// Numbas version: exam_results_page_options {"name": "Centroidal Moment of inertia: T shape", "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": [["question-resources/Tshape.ggb", "/srv/numbas/media/question-resources/Tshape.ggb"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Centroidal Moment of inertia: T shape", "tags": ["centroid", "Mechanics", "mechanics", "moment of inertia", "statics", "Statics"], "metadata": {"description": "

Find the centroidal moment of inertia of a sideways T shape. This requires first locating the centroid, then applying the parallel axis theorem.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

{geogebra_applet('wfhyktjn',['A':P1, 'B': P2])}

\n

Determine the moment of inertia of the T shape with respect to a vertical axis passing through the shape's centroid.  Let this axis be designated $a$. Grid units are {units}.

", "advice": "

\n

Number the parts:  

\n

Part 1 horizontal rectangle: $b_1$ = {qty(b1,units)}, $h_1$ = {qty(h1,units)}.

\n

Part 2 vertical rectangle: $b_2$ = {qty(b2,units)}, $h_2$ = {qty(h2,units)}.

\n

\n

Calculate the areas:

\n

$ A_1 = b_1 h_1=\\var{qty(A1,units+'^2')}$

\n

$ A_2 = b_2 h_2 = \\var{qty(A2,units+'^2')}$

\n

Locate the centroids of the parts.

\n

    $ \\bar{x}_1 = b_1/2 = \\var{qty(d1,units)} \\qquad \\bar{x}_2 = b_1 + b_2/2 = \\var{qty(d2,units)}$

\n

Locate the centroid of the whole.

\n

   $\\bar{x} = \\dfrac{ A_1 \\bar{x}_1 + A_2 \\bar{x}_2} {A_1 + A_2} = \\var{qty(siground(xbar,4),units)}$

\n

   $\\bar{y} = \\var{qty(0, units)} $, by symmetry

\n

Calculate the moment of inertia with respect to the y-axis for the parts and the whole.

\n

$\\begin{align} \\\\{I_y}_1 &= \\tfrac{1}{3} h_1 b_1^3 \\\\&= \\tfrac{1}{3}( \\var{h1})(\\var{b1})^3 \\\\&= \\var{qty(display(Iy1),units+'^4')} \\\\\\\\{I_y}_2 &= [\\bar{I} + A d^2]_2\\\\ &= \\frac{1}{12} h_2 b_2^3 + A_2 d_2^2 \\\\&= \\var{display(Ibar2)} + (\\var{display(A2)}) (\\var{display(d2)})^2\\\\&=\\var{qty(display(Iy2),units+'^4')} \\\\\\\\I_y &= {I_y}_1+{I_y}_2\\\\&=\\var{display(Iy1)}+\\var{display(Iy2)}\\\\&=\\var{qty(display(Iy),units+'^4')}\\end{align}$

\n

Use the parallel axis theorem $I  =  \\bar{I} + A d^2$ backwards to find the centroidal moment of inertia.

\n

$\\begin{align} \\bar{I}_a &= I_y - A (\\bar{x})^2 \\\\&= \\var{display(Iy)} - \\var{display(A)} (\\var{display(xbar)})^2\\\\&=\\var{qty(display(I_a),units+'^4')}\\end{align}$

\n

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width of P1

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true

", "templateType": "anything"}, "Iy1": {"name": "Iy1", "group": "Iy", "definition": "h1 b1^3/12 + A1 * (b1/2)^2", "description": "", "templateType": "anything"}, "P1": {"name": "P1", "group": "Inputs", "definition": "vector(random(5..12),random(1..2))", "description": "

Point A in GGB

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height of p1

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width of p2

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height of p2

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centroidal moi

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alternate calculation of Iy

", "templateType": "anything"}, "Iy2'": {"name": "Iy2'", "group": "check", "definition": "Ibar2 + a2 d2^2", "description": "", "templateType": "anything"}, "Iy": {"name": "Iy", "group": "check", "definition": "Iy1' + Iy2'", "description": "

Moment of intertia about y axis

", "templateType": "anything"}, "Qy": {"name": "Qy", "group": "check", "definition": "A1 d1 + A2 d2", "description": "", "templateType": "anything"}, "xbar": {"name": "xbar", "group": "check", "definition": "Qy/A", "description": "", "templateType": "anything"}, "I_a": {"name": "I_a", "group": "check", "definition": "Iy - A xbar^2", "description": "

Centroidal moment of inertia of total shape

", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Inputs", "variables": ["units", "debug", "applet", "P1", "P2", "b1", "h1", "b2", "h2"]}, {"name": "Area", "variables": ["A1", "A2", "A"]}, {"name": "Iy", "variables": ["Iy1", "Iy2", "ky"]}, {"name": "check", "variables": ["ibar1", "Ibar2", "d1", "d2", "Iy1'", "Iy2'", "Iy", "Qy", "xbar", "I_a"]}], "functions": {"display": {"parameters": [["q", "number"]], "type": "number", "language": "jme", "definition": "(siground(q,4))"}}, "preamble": {"js": "", "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]] $\\qquad \\bar{y} = $ [[1]]

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$\\bar{I}_a$ = [[0]] {display(I_a')}

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