids_3A0rXlj.png", "/srv/numbas/media/question-resources/centroids_3A0rXlj.png"], ["question-resources/centroids_zSOgoBb.png", "/srv/numbas/media/question-resources/centroids_zSOgoBb.png"], ["question-resources/centroid-t-r.ggb", "/srv/numbas/media/question-resources/centroid-t-r.ggb"], ["question-resources/centroid-integration.ggb", "/srv/numbas/media/question-resources/centroid-integration.ggb"], ["question-resources/dist-load.ggb", "/srv/numbas/media/question-resources/dist-load.ggb"]]}