// Numbas version: exam_results_page_options {"name": "Centroid of a composite area: shape with hole", "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

\n

1. replacing \"ohms\" with \"ohm\"  case insensitive

\n

2. replacing '-' with ' ' 

\n

3. replacing '°' with ' deg' 

\n

to 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.  

\n

If student_units are wrong  - replace with correct units

\n

If student_scalar has the wrong sign - replace with right sign

\n

If 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%,
99  N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.
If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.
This value would be close if the expected units were provided.  If the correct answer is 100 N, and close is ±1%,
99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Centroid of a composite area: shape with hole", "tags": ["centroids", "composite area method", "Mechanics", "mechanics", "Statics", "statics"], "metadata": {"description": "

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]])}

\n

Complete the table below and detemine the coordinates of the centroid of the composite shape.

\n

Consider the shape to be made up of a {if (m=1,'large','')} rectangle {if (m=0,'and a triangle with a circle','with a triangle and circle')} removed. 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

\n

1. Divide the shape into three subshapes as described in the problem statement. 

\n

2. You should be able to set up a table to gather the required information like the one provided in this problem.

\n

3. Determine and enter the area and centroidal coordinates for each subshape into the table

\n

$\\qquad A_i, \\bar{x}_i,\\bar{y}_i$

\n

4. Multiply area by the centroidal coordinates to get the moment of areas for the pieces.

\n

$\\qquad (Q_x)_i = A_i\\bar{y}_i ,\\quad(Q_y)_i=A_i\\bar{x}_i$.

\n

5. Sum columns 1, 4, and 5 to find the total area and moments of area.

\n

$\\qquad A, Q_x, Q_y$

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Part $A_i$ [{units}2]$\\bar{x}_i$ [{units}]$\\bar{y}_i$ [{units}]$A_i\\bar{x}_i$ [{units}3]$A_i\\bar{y}_i$ [{units}3]
rectangle {area_rect[m]}{C_rect[m][0]}{C_rect[m][1]}{Q_rect[1]}{Q_rect[0]}
triangle {area_tri[m]}{siground(C_tri[m][0],3)}{siground(C_tri[m][1],3)}{Q_tri[1]}{Q_tri[0]}
circle {siground(area_circ[m],3)}{C_circ[m][0]}{C_circ[m][1]}{siground(Q_circ[1],3)}{siground(Q_circ[0],3)}
$\\Sigma$ {siground(area_total,3)}{siground(Q_total[1],3)}{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": {}, "extensions": ["geogebra"], "variables": {"ht": {"name": "ht", "group": "Input values", "definition": "random(3..9#3)", "description": "

\"height\" of triangle  

\n

horizontal for n = 4,5,6,10,11,12

\n

vertical 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\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
987
106
11rectangle5
124
123
", "templateType": "randrange"}, "C_tri": {"name": "C_tri", "group": "centroids", "definition": "// determines location of centroid\n// returns array of centroid coordinates, first term for m=0 \n[\nswitch(\n n=1, vector(b1/3,-ht/3),\n n=2, vector(b1/2,-ht/3),\n n=3, vector(2*b1/3,-ht/3),\n n=4, vector(b1+ht/3,h1/3),\n n=5, vector(b1+ht/3,h1/2),\n n=6, vector(b1+ht/3,2*h1/3),\n n=7, vector(2 * b1/3, h1+ht/3),\n n=8, vector(b1/2, h1+ht/3),\n n=9, vector(b1/3, h1+ht/3),\n n=10, vector(-ht/3,2*h1/3),\n n=11, vector(-ht/3,h1/2),\n n=12, vector(-ht/3,h1/3)\n ) + A\n ,\n switch(\n n=3, vector(b1/3,-2*ht/3),\n n=2, vector(b1/2,-2*ht/3),\n n=1, vector(2*b1/3,-2*ht/3),\n n=6, vector(b1+2*ht/3,h1/3),\n n=5, vector(b1+2*ht/3,h1/2),\n n=4, vector(b1+2*ht/3,2*h1/3),\n n=9, vector(2 * b1/3, h1+2*ht/3),\n n=8, vector(b1/2, h1+2*ht/3),\n n=7, vector(b1/3, h1+2*ht/3),\n n=12, vector(-2*ht/3,2*h1/3),\n n=11, vector(-2*ht/3,h1/2),\n n=10, vector(-2*ht/3,h1/3)\n ) + A\n ]", "description": "

determines location of centroid of triangle based on location and method
returns array of centroid coordinates, first term for m=0

", "templateType": "anything"}, "m": {"name": "m", "group": "Input values", "definition": "if(n in [2,5,8,11],0,random(0..1))\n", "description": "

This is the method used to solve the problem: 

\n

m=0: small rectangle + triangle - circle

\n

m=1: big rectangle - triangle - circle

\n

when 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": "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Part \n

$A_i$ 

\n
\n

$\\bar{x}_i$ 

\n
\n

$\\bar{y}_i$ 

\n
\n

$A_i\\bar{x}_i$ 

\n
\n

$A_i\\bar{y}_i$ 

\n
rectangle [[0]][[4]][[7]][[10]][[14]]
triangle [[1]][[5]][[8]][[11]][[15]]
circle [[2]][[6]][[9]][[12]][[16]]
$\\Sigma$ [[3]][[13]][[17]]
\n

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{"correctAnswer": "qty(area_tri[m],units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Ac", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(area_circ[m],units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Area", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(area_total,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "xr", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(C_rect[m][0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "xt", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, 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