// Numbas version: finer_feedback_settings {"name": "Chapter 5 Exercises", "metadata": {"description": "

End of chapter exercises for Engineering Statics: Open and Interactive

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["Tension in a cable", "Raise pole", "Cantilever beam", "EquBeam and pulley", "Bell crank", "Car on a hill", "Hand truck", "Triangle", "Truss"], "variable_overrides": [[], [], [], [], [], [], [], [], []], "questions": [{"name": "Moment Balance: Tension in a cable", "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

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

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.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["Mechanics, statics, moment, 2-d, tension"], "metadata": {"description": "

Find the force required to produce a given moment, or vice-versa.

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

{applet}

Control arm $AB$ is subjected to a {direction} moment $M$ and held in position by cable $AC$.

Knowing that the moment is {M} {direction}, determine the tension in the cable.

Knowing that the tension in the cable is {T}, determine the magnitude of the moment $M$.

", "advice": "

Equate the applied moment $M$ to the moment produced by the force.

$\\Sigma M_B = 0 \\therefore M = F d_\\perp$

Use geometry to find $d_\\perp$ then solve for the unknown quantity.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"dperp": {"name": "dperp", "group": "Ungrouped variables", "definition": "L sin(radians(alpha))", "description": "", "templateType": "anything", "can_override": false}, "T": {"name": "T", "group": "Inputs", "definition": "qty(random(1..5)random(2,4,5,10),units[1])", "description": "

Used when T is given.

", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "ggb", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "direction": {"name": "direction", "group": "Ungrouped variables", "definition": "if(A[0]>C[0],'clockwise','counterclockwise')", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "Inputs", "definition": "vector(random(0..24#4),random(0..32#4))", "description": "", "templateType": "anything", "can_override": false}, "L": {"name": "L", "group": "Ungrouped variables", "definition": "qty(abs(A),units[0])", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Inputs", "definition": "vector(random(-28..28#4 except 0),random(8..28#4))", "description": "", "templateType": "anything", "can_override": false}, "answers": {"name": "answers", "group": "Inputs", "definition": "[['T', M/dperp], \n ['M', T*dperp]]\n\n", "description": "", "templateType": "anything", "can_override": false}, "M": {"name": "M", "group": "Inputs", "definition": "qty(random(1..9)random(12, 24,36,48), units[0] + \" \" + units[1])\n", "description": "

Used when M is given.

", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Inputs", "definition": "['in','lb']\n", "description": "", "templateType": "anything", "can_override": false}, "version": {"name": "version", "group": "Inputs", "definition": "random(0..1)", "description": "

Which version?

", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Ungrouped variables", "definition": "degrees(angle(-A,C-A))", "description": "", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "ggb", "definition": "geogebra_applet('msspdvgu', params)", "description": "", "templateType": "anything", "can_override": false}, "params": {"name": "params", "group": "ggb", "definition": "[A: A, C: C, show: [definition: 'false', visible: false]]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(A) > 18 and abs(A-C) > 16 and abs(C) > 16", "maxRuns": 100}, "ungrouped_variables": ["L", "alpha", "dperp", "direction"], "variable_groups": [{"name": "Inputs", "variables": ["C", "A", "T", "M", "version", "answers", "units"]}, {"name": "ggb", "variables": ["applet", "params", "debug"]}], "functions": {}, "preamble": {"js": "question.signals.on('adviceDisplayed',function() {\n try{\n var app = question.scope.variables.applet.app; \n app.setVisible(\"show\", true,false);\n app.setValue(\"show\", 1);\n }\n catch(err){} \n})", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Answer", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

{latex(answers[version][0])} = [[0]]

{answers[version][0]} = {siground(answers[version][1],5)}

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Answer", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "answers[version][1]", "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": "Equilibrium of a rigid body: raise pole", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 12, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/12/edit"}, "name": "Angle quantity 2020", "short_name": "angle", "description": "

Adjusts all angles to 0 < $\\theta$ < 360.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

90° = -270° = 450°

", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['expected_answer']) ", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "original_student_scalar:\nmatchnumber(studentAnswer,['plain','en'])[1]\n\nstudent_scalar:\nmod(original_student_scalar,360)\n\n\nstudent_unit:\nstudentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]\n\ninterpreted_unit:\nif(trim(student_unit)='\u00b0','deg',student_unit)\n\ninterpreted_answer:\nqty(mod(student_scalar,360),'deg')\n\nclose:\nwithintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))\n\ncorrect_scalar:\nmod(scalar(settings['expected_answer']),360)\n\nright:\nwithintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))\n\ngood_unit:\nsame(qty(1,interpreted_unit),qty(1,'deg'))\n\nmark:\nassert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))", "marking_notes": [{"name": "original_student_scalar", "description": "

Retuns the scalar part of students answer (which is a quantity) as a number.

", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "

Normalize angle with mod 360

", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "

matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"

", "definition": "studentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]"}, {"name": "interpreted_unit", "description": "

Allows student to use degree symbol or 'deg' for units.

", "definition": "if(trim(student_unit)='\u00b0','deg',student_unit)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(mod(student_scalar,360),'deg')"}, {"name": "close", "description": "", "definition": "withintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))"}, {"name": "correct_scalar", "description": "

Normalize expected_answer with mod 360

", "definition": "mod(scalar(settings['expected_answer']),360)"}, {"name": "right", "description": "", "definition": "withintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))"}, {"name": "good_unit", "description": "", "definition": "same(qty(1,interpreted_unit),qty(1,'deg'))"}, {"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "assert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))"}], "settings": [{"name": "expected_answer", "label": "Expected Answer", "help_url": "", "hint": "Expected angle as a quantity.", "input_type": "code", "default_value": "qty(30,'deg')", "evaluate": true}, {"name": "unit_penalty", "label": "Unit penalty", "help_url": "", "hint": "Penalty for not including degree sign or 'deg'.", "input_type": "percent", "default_value": "20"}, {"name": "close_penalty", "label": "Close Penalty", "help_url": "", "hint": "Penalty for close answer.", "input_type": "percent", "default_value": "20"}, {"name": "close_tol", "label": "Close", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked close. ", "input_type": "code", "default_value": "0.5", "evaluate": false}, {"name": "right_tol", "label": "Right ", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked correct. ", "input_type": "code", "default_value": "0.1", "evaluate": false}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"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.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["angle from reference", "Equilibrium", "equilibrium", "Mechanics", "mechanics", "Rigid Body", "rigid body", "Statics", "statics"], "metadata": {"description": "

Equilibrium of a rigid body. Find tension to raise a pole.

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

{geogebra_applet('pf8c3vcn',[['α',alpha +'°'],['β',beta +'°']])}

A {mass} homogeneous pole with a length of {L} is being raised by pulling with a cable at $B$.

", "advice": "

This problem can be solved by the standard method:

Draw a free body diagram of the pole. Include the weight of the pole at the center of gravity. Note that mass must be converted to weight.
Use $\\Sigma M_A = 0$ to find $T$.
Use $\\Sigma F_x = 0$ and $\\Sigma F_y = 0$ to find $A_x$ and $A_y$.
Resolve $A_x$ and $A_y$ to find magnitude and direction of $\\mathbf{A}$.

It can also be solved using the three force body principle.

Find the point of intersection of the lines of action of the weight and the tension.
Determine the direction of force $\\mathbf{A}$. Its line of action must pass through the point.
Draw a force triangle.
Determine the angles in the force triangle.
Use the known weight and the law of sines to solve for the tension and the reaction at $A$.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"L": {"name": "L", "group": "inputs", "definition": "qty(random(3..5#0.2),'m')", "description": "", "templateType": "anything", "can_override": false}, "theta_T": {"name": "theta_T", "group": "Ungrouped variables", "definition": "180 + alpha - beta", "description": "", "templateType": "anything", "can_override": false}, "T": {"name": "T", "group": "Ungrouped variables", "definition": "scalar(weight) cos(radians(alpha))/(2 sin(radians(beta)) )\nvector(cos(radians(theta_t)),sin(radians(theta_t)))", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "-(W+T)", "description": "", "templateType": "anything", "can_override": false}, "W": {"name": "W", "group": "Ungrouped variables", "definition": "vector(0,-scalar(weight))", "description": "", "templateType": "anything", "can_override": false}, "theta_A": {"name": "theta_A", "group": "Ungrouped variables", "definition": "mod(degrees(atan2(A[1],A[0])),360)", "description": "", "templateType": "anything", "can_override": false}, "mass": {"name": "mass", "group": "inputs", "definition": "qty(random(10..150#5),'kg')", "description": "", "templateType": "anything", "can_override": false}, "beta": {"name": "beta", "group": "inputs", "definition": "random(20..(90+alpha-20))", "description": "

angle between pole and rope

", "templateType": "anything", "can_override": false}, "weight": {"name": "weight", "group": "inputs", "definition": "mass * qty(9.81,'m/s^2') in 'N'", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "inputs", "definition": "random(20..80)", "description": "

angle of pole

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["W", "T", "theta_T", "A", "theta_A", "debug"], "variable_groups": [{"name": "inputs", "variables": ["alpha", "mass", "beta", "weight", "L"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Tension", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the tension in the cable?

$T$= [[0]] T = {siground(abs(T),4)} N

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What is the magnitude and direction of the reaction force at point A?

$\\mathbfy{A}$ = [[3]]

at an angle of [[0]] measured [[1]] from the [[2]].

A= {siground(abs(A),4)} N @ {siground(theta_A,4)}°

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Adjusts all angles to 0 < $\\theta$ < 360.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

90° = -270° = 450°

Retuns the scalar part of students answer (which is a quantity) as a number.

", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "

Normalize angle with mod 360

", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "

matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"

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Allows student to use degree symbol or 'deg' for units.

Normalize expected_answer with mod 360

A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

Only marked close if the student actually has the right sign.

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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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["angle_from_ref", "equilibrium", "Equilibrium", "fixed support", "mechanics", "Mechanics", "rigid body", "Rigid Body", "statics", "Statics"], "metadata": {"description": "

Determine the reactions supporting a cantilever beam carrying concentrated forces and moments.

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

{geogebra_applet('v5xfnaym',[['A',A],['B',B],['L',L],['units','\"'+units[1]+'\"'],['fa',FA], ['fc',FC], ['M',M]])}

A beam of length $L$ = {L} {units[1]} is supported by a fixed (cantilever) support at $O$. Detemine the reactions at $O$ when the beam supports these loads:

$A$ = {magA} {units[0]}, $B$ = {abs(M)} {units[0]}-{units[1]} and $C$ = {magC} {units[0]}, as shown.

", "advice": "

Draw a free body diagaram of the beam, then apply the equations of equilibrium.

$\\Sigma M = 0$

$M_O + M_A + M_B + M_C = 0$

$M_A = d_1 A_y$ = ({OA}) ({qty(abs(FA[1]),units[0])}) = {abs(MA)} {if(sign(MA)>0,'counterclockwise','clockwise')}

$M_B =$ {abs(MB)} {if(sign(MB)>0,'counterclockwise','clockwise')}

$M_C = L C_y$ = ({OC}) ({format(qty(abs(FC[1]),units[0]))}) = {format(abs(MC))} {if(sign(MC)>0,'counterclockwise','clockwise')}

$ M_O = - ( \\var{format(MA)} + \\var{format(MB)} + \\var{format(MC)} ) = \\var{format(abs(MO))}$ {if(sign(MO)>0,'counterclockwise','clockwise')}

$\\Sigma F_x = 0$

$O_x + A_x + C_x = 0$

$O_x = 0 - C_x = \\var{format(qty(abs(FO[0]), units[0]))}$ {if(sign(FO[0])>=0,'right','left')}

$\\Sigma F_y = 0$

$O_y + A_y + C_y = 0$

$O_y = - (A_y + C_y) = - ( \\var{FA[1]} + \\var{siground(FC[1],4)} )= \\var{format(qty(abs(FO[1]), units[0]))} $ {if(sign(FO[1])>=0,'up','down')}

Resolve $O_x$ and $O_y$ to get

Force $O = \\var{format(qty(abs(FO), units[0]))} $ at an angle of {format(dirO)} from the positve x-axis.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"FO": {"name": "FO", "group": "output", "definition": "-(FA+FC)", "description": "

The resultant force at O as a vector.

", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Input", "definition": "random(0.2..0.8#0.1)", "description": "", "templateType": "anything", "can_override": false}, "FC": {"name": "FC", "group": "Input", "definition": "magC vector(cos(radians(theta_C)),sin(radians(theta_C)))", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Input", "definition": "random(A..0.9#0.1)", "description": "", "templateType": "anything", "can_override": false}, "OA": {"name": "OA", "group": "output", "definition": "qty(A L, units[1])", "description": "

distance from O to A

", "templateType": "anything", "can_override": false}, "MA": {"name": "MA", "group": "output", "definition": "qty(cross(vector(scalar(OA),0,0),vector(FA[0],\n FA[1],0))[2],\nunits[0] + \" \" + units[1])\n\n", "description": "

Moment of force A about point O.

", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Input", "definition": "random(['N','m'],['lb','ft'])", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Input", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "MB": {"name": "MB", "group": "output", "definition": "qty(M,units[0] + \" \" + units[1])\n", "description": "

The concentrated moment.

", "templateType": "anything", "can_override": false}, "magA": {"name": "magA", "group": "Input", "definition": "random(10..150#10)", "description": "", "templateType": "anything", "can_override": false}, "OB": {"name": "OB", "group": "output", "definition": "qty(B L, units[1])", "description": "

distance from O to B

", "templateType": "anything", "can_override": false}, "L": {"name": "L", "group": "Input", "definition": "if(units[1]='ft',random(2..12#2),random(1..5))", "description": "", "templateType": "anything", "can_override": false}, "MagC": {"name": "MagC", "group": "Input", "definition": "random(10..150#10)", "description": "", "templateType": "anything", "can_override": false}, "dirO": {"name": "dirO", "group": "output", "definition": "qty(mod(degrees(atan2(FO[1],FO[0])),360),'deg')", "description": "", "templateType": "anything", "can_override": false}, "FA": {"name": "FA", "group": "Input", "definition": "MagA vector(0,random(1,-1))", "description": "", "templateType": "anything", "can_override": false}, "OC": {"name": "OC", "group": "output", "definition": "qty(L, units[1])", "description": "

distance from O to C

", "templateType": "anything", "can_override": false}, "MO": {"name": "MO", "group": "output", "definition": "-(MA + MB + MC)", "description": "

The reaction moment at O.

", "templateType": "anything", "can_override": false}, "M": {"name": "M", "group": "Input", "definition": "random(100..500#25) random(1,-1)", "description": "

The magnitude of the moment.

", "templateType": "anything", "can_override": false}, "theta_c": {"name": "theta_c", "group": "Input", "definition": "random(0..355#5 except [0,90,180,270])", "description": "", "templateType": "anything", "can_override": false}, "MC": {"name": "MC", "group": "output", "definition": "qty(cross(vector(scalar(OC),0,0),\n vector(FC[0],FC[1],0))[2],\n units[0] + \" \" + units[1])\n \n \n ", "description": "

Moment of force C about point O.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "B-A > 0.2", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Input", "variables": ["L", "A", "B", "units", "FA", "magA", "MagC", "theta_c", "FC", "M", "debug"]}, {"name": "output", "variables": ["OA", "OC", "OB", "MA", "MC", "MB", "MO", "FO", "dirO"]}], "functions": {"format": {"parameters": [["q", "quantity"]], "type": "string", "language": "jme", "definition": "string(siground(q,4))"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Moment at O", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Determine the magnitude and direction of the moment at the fixed support at $O$.

$M_O$ = [[0]] [[1]] {format(MO)}

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Determine the magnitude and direction of the reaction force at $O$.

$O$ = [[3]] at an angle of [[0]] measured [[1]] from the [[2]].

{format(qty(abs(FO),units[0]))} at {format(dirO)}

", "gaps": [{"type": "angle", "useCustomName": true, "customName": "angle", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "dirO", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.2"}}, {"type": "1_n_2", "useCustomName": true, "customName": "sign", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+x axis", "+y axis", "-x axis", "-y axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "engineering-answer", "useCustomName": true, "customName": "Magnitude", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(abs(FO),units[0])", "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": "Equilibrium of a rigid body: beam and pulley", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 12, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/12/edit"}, "name": "Angle quantity 2020", "short_name": "angle", "description": "

Adjusts all angles to 0 < $\\theta$ < 360.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

90° = -270° = 450°

Retuns the scalar part of students answer (which is a quantity) as a number.

", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "

Normalize angle with mod 360

", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "

matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"

", "definition": "studentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]"}, {"name": "interpreted_unit", "description": "

Allows student to use degree symbol or 'deg' for units.

Normalize expected_answer with mod 360

A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["angle from reference", "Mechanics", "mechanics", "pulley", "rigid body equilibrium", "Rigid body equilibrium", "Statics", "statics"], "metadata": {"description": "

Rigid body equilibrium problem. Easiest to solve by replacing forces on the perimiter of the pulley with equivalent forces at the axle.

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

{geogebra_applet('nnkbvxb8',[['L',scalar(L)],['ab',scalar(ab)],['r',scalar(r)/12],['alpha',alpha+'°'],['theta',theta+'°']])}

{L} long beam $ABC$ supports a frictionless pulley with {r} radius at point $B$, located {ab} from the left end. Determine the reactions at $A$ and $C$ when it supports {W} weight $W$ as shown.

", "advice": "

Known: $L = \\var{l} \\qquad d = \\var{ab} \\qquad \\theta = \\var{theta}° \\qquad \\alpha = \\var{alpha}° \\qquad W = T = \\var{W}$

\n
1. Draw a free body diagram of the beam. It simplifies the solution to replace the forces of the rope on the pulley with equivalent forces at point $B$. The force at $C$ acts perpendicular to the surface the roller rests on.\n
  {geogebra_applet('kggckbyp',[['L',scalar(L)],['ab',scalar(ab)],['r',scalar(r)/12],['alpha',alpha+'°'],['theta',theta+'°']])}
  \n
2. Take moments about point $A$ to find the reaction at $C$.\n
  $\\begin{align}\\Sigma M_A &= 0 \\\\+ C_y L+ T_y d - W d&= 0 \\\\ C_y &=\\dfrac{ d (W - T \\cos \\theta)}{L} = \\var{display(Cy)}\\\\C &= \\dfrac{C_y}{\\cos \\alpha} = \\var{display(magC)}\\end{align}$
  \n
3. Apply $F_x=0$ to find $A_x$.\n
  $\\begin{align}F_x&=0\\\\A_x - T_x - C_x &= 0 \\\\A_x &= C_x + T_x\\\\A_x&= C \\sin \\alpha + T \\sin \\theta = \\var{display(Ax)}\\end{align}$
  \n
4. Apply $\\Sigma F_y = 0$ to find $A_y$.\n
  $\\begin{align}F_y&=0\\\\A_y + C_y + T_y - W &= 0 \\\\A_y &= W - C_y - T_y\\\\A_y&= W - C \\cos \\alpha - T \\cos \\theta= \\var{display(Ay)}\\end{align}$
  \n
5. Resolve $A_x$ and $A_y$ to get magnitude and direction of force $\\mathbf{A}$.\n
  $A = \\sqrt{(A_x)^2+(A_y)^2} = \\var{display(magA)}$
  \n
  $\\phi = \\tan^{-1} \\left(\\dfrac{A_y}{A_x}\\right) = \\var{precround(dirA,2)}$° from the positive x-axis.
  \n
6. Check with $\\Sigma \\mathbf{F} = 0$.\n
  $ \\mathbf{A} + \\mathbf{C} + \\mathbf{W} + \\mathbf{T} = 0$
  \n
  $\\var{precround(vecA,2)} + \\var{precround(vecC,2)} + \\var{vecW} + \\var{precround(vecT,2)} = \\var{precround(sum,2)}$
  \n
\n

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Determine the magnitude and direction of the reaction at the roller at $C$.

Force $\\mathbf{C}$ has a magnitude of [[3]]

acting at an angle of [[0]] measured [[1]] from the [[2]].

C = {magC}, angle={dirC}°

", "gaps": [{"type": "angle", "useCustomName": true, "customName": "angleC", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "dir_C_from_X", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.2"}}, {"type": "1_n_2", "useCustomName": true, "customName": "sign", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+x axis", "+y axis", "-x axis", "-y axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "engineering-answer", "useCustomName": true, "customName": "magC", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "magC", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Reaction at A", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_angle: // a qty string corrected to standard angle\n student_angle[2] + student_angle[1] * student_angle[0] + student_units\n\nmagnitude:\n studentAnswer[3]\n\nstudent_angle:\n [mod(matchnumber(studentAnswer[0],['plain','en'])[1],360), // angle\n [1,-1][indices(studentAnswer[1],[true])[0]], // ccw = 1 cw = -1\n [0,90,180,-90][indices(studentAnswer[2],[true])[0]]] // reference axis\n\nstudent_units:\n studentAnswer[0][len(matchnumber(studentAnswer[0],['plain','en'])[0])..len(studentAnswer[0])]\n\ninterpreted_answers:\n [interpreted_angle, studentAnswer[1], studentAnswer[2], studentAnswer[3]]\n\ngap_feedback (Feedback on each of the gaps):\n map(\n try(\n let(\n result, submit_part(gaps[gap_number][\"path\"],answer),\n gap, gaps[gap_number],\n name, gap[\"name\"], \n noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n assert(name=\"\" or len(gaps)=1,feedback(translate('part.gapfill.feedback header',[\"name\": name])));\n concat_feedback(filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]), if(marks>0,result[\"marks\"]/marks,1), noFeedbackIcon);\n result\n ),\n err,\n fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n ),\n [gap_number,answer,index],\n zip([3,0],[studentAnswer[3], interpreted_angle],[1,2])\n )\n\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Determine the magnitude and direction of the reaction at pin $A$.

Force $\\mathbf{A}$ has a magnitude of [[3]]

acting at an angle of [[0]] measured [[1]] from the [[2]].

A = {magA}, angle={dirA}°

", "gaps": [{"type": "angle", "useCustomName": true, "customName": "angleA", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(dirA,'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.2"}}, {"type": "1_n_2", "useCustomName": true, "customName": "sign", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+x axis", "+y axis", "-x axis", "-y axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "engineering-answer", "useCustomName": true, "customName": "magA", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "magA", "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": "Equilibrium of a rigid body: bell crank", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 12, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/12/edit"}, "name": "Angle quantity 2020", "short_name": "angle", "description": "

Adjusts all angles to 0 < $\\theta$ < 360.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

90° = -270° = 450°

Retuns the scalar part of students answer (which is a quantity) as a number.

", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "

Normalize angle with mod 360

", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "

matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"

", "definition": "studentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]"}, {"name": "interpreted_unit", "description": "

Allows student to use degree symbol or 'deg' for units.

Normalize expected_answer with mod 360

A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["angle from reference", "mechanics", "Mechanics", "rigid body equilibrium", "Rigid body equilibrium", "Statics", "statics", "three force body", "Three force body"], "metadata": {"description": "

Two forces act on a bell crank. This problem has two unknown magnitudes and an unknown direction which makes it tricky to solve by the equilibrium equation method.

The solution is much simpler if three force body principle is used.

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

{geogebra_applet('at35nexv',[['L_B',scalar(L_B)],['L_C',scalar(L_C)],['α',alpha+'°'],['β',beta+'°']])}

Two forces, $\\mathbf{B}$ and $\\mathbf{C}$, act on the arms of the rigid bell crank shown. Arm $AB$ is {L_B} long, and arm $AC$ is {L_C} long, and the bell crank is free to pivot on pin $A$.

", "advice": "

Equilibrium Equation approach :

Four Unknowns: Magnitudes of $\\mathbf{B}$ and $\\mathbf{C}$, $A_x$ , $A_y$

Four Equations: Three equations of equilibrium plus $A = \\sqrt{A_x^2 + A_y^2} = \\var{limit}$

\\[\\begin{align}\\Sigma M_A &= 0\\\\ M_B &= M_C \\\\B \\cdot d_{AB}\\, \\cos \\beta &= C \\cdot d_{AC}\\\\C&= B \\,\\cos \\var{beta}°\\left( \\frac{\\var{L_B}}{\\var{L_C}}\\right)\\\\C &=\\var{siground(cos(radians(beta)) * (L_B /L_C),4)}B \\end{align}\\]

\\[\\begin{align}\\Sigma F_x &= 0\\\\A_x &= C_x\\\\&=C \\,\\sin \\var{alpha}°\\\\&=(\\var{siground(cos(radians(beta)) * (L_B /L_C),4)} B)\\, \\sin \\var{alpha}°\\\\&=\\var{siground(mag_c * sin(radians(alpha)),4) } B \\end{align}\\]

\\[\\begin{align}\\Sigma F_y &= 0\\\\A_y &=B+ C_y\\\\&= B +C \\cos \\var{alpha}°\\\\ &= B +(\\var{siground(mag_C,4)} B ) \\cos \\var{alpha}° \\\\ &= \\var{siground(1 + mag_c * cos(radians(alpha)),4) } B \\end{align}\\]

\\[\\begin{align}A=\\sqrt{A_x^2 + A_y^2} &= \\var{limit}\\\\ \\sqrt{(\\var{siground(mag_c * sin(radians(alpha)),4) } B)^2 + (\\var{siground(1 + mag_c * cos(radians(alpha)) ,4) } B)^2 }&= \\var{limit}\\\\B\\sqrt{(\\var{siground(mag_c * sin(radians(alpha)),4) })^2 + (\\var{siground(1 + mag_c * cos(radians(alpha)) ,4) })^2 }&= \\var{limit}\\\\B=\\var{siground(limit/mag_A,4)}\\end{align}\\]

Three force body approach:

Three unknowns: Magnitudes of $\\mathbf{B}$ and $\\mathbf{C}$, direction of $\\mathbf{A}$.

The lines of action of $\\mathbf{B}$ and $\\mathbf{C}$ are known so you can use geometry to find their intersection point. Force $\\mathbf{A}$ passes through this point too, so you can determine from this the direction of $\\mathbf{A}$.

With the three directions known as well as the magnitude of $\\mathbf{A}$, draw a force triangle and use the law of sines to solve for $B$ and $C$.

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Determine the maximum force which can be applied at $B$ if the magnitude of the reaction at $A$ is not to exceed {limit}.

$B =$ [[0]]

B = {siground(limit/mag_A,4)}

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "B max", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "limit/mag_A", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Reaction at C", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the corresponding magnitude of the force at $C$ ?

$C= $ [[0]]

C = {siground(mag_C limit/mag_A,4)}

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "C", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "mag_C limit/mag_A", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Direction of A", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_angle: // a qty string corrected to standard angle\n student_angle[2] + student_angle[1] * student_angle[0] + student_units\n\n\nstudent_angle:\n [mod(matchnumber(studentAnswer[0],['plain','en'])[1],360), // angle\n [1,-1][indices(studentAnswer[1],[true])[0]], // ccw = 1 cw = -1\n [0,90,180,-90][indices(studentAnswer[2],[true])[0]]] // reference axis\n\nstudent_units:\n studentAnswer[0][len(matchnumber(studentAnswer[0],['plain','en'])[0])..len(studentAnswer[0])]\n\ninterpreted_answers:\n [interpreted_angle, studentAnswer[1], studentAnswer[2]]\n\ngap_feedback (Feedback on each of the gaps):\n map(\n try(\n let(\n result, submit_part(gaps[gap_number][\"path\"],answer),\n gap, gaps[gap_number],\n name, gap[\"name\"], \n noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n assert(name=\"\" or len(gaps)=1,feedback(translate('part.gapfill.feedback header',[\"name\": name])));\n concat_feedback(filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]), if(marks>0,result[\"marks\"]/marks,1), noFeedbackIcon);\n result\n ),\n err,\n fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n ),\n [gap_number,answer,index],\n zip([0],[interpreted_angle],[1])\n )\n\n\n\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

In what direction does the force at $A$ act?

$\\theta_A$ = [[0]] measured [[1]] from the [[2]].

$\\theta_A$ = {theta_A}

", "gaps": [{"type": "angle", "useCustomName": true, "customName": "theta A", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "interpreted_angle: // a qty string corrected to standard angle\n student_angle[2] + student_angle[1] * student_angle[0] + student_units\n\n\nstudent_angle:\n [mod(matchnumber(studentAnswer[0],['plain','en'])[1],360), // angle\n [1,-1][indices(studentAnswer[1],[true])[0]], // ccw = 1 cw = -1\n [0,90,180,-90][indices(studentAnswer[2],[true])[0]]] // reference axis\n\nstudent_units:\n studentAnswer[0][len(matchnumber(studentAnswer[0],['plain','en'])[0])..len(studentAnswer[0])]\n\ninterpreted_answers:\n [interpreted_angle, studentAnswer[1], studentAnswer[2]]\n\ngap_feedback (Feedback on each of the gaps):\n map(\n try(\n let(\n result, submit_part(gaps[gap_number][\"path\"],answer),\n gap, gaps[gap_number],\n name, gap[\"name\"], \n noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n assert(name=\"\" or len(gaps)=1,feedback(translate('part.gapfill.feedback header',[\"name\": name])));\n concat_feedback(filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]), if(marks>0,result[\"marks\"]/marks,1), noFeedbackIcon);\n result\n ),\n err,\n fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n ),\n [gap_number,answer,index],\n zip([0],[interpreted_angle],[1])\n )\n\n\n\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "precround(qty(theta_A,'deg'),1)", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.2"}}, {"type": "1_n_2", "useCustomName": true, "customName": "sign", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+x axis", "+y axis", "-x axis", "-y axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Equilibrium of a rigid body: Car on a hill", "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.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["Equilibrium", "equilibrium", "Mechanics", "mechanics", "Rigid Body", "rigid body", "Statics", "statics", "three force body", "Three force body"], "metadata": {"description": "

Classic problem of a vehicle parked on an incline. Best solved by rotating the coordinate system.

Image Credit: https://svgsilh.com/image/34325.html CC-0

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

{geogebra_applet('w4xb6n95',['alpha': radians(alpha), 'fbd': [visible: false] ])}

A car is parked on a {alpha}° slope, with the rear wheels locked by the parking brake. Find the components of the forces acting on each of the front and rear wheels, parallel and perpendicular to the roadbed.

Vehicle Specifications

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Wheelbase	$L = $ {wb} mm
Curb weight	$m = $ {m} kg
Center of Gravity	$d = $ {d} mm $h = $ {h} mm

", "advice": "

{geogebra_applet('w4xb6n95',['alpha': radians(alpha), 'fbd': [definition: 'true', visible: true] ])}

First, draw a free body diagram of the vehicle.

For convenience, let the x- and y- directions be parallel and perpendicular to the roadbed and define $\\alpha$ as the the angle the road makes with the horizontal. Note that $\\alpha$ is also the angle between the weight and the y-direction. Treat the front wheels like a roller, the rear wheels like a rough surface.

$\\alpha = \\var{alpha}°$

Define $L$ as the distance between the front and rear wheels:

$L= \\var{qty(wb,'mm')}$

Note that the curb 'weight' is actually a mass, so let:

$\\begin{align}W &= m g\\\\ &= (\\var{qty(m,'kg')}) \\cdot (\\var{qty(g, 'm/s^2')}) =\\var{show(w)}\\\\ W_x& = W \\sin \\alpha = \\var{show(w_x)}\\\\W_y& = W \\cos \\alpha = \\var{show(w_y)}\\end{align}$

Apply the equations of equilibrium, starting with the sum of the moments about either A or B, since two unknown forces intersect there.

$\\begin{align}\\Sigma M_A &= 0\\\\ B_y (L) &= W_y(d) + W_x (h)\\\\ B_y &= W \\left(\\dfrac{d \\cos \\alpha + h \\sin \\alpha}{L}\\right)\\\\&= \\var{show(B_y)}\\\\\\\\ \\Sigma F_x &= 0\\\\ B_x &= W_x\\\\ B_x &= \\var{show(w_x)}\\\\\\\\ \\Sigma F_y &= 0\\\\A + B_y &= W_y \\\\A &= W_y-B_y\\\\&=\\var{show(A)}\\end{align}$

Since there are two front wheels and two rear wheels, the forces acting on each wheel are half of these values:

$A_{||} = 0 \\text{ N} \\qquad A_\\perp = A/2 = \\var{show(A/2)} \\qquad B_{||} = B_x/2 = \\var{show(B_x/2)} \\qquad B_\\perp = B_y/2 = \\var{show(B_y/2)}$

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curb weight in kg

", "templateType": "anything", "can_override": false}, "W": {"name": "W", "group": "answers", "definition": "m g ", "description": "

weight of vechicle

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wheelbase in mm

", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Ungrouped variables", "definition": "random([10,15,20,25,30])", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "['N','mm']", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "answers", "definition": "false", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["alpha", "m", "wb", "units", "d", "h", "g"], "variable_groups": [{"name": "answers", "variables": ["w_y", "A", "w_x", "B_x", "B_y", "W", "debug"]}], "functions": {"show": {"parameters": [["f", "number"]], "type": "number", "language": "jme", "definition": "siground(qty(f,'N'),4)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"mark": {"script": "//numbasGGBApplet0.setValue('fbd',true)\n//numbasGGBApplet0.setVisible('fbd',true)", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

$A_{||} =$ [[0]] $\\qquad A_\\perp = $ [[3]] $0 B_{\\perp} = \\var{qty(A/2 ,'N')}$

$B_{||} =$ [[1]] $\\qquad B_\\perp = $ [[2]] $B_{||}= \\var{qty(B_x/2,'N')} B_{\\perp} = \\var{qty(B_y/2,'N')}$

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A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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/fbd.png", "/srv/numbas/media/question-resources/fbd.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["equilibrium", "Equilibrium", "equilibrium of a rigid body", "mechanics", "Mechanics", "Statics", "statics"], "metadata": {"description": "

A hand truck on wheels. Easiest to solve by rotating coordinate system.

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

{geogebra_applet('kptuqdfk',[['α',alpha+\"°\"],['d1','\"'+string(d1)+'\"'],['d2','\"'+string(d2)+'\"'],['d3','\"'+string(d3)+'\"']])}

A hand truck is used to move a{random(' nitrogen', 'n oxygen', 'n R-134a', ' compressed air', ' refrigerant')} cylinder. Knowing that the combined weight of the truck and cylinder is {W} acting at the center of gravity $G$, determine the vertical force $A$ which must be applied to the handle to maintain the cylinder at this {alpha}° angle, and also the corresponding reaction at each of the two wheels.

", "advice": "

Start by drawing a free body diagram and gathering the known values:

$W = \\var{W}, \\alpha = \\var{alpha}°, d_1 = \\var{d1}, d_2 = \\var{d2}$ and $d_3 = \\var{d3}$.

It's easiest to solve this problem if you resolve the weight into components parallel and perpendicular to the axis of the cylinder, since the dimensions in these directions are given, so:

$W_{\\perp} = W \\cos \\alpha = \\var{display(W * cos(radians(alpha)))}$ and

$W_{\\|} = W \\sin \\alpha = \\var{display(W * sin(radians(alpha)))}$

To find $A$, apply the sum of the moments about point $B$:

$\\begin{align} \\Sigma M_B &= 0\\\\ A d_3 + W_{\\|} d_1 &= W_{\\perp} d_2 \\\\ A &= \\dfrac{ W_{\\perp} d_2 -W_{\\|} d_1 }{d_3}\\\\ &= \\frac{\\var{display(W_perp)}(\\var{d2}) -\\var{display(W_par)}(\\var{d1}) }{\\var{d3}}\\\\&= \\var{display(A)}\\end{align}$

To find B, the force on one wheel, apply the sum of the forces in the y-direction:

$\\begin{align}\\Sigma F_y &= 0\\\\ A - W + 2 B &= 0\\\\B &= \\frac{W-A}{2} \\\\&=\\frac{\\var{W} - \\var{display(A)}}{2}\\\\& = \\var{display(B)}\\end{align}$

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"W_par": {"name": "W_par", "group": "solution", "definition": "W sin(radians(alpha))", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "(W-A)/2", "description": "", "templateType": "anything", "can_override": false}, "W": {"name": "W", "group": "Ungrouped variables", "definition": "qty(random(180..180#5),'lb')", "description": "", "templateType": "anything", "can_override": false}, "d1": {"name": "d1", "group": "Ungrouped variables", "definition": "qty(random(8..14),'in')", "description": "", "templateType": "anything", "can_override": false}, "d3": {"name": "d3", "group": "Ungrouped variables", "definition": "round(qty(random(36..40) cos(radians(alpha)),'in'),'1 in')\n \n ", "description": "", "templateType": "anything", "can_override": false}, "d2": {"name": "d2", "group": "Ungrouped variables", "definition": "qty(random(20..26#2),'in')", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Ungrouped variables", "definition": "random(40..60 except 45)", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "(-W_par d1 + W_perp d2)/d3", "description": "", "templateType": "anything", "can_override": false}, "W_perp": {"name": "W_perp", "group": "solution", "definition": "W cos(radians(alpha))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["alpha", "W", "d1", "d2", "d3", "A", "B"], "variable_groups": [{"name": "solution", "variables": ["W_perp", "W_par"]}], "functions": {"display": {"parameters": [["q", "quantity"]], "type": "string", "language": "jme", "definition": "string(siground(q,4))"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Handle", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Determine the force on the handle:

$A =$ [[0]]

", "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": "A", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Wheels", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Determine the force acting on each wheel:

$B =$ [[0]]

", "gaps": [{"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": "B", "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": "Equilibrium of a rigid body: triangle", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 12, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/12/edit"}, "name": "Angle quantity 2020", "short_name": "angle", "description": "

Adjusts all angles to 0 < $\\theta$ < 360.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

90° = -270° = 450°

Retuns the scalar part of students answer (which is a quantity) as a number.

", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "

Normalize angle with mod 360

", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "

matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"

", "definition": "studentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]"}, {"name": "interpreted_unit", "description": "

Allows student to use degree symbol or 'deg' for units.

Normalize expected_answer with mod 360

A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["angle from reference", "equilibrium", "Equilibrium", "Mechanics", "mechanics", "rigid body", "Rigid Body", "Statics", "statics"], "metadata": {"description": "

Find the reactions of a rigid body (a triangular plate) at a pin and roller. The load is at an angle.

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

{applet}

The triangular plate is secured by a pin at $A$ and a roller at $C$. Determine the reactions at the pin and the roller when the plate is subjected to a {FB} load as shown by applying the equations of equilibrium.

B = ({abs(B)};{mod(degrees(atan2(B[1],B[0]))+360,360)}) {units[0]}

", "advice": "

Draw a free body diagram.
Apply $\\Sigma M_A$=0 to find the reaction at $C$. There's no x-component at $C$, because the support there is a roller. This should have been indicated on your free body diagram.
Once $C$ and is known, apply $\\sum F_x = 0$ and $\\sum F_y=0$ to find components $A_x$ and $A_y$.
With $A_x$ and $A_y$ known, use the pathagorean theorem to calculate the magnitude of $A$, and use trig to get the its direction.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"debug": {"name": "debug", "group": "Inputs", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "FB": {"name": "FB", "group": "Ungrouped variables", "definition": "qty(magB,units[0])", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "vector(0,cross(B,rb)[2]/L)", "description": "", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Inputs", "definition": "random(alpha+180..360+alpha#5)", "description": "

reference direction. Set by student choice.

", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "-(B+C)", "description": "", "templateType": "anything", "can_override": false}, "L": {"name": "L", "group": "Inputs", "definition": "random(2..6#0.2)", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "magB vector(cos(radians(theta)),sin(radians(theta)),0)", "description": "", "templateType": "anything", "can_override": false}, "dirA": {"name": "dirA", "group": "Ungrouped variables", "definition": "mod(degrees(atan2(A[1],A[0])),360)", "description": "", "templateType": "anything", "can_override": false}, "magB": {"name": "magB", "group": "Inputs", "definition": "random(1..15)random(10,20,50)", "description": "", "templateType": "anything", "can_override": false}, "rb": {"name": "rb", "group": "Ungrouped variables", "definition": "L/2 vector(1,tan(radians(alpha)),0)", "description": "

position vector to point B

", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Inputs", "definition": "65//random(25..65#5)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Inputs", "definition": "random([['kN','m'],['lb','ft'],['N','cm'],['lb','in']])", "description": "", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "Inputs", "definition": "geogebra_applet('n3rkawce',params)", "description": "", "templateType": "anything", "can_override": false}, "params": {"name": "params", "group": "Inputs", "definition": "[text1: '\" '+ string(L) +' ' + units[1] + ' \"', alpha: radians(alpha), theta: radians(theta)]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "theta <> 180 + alpha and theta <> 360 + alpha \nand C[1] > 0", "maxRuns": 100}, "ungrouped_variables": ["B", "rb", "C", "A", "dirA", "FB"], "variable_groups": [{"name": "Inputs", "variables": ["theta", "units", "debug", "alpha", "magB", "L", "applet", "params"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Reaction at C", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Draw and label a neat free body diagram of the triangular plate.
Determine any needed distance or angles.
Use $\\Sigma M_A = 0$ to find the reaction at C.

$C = $ [[0]]

C = {abs(C)} {units[0]}

Use $\\Sigma F_x = 0$ and $\\Sigma F_y=0$ to find the magnitude and direction of the components of the reaction at A.

$A_x = $ [[0]] [[1]]

$A_y = $ [[2]] [[3]]

A= {A} {units[0]}

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Ax", "marks": "8", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "abs(qty(A[0],units[0]))", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "1_n_2", "useCustomName": true, "customName": "dir Ay", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["→ (right)", "← (left)", "Neither"], "matrix": "map(if(sign(A[0])=x,2,0),x,[1,-1,0])"}, {"type": "engineering-answer", "useCustomName": true, "customName": "Ay", "marks": "8", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "abs(qty(A[1],units[0]))", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "1_n_2", "useCustomName": true, "customName": "dir Ay", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["↑ (up)", "↓ (down)", "Neither"], "matrix": "map(if(sign(A[1])=x,2,0),x,[1,-1,0])"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Magnitude and direction of A", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_angle: // a qty string corrected to standard angle\n student_angle[2] + student_angle[1] * student_angle[0] + student_units\n\nmagnitude:\n studentAnswer[3]\n\nstudent_angle:\n [mod(matchnumber(studentAnswer[0],['plain','en'])[1],360), // angle\n [1,-1][indices(studentAnswer[1],[true])[0]], // ccw = 1 cw = -1\n [0,90,180,-90][indices(studentAnswer[2],[true])[0]]] // reference axis\n\nstudent_units:\n studentAnswer[0][len(matchnumber(studentAnswer[0],['plain','en'])[0])..len(studentAnswer[0])]\n\ninterpreted_answers:\n [interpreted_angle, studentAnswer[1], studentAnswer[2], studentAnswer[3]]\n\ngap_feedback (Feedback on each of the gaps):\n map(\n try(\n let(\n result, submit_part(gaps[gap_number][\"path\"],answer),\n gap, gaps[gap_number],\n name, gap[\"name\"], \n noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n assert(name=\"\" or len(gaps)=1,feedback(translate('part.gapfill.feedback header',[\"name\": name])));\n concat_feedback(filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]), if(marks>0,result[\"marks\"]/marks,1), noFeedbackIcon);\n result\n ),\n err,\n fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n ),\n [gap_number,answer,index],\n zip([3,0],[studentAnswer[3], interpreted_angle],[1,2])\n )\n\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Determine the magnitude and direction of the resultant force $\\textbf{A}$ by resolving the components found in part b).

Indicate direction as an angle less than 90° measured from a chosen reference direction. Positive angle = counterclockwise.

Force $\\textbf{A}$ has a magnitude of [[3]]

acting at an angle of [[0]] measured [[1]] from the [[2]].

A= ({abs(A)};{mod(degrees(atan2(A[1],A[0]))+360,360)}) {units[0]}

", "gaps": [{"type": "angle", "useCustomName": true, "customName": "angle", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(dirA,'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.2"}}, {"type": "1_n_2", "useCustomName": true, "customName": "sign", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+x axis", "+y axis", "-x axis", "-y axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "engineering-answer", "useCustomName": true, "customName": "Mag A", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(abs(A),units[0])", "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": "Equilibrium of a rigid body: truss", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 12, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/12/edit"}, "name": "Angle quantity 2020", "short_name": "angle", "description": "

Adjusts all angles to 0 < $\\theta$ < 360.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

90° = -270° = 450°

Retuns the scalar part of students answer (which is a quantity) as a number.

", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "

Normalize angle with mod 360

", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "

matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"

", "definition": "studentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]"}, {"name": "interpreted_unit", "description": "

Allows student to use degree symbol or 'deg' for units.

Normalize expected_answer with mod 360

A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["angle from reference", "Equilibrium", "equilibrium", "Mechanics", "mechanics", "reactions", "Rigid Body", "rigid body", "Statics", "statics"], "metadata": {"description": "

Find the reactions of a rigid body (a truss) at a pin and roller. All loads are either horizontal or vertical.

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

{applet}

The truss shown consists of three sections {b} {units[1]} wide and {h} {units[1]} tall, subjected to the loads shown.

Determine the reactions at the pin and the roller.

D: {siground(D,3)} {units[0]}

A: {siground(magA,3)} {units[0]} at {siground(dirA,4)}° from the x-axis

Ax: {Ax} Ay: {Ay}

", "advice": "

Draw a free body diagram.
Apply $\\Sigma M_A$ = 0 to find the reaction at $D$. There's no x-component at $D$, because the support there is a roller. This should have been indicated on your free body diagram.
Once force $D$ and the loads are known, apply $\\Sigma F_x = 0$ and $\\Sigma F_y=0$ to find components $A_x$ and $A_y$.
With $A_x$ and $A_y$ known, use the pythagorean theorem to calculate the magnitude of force $A$, and use trig to get the its direction.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Ay": {"name": "Ay", "group": "Ungrouped variables", "definition": "Fe + Ff - D", "description": "

x-component of reaction at A. up is positive

", "templateType": "anything", "can_override": false}, "FC": {"name": "FC", "group": "inputs", "definition": "random(0..5)", "description": "", "templateType": "anything", "can_override": false}, "dirA": {"name": "dirA", "group": "Ungrouped variables", "definition": "mod(degrees(atan2(Ay,Ax)),360)", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "vector(Ax,Ay)", "description": "", "templateType": "anything", "can_override": false}, "FB": {"name": "FB", "group": "inputs", "definition": "random(0..5)", "description": "", "templateType": "anything", "can_override": false}, "magA": {"name": "magA", "group": "Ungrouped variables", "definition": "abs(A)", "description": "

magnitude of A

", "templateType": "anything", "can_override": false}, "D": {"name": "D", "group": "Ungrouped variables", "definition": "(Fb * h + Fc * h + Ff * b + Fe * 2 * b)/(3*b)", "description": "

Reaction at D. Up is positive

", "templateType": "anything", "can_override": false}, "FF": {"name": "FF", "group": "inputs", "definition": "random(0..5)", "description": "", "templateType": "anything", "can_override": false}, "Ax": {"name": "Ax", "group": "Ungrouped variables", "definition": "-(Fb+Fc)", "description": "

x- component of reaction at A. positive is to the right

", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "inputs", "definition": "random(2..4#0.4)", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "inputs", "definition": "random(2..4#0.2)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "inputs", "definition": "['kN','m']", "description": "", "templateType": "anything", "can_override": false}, "FE": {"name": "FE", "group": "inputs", "definition": "random(0..5)", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "GGB", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "params": {"name": "params", "group": "GGB", "definition": "[\nb: b, h: h,\nF_F: FF, F_E: FE, F_C: FC, F_B: FB,\nunitsF: '\"{units[0]}\"',\nunitsD: '\"{units[1]}\"',\nR_A: [visible: debug], R_D: [visible: debug]\n]", "description": "", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "GGB", "definition": "geogebra_applet('xqsbgp9c',params)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "len(filter(x>0,x,[Fb,Fc,Fe,Ff]))>1", "maxRuns": 100}, "ungrouped_variables": ["D", "dirA", "Ay", "Ax", "A", "magA"], "variable_groups": [{"name": "inputs", "variables": ["h", "b", "FB", "FC", "FF", "FE", "units"]}, {"name": "GGB", "variables": ["params", "applet", "debug"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Reactions at D", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Use $\\Sigma M_A = 0$ to find the vector components of $\\textbf{D}$.

$\\textbf{D}_x = $ [[0]] [[1]] $\\qquad \\textbf{D}_y = $ [[2]] [[3]]

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Dx Magnitude", "marks": "9", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(0,units[0])", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "1_n_2", "useCustomName": true, "customName": "Dx Direction", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["→ (right)", "← (left)", "Neither"], "matrix": [0, 0, "1"], "distractors": ["", "", ""]}, {"type": "engineering-answer", "useCustomName": true, "customName": "Dy Magnitude", "marks": "9", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "engineering-answer", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "settings": {"correctAnswer": "qty(abs(D),units[0])", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "settings": {"correctAnswer": "qty(abs(D),units[0])", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "1_n_2", "useCustomName": true, "customName": "Dy Direction", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["↑ (up)", "↓ (down)", "Neither"], "matrix": ["if(D>0,1,0)", "if(D<0,1,0)", "If(D=0,1,0)"], "distractors": ["", "", ""]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Reactions at A", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Use $\\Sigma F_x = 0$ and $\\Sigma F_y=0$ to find the vector components of the reaction at $\\textbf{A}$.

$\\textbf{A}_x = $ [[0]] [[1]] $\\qquad \\textbf{A}_y = $ [[2]] [[3]]

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Ax Magnitude", "marks": "9", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(abs(Ax),units[0])", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "1_n_2", "useCustomName": true, "customName": "Ax Direction", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["→ (right)", "← (left)", "Neither"], "matrix": "[if(sign(Ax) >= 0,1,0), if(sign(Ax) <=0,1,0), if(sign(Ax)=0,1,0)]"}, {"type": "engineering-answer", "useCustomName": true, "customName": "Ay Magnitude", "marks": "9", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(precround(abs(Ay),6),units[0])", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "1_n_2", "useCustomName": true, "customName": "Ay Direction", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["↑ (up)", "↓ (down)", "Neither"], "matrix": "[if(sign(Ay) >= 0,1,0), if(sign(Ay) <=0,1,0), if(sign(Ay)=0,1,0)]"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Resultant at A", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_angle: // a qty string corrected to standard angle\n student_angle[2] + student_angle[1] * student_angle[0] + student_units\n\nmagnitude:\n studentAnswer[3]\n\nstudent_angle:\n [mod(matchnumber(studentAnswer[0],['plain','en'])[1],360), // angle\n [1,-1][indices(studentAnswer[1],[true])[0]], // ccw = 1 cw = -1\n [0,90,180,-90][indices(studentAnswer[2],[true])[0]]] // reference axis\n\nstudent_units:\n studentAnswer[0][len(matchnumber(studentAnswer[0],['plain','en'])[0])..len(studentAnswer[0])]\n\ninterpreted_answers:\n [interpreted_angle, studentAnswer[1], studentAnswer[2], studentAnswer[3]]\n\ngap_feedback (Feedback on each of the gaps):\n map(\n try(\n let(\n result, submit_part(gaps[gap_number][\"path\"],answer),\n gap, gaps[gap_number],\n name, gap[\"name\"], \n noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n assert(name=\"\" or len(gaps)=1,feedback(translate('part.gapfill.feedback header',[\"name\": name])));\n concat_feedback(filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]), if(marks>0,result[\"marks\"]/marks,1), noFeedbackIcon);\n result\n ),\n err,\n fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n ),\n [gap_number,answer,index],\n zip([3,0],[studentAnswer[3], interpreted_angle],[1,2])\n )\n\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Determine the magnitude and direction of the resultant force $\\textbf{A}$ by resolving $\\textbf{A}_x$ and $\\textbf{A}_y$.

Force $\\textbf{A}$ has a magnitude of [[3]],

acting at an angle of [[0]] measured [[1]] from the [[2]].

", "gaps": [{"type": "angle", "useCustomName": true, "customName": "angle", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(siground(dirA,5),'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.2"}}, {"type": "1_n_2", "useCustomName": true, "customName": "sign", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+x axis", "+y axis", "-x axis", "-y axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "engineering-answer", "useCustomName": true, "customName": "magA", "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(magA,5),units[0])", "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": "Three-force Body Method", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["Triangle", " Beam with angled load"], "variable_overrides": [[], []], "questions": [{"name": "Three-force body method: triangle", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 24, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/24/edit"}, "name": "Angle quantity", "short_name": "angle-quantity-from-reference", "description": "

Angle as a quantity in degrees.

", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['correct_quantity'])", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\ncorrect_scalar:\nscalar(correct_quantity)\n \n\ncorrect_quantity:\nsettings['correct_quantity']\n\ncorrect_units:\nunits(correct_quantity)\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:\njoin(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n\n\ngood_units:\ntry(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)\n\nstudent_quantity:\nswitch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)\n\nangle_in_range:\nif(settings['restrict_angle'], abs(student_scalar) <= 90, true)\n\nright:\nwithinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])\n\nclose:\nwithinTolerance(student_scalar, correct_scalar, settings['close'])", "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( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)"}, {"name": "correct_scalar", "description": "", "definition": "scalar(correct_quantity)\n "}, {"name": "correct_quantity", "description": "", "definition": "settings['correct_quantity']"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"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": "", "definition": "join(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n"}, {"name": "good_units", "description": "", "definition": "try(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)"}, {"name": "student_quantity", "description": "", "definition": "switch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity)"}, {"name": "angle_in_range", "description": "", "definition": "if(settings['restrict_angle'], abs(student_scalar) <= 90, true)"}, {"name": "right", "description": "

Will check for correct sign elswhere.

", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "

Must have correct sign to be close.

", "definition": "withinTolerance(student_scalar, correct_scalar, settings['close'])\n"}], "settings": [{"name": "correct_quantity", "label": "Correct Angle as quantity ", "help_url": "", "hint": "", "input_type": "code", "default_value": "qty(45,'deg')", "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 amount from the correct value.", "input_type": "code", "default_value": "0.1", "evaluate": true}, {"name": "restrict_angle", "label": "Less than 90\u00b0", "help_url": "", "hint": "When checked, angle must be between -90° and +90°.", "input_type": "checkbox", "default_value": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.", "input_type": "percent", "default_value": "75"}, {"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 amount from the correct value.", "input_type": "code", "default_value": "0.5", "evaluate": true}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value without units.", "input_type": "percent", "default_value": "25"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"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.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

Only marked close if the student actually has the right sign.

Find the reactions of a rigid body (a triangular plate) at a pin and roller, using the three-force body principle.

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

The triangular plate is secured by a pin at $A$ and a roller at $C$ and is subjected to a {FB} load acting at point $B$ as shown.

Determine the reactions at the pin and the roller using the three-force body principle.

{geogebra_applet('whu5xquv',[ 'FB': scalar(FB), 'L': scalar(L), 'θ': radians(theta), 'α': radians(alpha1), 'units': '\"'+units[1]+'\"', 'show': 'false', 'debug': 'false' ])}

", "advice": "

Draw a free body diagram.
Apply $\\Sigma M_A=0$ to find the reaction at $C$. There's no $x$-component at $C$, because the support there is a roller. This should have been indicated on your free body diagram.
Once $C$ and is known, apply $F_x = 0$ and $F_y=0$ to find components $A_x$ and $A_y$.
With $A_x$ and $A_y$ known, use the pathagorean theorem to calculate the magnitude of $A$, and use trig to get the its direction.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"theta": {"name": "theta", "group": "Inputs", "definition": "random(300..380#5)", "description": "

reference direction. Set by student choice.

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this is the y-coordinate of the intersection point

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A three-force body is an object acted upon by exactly three forces. When a three-force body is in equilibrium the lines of action of the three forces must either intersect at a common point or be parallel to each other. We can use this idea to find the reaction forces for three-force bodies.

In this problem the lines of action of force $\\mathbf{B}$ and force $\\mathbf{C}$ are known and their intersection point $X$ may be determined.

Use the given geometric information to determine distance $h$.

$h$ = [[0]]

h = {h}

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With h known, the direction of force $\\mathbf{A}$ can be found since its line of action must pass through $X$.

Use the given geometric information and determine $\\angle CAX $, which we will call $\\theta_A$

$\\theta_A=$ [[0]]

$\\theta_a$ = {theta_a}

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The object is in equilibrium so when the three forces are added tip-to-tail they form a closed triangle as shown below.

Determine the three angles in the force triangle.

{geogebra_applet('sckn26vg',[ ['FB',scalar(FB)] , ['L',scalar(L)], ['θ',radians(theta)], ['α',radians(alpha1)],['units','\"'+units[1]+'\"' ]])}

$\\alpha$ = [[0]] $\\beta$ = [[1]] $\\gamma$ = [[2]]

$\\alpha$ = {alpha} $\\beta$ = {beta} $\\gamma$ = {gamma}

A = {FA} B = {FB} C = {FC}

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Use the law of sines to determine the magnitudes of forces $\\mathbf{A}$ and $\\mathbf{C}$.

$A$ = [[0]]

$C$ = [[1]]

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A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

Only marked close if the student actually has the right sign.

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{geogebra_applet(\"xfpyfgd9\",[['split', split], ['θ',theta+'°']])}

A beam is loaded with a {F} force at a {theta}° angle from the horizontal, as shown. Distance $\\overline{AB}$ is {AB}, and $\\overline{BC}$ is {BC}.

Use the three-force body method to determine the magnitudes of the reactions at pin $A$ and roller $C$.

", "advice": "

Given:

$F$ = {F}
$\\theta$ = {theta}°
$\\overline{AB}$ = {AB}
$\\overline{BC}$ = {BC}
Force $\\mathbf{C}$ acts straight up, due to the roller.

Required:

magnitudes of $\\mathbf{A}$ and $\\mathbf{C}$.

Procedure:

Start by drawing a clear diagram representing the situation and locate point \"$x$\" where the lines of action of $\\mathbf{F}$ and $\\mathbf{C}$ intersect. In three-force-bodies, the line of action of $\\mathbf{A}$ must pass through that point too.
Draw the line of action of $\\mathbf{A}$ and define $\\alpha$.\n
\n
Find $h$, using: \\[\\tan\\theta = \\frac{h}{\\overline{BC}}\\]
Find $\\alpha$: \\[\\tan\\alpha =\\frac{h}{(\\overline{AB} + \\overline{BC})}\\]
Rearrange the forces into a force triangle, tip-to-tail, and label it.\n
\n
\n
Use the law of sines to solve for the unknown magnitudes. \\[ \\frac{F}{\\sin (90 + \\alpha)} = \\frac{A}{\\sin (90° - \\theta)} = \\frac{C}{\\sin (\\theta-\\alpha)}\\]
\n

length of beam

", "templateType": "anything", "can_override": false}, "split": {"name": "split", "group": "inputs", "definition": "random(0.2..0.8#0.5)", "description": "

percentage position of point B

", "templateType": "anything", "can_override": false}, "AB": {"name": "AB", "group": "Ungrouped variables", "definition": "split l", "description": "

segment AB

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$A$ = [[0]] $\\qquad C$ = [[1]]

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Angle as a quantity in degrees.

Will check for correct sign elswhere.

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Must have correct sign to be close.

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Adjusts all angles to 0 < $\\theta$ < 360.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

90° = -270° = 450°

Retuns the scalar part of students answer (which is a quantity) as a number.

", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "

Normalize angle with mod 360

", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "

matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"

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Allows student to use degree symbol or 'deg' for units.

Normalize expected_answer with mod 360

A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

Only marked close if the student actually has the right sign.

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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.
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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/fbd.png", "/srv/numbas/media/question-resources/fbd.png"], ["question-resources/diagram_1.png", "/srv/numbas/media/question-resources/diagram_1.png"], ["question-resources/diagram_2.png", "/srv/numbas/media/question-resources/diagram_2.png"]]}