![](\"resources/question-resources/centroids_zSOgoBb.png\")
End of chapter exercises for Engineering Statics: Open and Interactive
", "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": "A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "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": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "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": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "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": "Only marked close if the student actually has the right sign.
", "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. if correct answer is 100 N and close is ±1%,Locate the centroid of a rectangle, triangle, and semi-circle on a coordinate grid.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "Determine the coordinates of the centroids of the three shapes. Grid units are [{units}].
\n{geogebra_applet('xjjm7qqr',[['R_1',R1],['R_2',R2],['T_1',T1],['T_2',T2],['C_1',C1],['C_2',C2]])}
\n\n", "advice": "For a rectangle, the centroid is at the geometric center.
\nFor a right triangle, divide the base and height into thirds. The centroid is located at the intersection point nearest to the right angle.
\nFor a semicircle, the centroid is located on the axis of symmetry, a distance of $\\frac{4r}{3\\pi}$ from the straight edge.
\n\n
| Part | \n$\\bar{x}$ | \n$\\bar{y}$ | \n
|---|---|---|
| Rectangle | \n[[0]] | \n[[1]] | \n
| Triangle | \n[[2]] | \n[[3]] | \n
| Semicircle: | \n[[4]] | \n[[5]] | \n
{RC} {units}
\n{TC} {units}
\n{CC} {units}
", "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", "type": "question"}, {"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": "A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "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": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "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": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "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": "Only marked close if the student actually has the right sign.
", "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. if correct answer is 100 N and close is ±1%,Find the centroid of a shape made from a rectangle, triangle, and circle.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "{geogebra_applet('fcfsjuv9',[ ['A',A],['b_1',b1],['h_1',h1],['h_t',ht],['n',n],['Center',center],['radius',radius]])}
\nComplete the table below and detemine the coordinates of the centroid of the composite shape.
\nConsider 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. 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]}).
", "advice": "{geogebra_applet('fcfsjuv9',[ ['A',A],['b_1',b1],['h_1',h1],['h_t',ht],['n',n],['Center',center],['radius',radius],['visibility',m]])}
\n\n1. Divide the shape into three subshapes as described in the problem statement.
\n2. You should be able to set up a table to gather the required information like the one provided in this problem.
\n3. Determine and enter the area and centroidal coordinates for each subshape into the table
\n$\\qquad A_i, \\bar{x}_i,\\bar{y}_i$
\n4. Multiply area by the centroidal coordinates to get the moment of areas for the pieces.
\n$\\qquad (Q_x)_i = A_i\\bar{y}_i ,\\quad(Q_y)_i=A_i\\bar{x}_i$.
\n5. Sum columns 1, 4, and 5 to find the total area and moments of area.
\n$\\qquad A, Q_x, Q_y$
\n\n| Part | \n$A_i$ [{units}2] | \n$\\bar{x}_i$ [{units}] | \n$\\bar{y}_i$ [{units}] | \n$A_i\\bar{x}_i$ [{units}3] | \n$A_i\\bar{y}_i$ [{units}3] | \n
| rectangle | \n{area_rect[m]} | \n{C_rect[m][0]} | \n{C_rect[m][1]} | \n{Q_rect[1]} | \n{Q_rect[0]} | \n
| triangle | \n{area_tri[m]} | \n{siground(C_tri[m][0],3)} | \n{siground(C_tri[m][1],3)} | \n{Q_tri[1]} | \n{Q_tri[0]} | \n
| circle | \n{siground(area_circ[m],3)} | \n{C_circ[m][0]} | \n{C_circ[m][1]} | \n{siground(Q_circ[1],3)} | \n{siground(Q_circ[0],3)} | \n
| $\\Sigma$ | \n{siground(area_total,3)} | \n\n | \n | {siground(Q_total[1],3)} | \n{siground(Q_total[0],3)} | \n
6. Find answers with
\n\n$\\qquad \\bar{x} = \\dfrac{Q_y}{A} =\\dfrac{\\Sigma A_i \\bar{x}_i}{\\Sigma A_i} = \\dfrac{\\var{siground(Q_total[1],3)}}{\\var{siground(area_total,3)}} = \\var{siground(centroid[0],3)}\\, \\var{units}$
\n$\\qquad \\bar{y} = \\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} $
", "rulesets": {}, "variables": {"ht": {"name": "ht", "group": "Input values", "definition": "random(3..9#3)", "description": "\"height\" of triangle
\nhorizontal for n = 4,5,6,10,11,12
\nvertical for n = 1,2,3,7,8,9
", "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": "Offset of bottom right corner from originl
", "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": "center of the circle measured from bottom left of the rectangle
", "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": "radius of the circle
", "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": "This offsets the shape to one of the corners of the rect, the center of the rect, or the center of the circle.
", "templateType": "anything"}, "h1": {"name": "h1", "group": "Input values", "definition": "random(4..12#2)", "description": "vertical height of rectangle
", "templateType": "anything"}, "b1": {"name": "b1", "group": "Input values", "definition": "random(4..12#2)", "description": "horizontal base of rectangle
", "templateType": "anything"}, "n": {"name": "n", "group": "Input values", "definition": "random(1 .. 12#1)", "description": "Selects the position of the triangle, index gives vertex location
\n| \n | 9 | \n8 | \n7 | \n\n |
| 10 | \n\n | \n | \n | 6 | \n
| 11 | \n\n | rectangle | \n\n | 5 | \n
| 12 | \n\n | \n | \n | 4 | \n
| \n | 1 | \n2 | \n3 | \n\n |
determines location of centroid of triangle based on location and method
returns array of centroid coordinates, first term for m=0
This is the method used to solve the problem:
\nm=0: small rectangle + triangle - circle
\nm=1: big rectangle - triangle - circle
\nwhen n is in [2,5,8,11], use method 0, becauses otherwise it would require 2 negative triangles.
", "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": "[Q_x,Q_y]
", "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": "| Part | \n\n $A_i$ \n | \n\n $\\bar{x}_i$ \n | \n\n $\\bar{y}_i$ \n | \n\n $A_i\\bar{x}_i$ \n | \n\n $A_i\\bar{y}_i$ \n | \n
| rectangle | \n[[0]] | \n[[4]] | \n[[7]] | \n[[10]] | \n[[14]] | \n
| triangle | \n[[1]] | \n[[5]] | \n[[8]] | \n[[11]] | \n[[15]] | \n
| circle | \n[[2]] | \n[[6]] | \n[[9]] | \n[[12]] | \n[[16]] | \n
| $\\Sigma$ | \n[[3]] | \n\n | \n | [[13]] | \n[[17]] | \n
$\\bar{x} =\\dfrac{Q_y}{A} =$ [[0]] $\\qquad \\bar{y} =\\dfrac{Q_x}{A} = $ [[1]]
A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "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": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "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": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "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": "Only marked close if the student actually has the right sign.
", "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. if correct answer is 100 N and close is ±1%,Find the centroid of a shape made up of a rectangle and two triangles.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "{applet()}
\nDetermine the coordinates of the centroid of the polygon shown. Grid units are [{units}].
\nConsider the polygon to be made up of a ({b0} $\\times$ {h0}) rectangle {sign1} a ({b1} $\\times$ {h1}) triangle {sign2} a ({b2} $\\times$ {h2}) triangle.
", "advice": "| Part | \n$A_i$ | \n$\\bar{x}_i$ | \n$\\bar{y}_i$ | \n$A_i\\bar{x}_i$ | \n$A_i\\bar{y}_i$ | \n
| Rectangle | \n{A0} | \n{bar(C0[0])} | \n{bar(C0[1])} | \n{Q(a0, c0[0])} | \n{Q(a0, c0[1])} | \n
| Triangle 1 | \n{A1} | \n{bar(C1[0])} | \n{bar(C1[1])} | \n{Q(a1, c1[0])} | \n{Q(a1, c1[1])} | \n
| Triangle 2 | \n{A2} | \n{bar(C2[0])} | \n{bar(C2[1])} | \n{Q(a2, c2[0])} | \n{Q(a2, c2[1])} | \n
| $\\Sigma$ | \n{AT} | \n\n | \n | {display(xbar AT)} | \n{display(ybar AT)} | \n
$\\qquad\\bar{x} = \\dfrac{\\Sigma A_i\\bar{x}_i}{\\Sigma A_i} = \\var{display(xbar)}$
\n$\\qquad \\bar{y} = \\dfrac{\\Sigma A_i\\bar{y}_i}{\\Sigma A_i} =\\var{display(ybar)}$
\n| Part | \n$A_i$ | \n$\\bar{x}_i$ | \n$\\bar{y}_i$ | \n$A_i\\bar{x}_i$ | \n$A_i\\bar{y}_i$ | \n
|---|---|---|---|---|---|
| Rectangle | \n[[0]] | \n[[4]] | \n[[7]] | \n[[10]] | \n[[13]] | \n
| Triangle 1 | \n[[1]] | \n[[5]] | \n[[8]] | \n[[11]] | \n[[14]] | \n
| Triangle 2 | \n[[2]] | \n[[6]] | \n[[9]] | \n[[12]] | \n[[15]] | \n
| $\\Sigma$ | \n[[3]] | \n\n | \n | [[16]] | \n\n [[17]] \n | \n
$\\bar{x} =\\dfrac{Q_y}{A} = $ [[0]] $\\qquad \\bar{y} =\\dfrac{Q_x}{A} =$ [[1]]
", "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", "type": "question"}]}, {"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": "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 centroid by integration.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "{geogebra_applet('tpndhsyt',[['version',version]])}
", "advice": "The area of the strip, dA is the width times the height of the strip.
\nThe narrow width of the element is either $dx$ or $dy$
\nThe coordinates of the centroid are found by averaging the coordinates of the top and bottom of the strip.
", "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": "Determine the properties of the differential strip in terms of the known coordinates.
\n$dA$ = [[0]]
\n$\\bar{x}_{el}$ = [[1]]
\n$\\bar{y}_{el}$ =[[2]]
", "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", "type": "question"}, {"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": "A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "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": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "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": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "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": "Only marked close if the student actually has the right sign.
", "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. if correct answer is 100 N and close is ±1%,Find roots and the area under a parabola
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "{applet()}
\nGiven the function $\\color{red}{y=\\simplify[!noleadingminus,unitfactor]{{A} x^2 + {B} x + {C}}}$, determine the area under the curve from the y-axis to the point where the curve crosses the positive x-axis. The x- and y- coordinates are in [{units}]. You may not use a graphing calculator to solve this problem.
\n\n\n", "advice": "$\\begin{align}A &= \\int dA \\\\&= \\int_0^a y\\,dx \\\\&= \\int_0^a(\\simplify[!noleadingminus,unitfactor]{{A} x^2 + {B} x + {C}})\\, dx\\\\& = \\left[ \\simplify[unitfactor,collectnumbers]{{A} x^3/3 + {B} x^2/2 + {C}x}\\right]_0^\\var{scalar(siground(root1,4))}\\\\&=\\var{siground(area,4)}\\end{align}$
", "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": "Determine the points where the curve crosses the axes.
\n$h$ = [[0]] {qty(C,units)}
\n$a$ = [[1]] {siground(root1,4)}
", "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": "Set up and evaluate the integral equation below to find the area under the curve.
\n$\\begin{align} A &= \\int{dA}\\\\&=\\int_0^a y\\, dx \\\\ \\vdots\\end{align}$
\n$A$ = [[0]] {siground(area,4)}
", "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", "type": "question"}, {"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": "Find the area, first moment of area, and coordinates of a general spandrel. The area may be above or below the function.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "{geogebra_applet('bqnqgpfp',[['n',n],['h',random(1,1.5)],['b',random(0.8,1.3)],['Above', above],['Vertical',vertical]])}
\nUse integration with {if(Vertical=1,'vertical','horizontal')} strips to determine the area 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')}$, and also find the coordinates of its centroid. Note: b and h are constants.
", "advice": "Note: The solutions below is for Vertical Strips.
\nThe procedure for horizontal strips is similar, but with these strip properties and limits:
\nStrip properties: $dA = (b-x)\\,dy$, $\\bar{x}_{el} = \\dfrac{x+b}{y}$, $\\bar{y}_{el} = y $ $dA = x \\,dy$, $\\bar{x}_{el} = x/2$, $\\bar{y}_{el} =y$
\nLimits: $x= 0 \\text{ to } h$
\nYou will get the same results for $A, Q_x, Q_y, \\bar{x} \\text{ and } \\bar{y}$, which ever strips you choose.
\n1. Bounding function: $y = f(x) = h - k \\simplify[all,fractionnumbers]{x^{n}}$
\n2. Constant $k$ in terms of $b$: at $x=b, y=0 \\therefore h - k \\simplify[all,fractionnumbers]{b^{n}} = 0 \\therefore k = \\dfrac{h}{\\simplify[all,fractionnumbers]{b^{n}}}$
\n3. Strip properties: $dA = y\\,dx$, $\\bar{x}_{el} = x$, $\\bar{y}_{el} = y/2$ $dA = (h-y)\\,dx$, $\\bar{x}_{el} = x$, $\\bar{y}_{el} = (h+y)/2$
\n4. Limits: $x= 0 \\text{ to } b$
\n5. Area under the curve:
\n$\\begin{align} A &= \\int dA\\\\&= \\int_0^b y\\, dx\\\\&= \\int_0^b (h - k \\simplify[all,fractionnumbers]{x^{n}})\\, dx\\\\&= \\left[ hx - k \\dfrac{\\simplify[all,fractionnumbers]{x^{n+1}}}{\\simplify[all,fractionnumbers]{{n+1}}}\\right]_0^b\\\\&= \\left[ hb - \\left(\\dfrac{h}{\\simplify[all,fractionnumbers]{b^{n}}}\\right) \\dfrac{\\simplify[all,fractionnumbers]{b^{n+1}}}{\\simplify[all,fractionnumbers]{{n+1}}}\\right]\\\\&=hb-\\dfrac{hb}{\\simplify[all,fractionnumbers]{{n}+1}}\\\\&=\\var[all,fractionnumbers]{{n}/({n}+1)} h b\\end{align}$
\n$\\begin{align} A &= \\int dA\\\\&= \\int_0^b (h-y)\\, dx\\\\&= \\int_0^b h - (h - k \\simplify[all,fractionnumbers]{x^{n}})\\, dx\\\\&=\\int_0^bk \\simplify[all,fractionnumbers]{x^{n}}dx\\\\&= \\left[k \\dfrac{\\simplify[all,fractionnumbers]{x^{n+1}}}{\\simplify[all,fractionnumbers]{{n+1}}}\\right]_0^b\\\\&= \\left[ \\left(\\dfrac{h}{\\simplify[all,fractionnumbers]{b^{n}}}\\right) \\dfrac{\\simplify[all,fractionnumbers]{b^{n+1}}}{\\simplify[all,fractionnumbers]{{n+1}}}\\right]\\\\&=\\dfrac{hb}{\\simplify[all,fractionnumbers]{{n}+1}}\\\\&=\\var[all,fractionnumbers]{1/({n}+1)} h b\\end{align}$
\n6. $Q_x$ and $Q_y$ Perform similar integrations to get:
\n$Q_x = \\int \\bar{y}_{el}\\,dA = \\simplify[all,simplifyfractions,fractionnumbers]{{n}^2 /(2{n}^2+3{n}+1) h^2b} \\qquad Q_y = \\int \\bar{x}_{el}\\,dA = \\simplify[all,fractionnumbers,simplifyfractions]{{n}/(2{n}+4)} hb^2$
\n$Q_x = \\int \\bar{y}_{el}\\,dA = \\simplify[all,simplifyfractions,fractionnumbers]{(3{n}+1)/(2({n}+1)(2{n}+1))}h^2b \\qquad Q_y = \\int \\bar{x}_{el}\\,dA = \\simplify[all,fractionnumbers,simplifyfractions]{1/({n}+2)} hb^2$
\n7. Centroid:
\n$\\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 \\qquad \\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} = \\simplify[all,collectnumbers,simplifyfractions]{{n}/(2{n}+1)}h $
\n$\\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 \\qquad \\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} = \\simplify[all,collectnumbers,simplifyfractions]{(3{n}+1)/(4{n}+2)}h $
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", "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": "area above or below the curve?
", "templateType": "anything", "can_override": false}, "version": {"name": "version", "group": "inputs", "definition": "2 above + vertical\n", "description": "0 = below horizontal
\n1 = below vertical
\n2 = above horizontal
\n3 = above vertical
\nhorizontal strips not implemented
", "templateType": "anything", "can_override": false}, "Vertical": {"name": "Vertical", "group": "inputs", "definition": "random(0,1)", "description": "0 = horizontal strips
\n1 = vertical strips? Horizontal strips not currently implemented.
\n\nCan't figure out how to pass a boolean to geogebra, so using {0,1} instead. Only exponents < 2 can be horizontal
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ok
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", "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": "The bounding funtion contains a constant $k$ which can be expressed in terms of $b$ and $h$. Determine the value of $k$ in terms of b and h by substituting in the coordinates of a point which is on the curve into the bounding function.
\n$k$ = [[0]] {k}
\n", "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": "Determine the area of the rectangular differential strip.
\n$dA$ = [[0]] {da}
\nDetermine expressions for the coordinates of the centroid of the strip.
\n$\\bar{x}_{el} = $ [[1]] $\\qquad\\bar{y}_{el} = $ [[2]] xbar= {xbar_el} ybar = {ybar_el}
", "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": "Determine the limits of integration for these strips.
\nLower limit is: [[0]] {0} $\\qquad$ Upper limit is: [[1]] {upper_limit}
", "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": "With the information determined above, evaluate this integral to find the area of the spandrel in terms of constants b and h.
\n$A = \\int dA = $ [[0]]
\narea = {area}
", "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": "Perform the following integrals to determine the first moments of area with respect to the x- and y-axis.
\n\n$Q_x = \\int \\bar{y}_{el} dA =$ [[0]] {Qx} $\\qquad Q_y = \\int \\bar{x}_{el} dA =$ [[1]] {Qy}
\n", "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": "Use the information you found above to determine the coordinates of the centroid of the shaded spandrel.
\n$\\bar{x} = \\dfrac{Q_y}{A} = $ [[0]] {xbar} $\\qquad\\bar{y} = \\dfrac{Q_x}{A} = $ [[1]] {ybar}
", "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", "type": "question"}, {"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": "A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "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": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "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": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "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": "Only marked close if the student actually has the right sign.
", "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. if correct answer is 100 N and close is ±1%,Use integration to find the centroid of an area bounded by a parabola, a sloping line, and the y-axis.
", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "{applet()}
\nDetermine 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 $B$.
\nGiven: $A = ( \\var{A[0]}, \\var{A[1]} ), B = (0, \\var{b}) $
", "advice": "Bounding Functions
\nParabola: $f(x) = k x^2$
\nat $x=\\var{A[0]}, f(x)=\\var{A[1]}$ , so $k = \\dfrac{\\var{A[1]}}{\\var{A[0]}^2}$
\nso, $f(x) = \\var[fractionNumbers]{A[1]/A[0]^2} x^2$
\nLine: $g(x) = m x + b$
\nwhere $m = \\dfrac{(\\var{A[1]}-\\var{b})}{\\var{x}}$, and $b = \\var{b}$
\nso, g(x) = $\\var[fractionNumbers]{(A[1]-b) /x} x + \\var{b}$
\nStrip Properties for Vertical strips
\n$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 $
\n$\\bar{x}_{el} = x$
\n$\\bar{y}_{el} = \\dfrac{g(x) + f(x)}{2} $
\nIntegrals
\n$A = \\int_0^\\var{x}\\; dA = \\var{siground(area,4)} \\text{ units}^2$
\n$Q_y = \\int_0^\\var{x} \\bar{x}_{el} \\; dA = \\var{siground(Qy,4)} \\text{ units}^3$
\n$Q_x = \\int_0^\\var{x} \\bar{y}_{el} \\; dA = \\var{siground(Qx,4)}\\text{ units}^3$
\nCentroid
\n$\\bar{x} = \\dfrac{Q_y}{A} = \\var{siground(xbar,4)}$ units
\n$\\bar{y} = \\dfrac{Q_x}{A} = \\var{siground(ybar,4)}$ units
", "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": "y component of point B
", "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": "slope
", "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": "$\\bar{x} = $ [[0]] units
\n$\\bar{y} = $ [[1]] units
", "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", "type": "question"}]}, {"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": "A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "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": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "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": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "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": "Only marked close if the student actually has the right sign.
", "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. if correct answer is 100 N and close is ±1%,Find the reactions for a beam with a uniformly distributed load.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "{geogebra_applet('kuhdcgxv',[ 'a': scalar(A),'b': scalar(B),'c': scalar(C),'d': scalar(D),'l': scalar(L)])}
\nA {L} long beam is subjected to a {loading} uniformly distributed load. Assume the weight of the beam is negligible.
\nw: {loading} W: {w} $F_A$: {FA} $F_B$ {FB}
", "advice": "To solve, replace the distributed load with an equivalent concentrated load. The equivalent concentrated load acts at the centroid of the rectangle, and its magnitude is the \"area\" of the rectangle.
\nOnce replaced, draw a free body diagram; then take moments at A to find B and vice-versa. Check your work by applying $\\Sigma F_y = 0$.
", "rulesets": {}, "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "(C+D)/2", "description": "midpoint of load
", "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": "magnitude of distributed loading [force/length]
", "templateType": "anything"}, "D": {"name": "D", "group": "inputs", "definition": "qty(random(scalar(C)..scalar(L)),units[1])", "description": "distributed load ends here
\nD-C > 3 and B-A > L/2 and A<>C and B<>D
", "templateType": "anything"}, "C": {"name": "C", "group": "inputs", "definition": "qty(random(0..scalar(L)),units[1])", "description": "distributed load starts here
", "templateType": "anything"}, "FA": {"name": "FA", "group": "Ungrouped variables", "definition": "W-FB", "description": "reaction at A
", "templateType": "anything"}, "B": {"name": "B", "group": "inputs", "definition": "qty(random(scalar(A)..scalar(L)),units[1])", "description": "location of right hand support
", "templateType": "anything"}, "W": {"name": "W", "group": "Ungrouped variables", "definition": "loading * (D-C)", "description": "Downward force
", "templateType": "anything"}, "L": {"name": "L", "group": "inputs", "definition": "qty(random(8,10,12,14,16),units[1])", "description": "length of beam
", "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": "reaction at B
", "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": "location of left hand support
", "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": "Determine the reactions at $A$ and $B$.
\n$A$ = [[0]] $B$ = [[1]]
", "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", "type": "question"}, {"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": "A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "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": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "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": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "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": "Only marked close if the student actually has the right sign.
", "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. if correct answer is 100 N and close is ±1%,Find the reactions for a beam with a uniformly varying distributed load.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "{applet}
\nA {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])}.
\nW: {w} beam: {wb} xbar: {x} check: {check}
\n$F_A$: {precround(FA,4)} $F_B$ {precround(FB,4)}
", "advice": "distributed load ends here
", "templateType": "anything", "can_override": false}, "L": {"name": "L", "group": "inputs", "definition": "random(8,10,12,14)", "description": "length of beam
\n", "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": "distributed loading [force/length]
", "templateType": "anything", "can_override": false}, "FA": {"name": "FA", "group": "Ungrouped variables", "definition": "(W + WB)-FB", "description": "reaction at A
", "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": "load at c (scaled)
", "templateType": "anything", "can_override": false}, "W": {"name": "W", "group": "Ungrouped variables", "definition": "precround(loading * (wc+wd)/2 * (D-C),5)", "description": "Downward force due to load
", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "inputs", "definition": "random(L-3..L)", "description": "location of right hand support
", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "inputs", "definition": "random(0..5 except A)", "description": "distributed load starts here
", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "inputs", "definition": "0", "description": "location of left hand support
", "templateType": "anything", "can_override": false}, "wd": {"name": "wd", "group": "inputs", "definition": "random(0..2#0.5 except 0.5)", "description": "loading at d scaled
", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "C + (wc / 6 + wd/ 3)(D-C) * 2/(wc+wd)", "description": "midpoint of load
", "templateType": "anything", "can_override": false}, "FB": {"name": "FB", "group": "Ungrouped variables", "definition": "precround(((x-A) * W + (CG-A) * WB) / (B-A),5)\n", "description": "reaction at B
", "templateType": "anything", "can_override": false}, "w_b": {"name": "w_b", "group": "inputs", "definition": "siground(random(0.1..1 #0.1) loading,3)", "description": "Weight of the beam in W/L units
", "templateType": "anything", "can_override": false}, "CG": {"name": "CG", "group": "Ungrouped variables", "definition": "L/2", "description": "center of the beam
", "templateType": "anything", "can_override": false}, "WB": {"name": "WB", "group": "Ungrouped variables", "definition": "w_b L ", "description": "Weight of the beam itself
", "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": "Determine the reactions at $A$ and $B$.
\n$A$ = [[0]] $B$ = [[1]]
", "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", "type": "question"}, {"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": "A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "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": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "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": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "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": "Only marked close if the student actually has the right sign.
", "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. if correct answer is 100 N and close is ±1%,Find the reactions of a simply-supported beam with a trapazoidal distributed load.
", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "{geogebra_applet('xgjx2s8s',[['a', a 10/L], ['b', b 10/L],['c', c 10/L],['showfbd','false']])}
\n$\\var{qty(L,unit[0])}$ long beam $AB$ is subjected to a distributed load which
\nDetermine the reactions at $A$ and $B$.
", "advice": "{geogebra_applet('xgjx2s8s',[['a', a 10/L], ['b', b 10/L],['c', c 10/L],['showfbd','true']])}
\n$\\begin{align}\\\\ W_R &= \\var{QWR} & x_R &= \\var{QxR} \\\\ W_T &= \\var{QWT} &x_T &= \\var{QxT}\\end{align}$
\n$\\begin{align}\\\\ \\Sigma M_A &= 0 \\\\W_R x_r + W_T x_T &= B L \\\\ B &= \\frac{W_R x_r + W_T x_T}{L} \\\\&= \\var{QRB} \\\\ \\\\ \\Sigma F_y &= 0 \\\\ A + B &= W_T + W_R \\\\ A &= W_T + W_R - B \\\\ &= \\var{QRA} \\end{align}$
\nhorizontal location of the starts of the triangular load.
\ncould be on the left or right of point B
", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(0..L)", "description": "horizontal position of point between triangle and rectangle. l
", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(0..L)", "description": "horizontal location of the end of the rectangular load.
\ncould be on the left or right of point B
", "templateType": "anything"}, "w": {"name": "w", "group": "Ungrouped variables", "definition": "random(50..150#10)", "description": "Max value of loading in [force/distance]
", "templateType": "anything"}, "WT": {"name": "WT", "group": "solution", "definition": "abs(a-b) w /2", "description": "weight of the triangular load
", "templateType": "anything"}, "WR": {"name": "WR", "group": "solution", "definition": "abs(b-c) w", "description": "weight of the rectangular load
", "templateType": "anything"}, "WTot": {"name": "WTot", "group": "solution", "definition": "WT+WR", "description": "Total weight of load
", "templateType": "anything"}, "xR": {"name": "xR", "group": "solution", "definition": "(b+c)/2", "description": "location of centroid of rect
", "templateType": "anything"}, "xT": {"name": "xT", "group": "solution", "definition": "b + (a-b)/3", "description": "Centroid of triangle
", "templateType": "anything"}, "L": {"name": "L", "group": "Ungrouped variables", "definition": "random([10,12,16,20])", "description": "length of beam
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", "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", "type": "question"}]}], "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": [], "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "inreview"}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "type": "exam", "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": "A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "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": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "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": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "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": "Only marked close if the student actually has the right sign.
", "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. if correct answer is 100 N and close is ±1%,