// Numbas version: exam_results_page_options
{"name": "Reactions for beam with uniformly varying load", "extensions": ["geogebra", "weh", "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/dist-load.ggb", "/srv/numbas/media/question-resources/dist-load.ggb"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Reactions for beam with uniformly varying load", "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": {}, "extensions": ["geogebra", "quantities", "weh"], "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", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}