// Numbas version: exam_results_page_options {"name": "Maria's copy of Vector Tip-Toe Method Addtion", "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.

Does clumsy substitution to

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1. replace '-' with ' '

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2. replace '°' with ' deg'

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to allow answers like 10 ft-lb and 30°

", "name": "student_units"}, {"definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n", "description": "", "name": "good_units"}, {"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", "description": "

This fixes the student answer for two common errors.

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If student_units are wrong  - replace with correct units

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If student_scalar has the wrong sign - replace with right sign

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If student makes both errors, only one gets fixed.

", "name": "student_quantity"}, {"definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n ", "description": "", "name": "percent_error"}, {"definition": "percent_error <= settings['right']\n", "description": "", "name": "right"}, {"definition": "right_sign and percent_error <= settings['close']", "description": "

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

", "name": "close"}, {"definition": "sign(student_scalar) = sign(correct_quantity) ", "description": "", "name": "right_sign"}], "settings": [{"input_type": "code", "evaluate": true, "hint": "The correct answer given as a JME quantity.", "default_value": "", "label": "Correct Quantity.", "help_url": "", "name": "correctAnswer"}, {"input_type": "code", "evaluate": true, "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "default_value": "0.2", "label": "% Accuracy for right.", "help_url": "", "name": "right"}, {"input_type": "code", "evaluate": true, "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "default_value": "1.0", "label": "% Accuracy for close.", "help_url": "", "name": "close"}, {"input_type": "percent", "hint": "Partial Credit for close value with appropriate units.  if correct answer is 100 N and close is ±1%,
99  N is accepted.", "default_value": "75", "label": "Close with units.", "help_url": "", "name": "C1"}, {"input_type": "percent", "hint": "Partial credit for forgetting units or using wrong sign.
If the correct answer is 100 N, both 100 and -100 N are accepted.", "default_value": "50", "label": "No units or wrong sign", "help_url": "", "name": "C2"}, {"input_type": "percent", "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.", "default_value": "25", "label": "Close, no units.", "help_url": "", "name": "C3"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"source": {"pk": 23, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/23/edit"}, "name": "Drop-down axis reference", "short_name": "drop-down-axis-reference", "description": "

Choose a reference axis. Returns an integer index between 0 and 3.  0 =+x axis 1 = +y axis 2 = -x axis 3 = -y axis

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To work with angle quantity part type, include a list variable angle_from_ref, and use the axis choice as index. Replace theta with name of angle.

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let(ang,theta,
[if(ang>180,ang-360,ang),
if(ang>270,ang-450,if(ang < -90,ang+270,ang-90)),
if(ang>0,ang-180,ang+180),
if(ang>90,ang-270,90+ang)])

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and this (modified as necessary) in the mark student answer (after) script:

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angles = Numbas.jme.unwrapValue(Numbas.exam.currentQuestion.scope.getVariable('angle_from_ref'));
ans = Qty(angles[index]+' deg');
this.parentPart.gaps[1].settings.correct_quantity.value=ans;
this.markingComment(\"For your axis, the direction is \" + ans.toString() +'.');

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", "help_url": "", "input_widget": "dropdown", "input_options": {"correctAnswer": "0", "hint": {"value": "", "static": true}, "choices": {"value": ["Positive x-axis", "Positive y-axis", "Negative x-axis", "Negative y-axis"], "static": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\ncorrect('You chose the ' \n+ ['positive x',\n 'positive y',\n 'negative x',\n 'negative y'][interpreted_answer] +'-axis.')\n \n \n \n\ninterpreted_answer:\nstudentAnswer", "marking_notes": [{"definition": "correct('You chose the ' \n+ ['positive x',\n 'positive y',\n 'negative x',\n 'negative y'][interpreted_answer] +'-axis.')\n \n \n ", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "name": "mark"}, {"definition": "studentAnswer", "description": "A value representing the student's answer to this part.", "name": "interpreted_answer"}], "settings": [{"label": "dummy", "input_type": "string", "name": "dummy", "hint": "", "subvars": false, "help_url": "", "default_value": "'ignore'"}], "public_availability": "restricted", "published": false, "extensions": []}, {"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.

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$\\Sigma F_x = R_x \\qquad R=\\sqrt{R_x^2 + R_y^2}\\\\\\\\ \\Sigma F_y = R_y \\qquad \\theta = \\tan^{-1}\\left(\\left|\\frac{R_y}{R_x}\\right| \\right)$

", "name": "Maria's copy of Vector Tip-Toe Method Addtion", "variablesTest": {"maxRuns": 100, "condition": "abs(alpha-beta) >= 15 and abs(beta-gamma) >= 15 and abs(gamma-alpha) >= 15 and r <=100 and r > 10"}, "extensions": ["geogebra", "quantities", "weh"], "statement": "

Three forces act on  point A:   A = {FA} {units[1]} at {alpha}°, B = {FB} {units[1]} at {beta}°  and, = {FC} {units[1]} at {gamma}°.

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Estimate the magnitude and direction of the resultant force R using the tip-to-tail method.

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Force A: {fa} {units[1]} at {alpha} = {forceA}

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Force B: {fb} {units[1]} at {beta} = {forceB}

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Force C: {fc}{units[1]} at {gamma} = {forceC}

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Resultant: {R}{units[1]}  at {rho}  = {forceR}

", "functions": {"direction": {"definition": "return Math.atan2(v[1],v[0])", "language": "javascript", "parameters": [["v", "vector"]], "type": "number"}}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

"}, "variable_groups": [{"name": "Inputs", "variables": ["alpha", "gamma", "beta", "FA", "FB", "FC", "units", "debug"]}, {"name": "Outputs", "variables": ["ForceA", "ForceB", "ForceC", "ForceR", "rho", "R", "angle_from_ref", "ref"]}], "preamble": {"js": "", "css": ".red{color:red;}\n.blue{color:blue;}\n.green{color:green;}"}, "ungrouped_variables": [], "tags": [], "variables": {"beta": {"definition": "(random(-180..180#15))", "name": "beta", "templateType": "anything", "group": "Inputs", "description": "

Direction of force B

"}, "FB": {"definition": "random(20..80#5)", "name": "FB", "templateType": "anything", "group": "Inputs", "description": "

Magnitude of Force B

"}, "alpha": {"definition": "(random(-180..180#15))\n", "name": "alpha", "templateType": "anything", "group": "Inputs", "description": "

direction of force A

"}, "ForceA": {"definition": "FA *( vector(cos(radians(alpha)),sin(radians(alpha))))", "name": "ForceA", "templateType": "anything", "group": "Outputs", "description": "

force A as a vector

"}, "gamma": {"definition": "(random(-180..180#15))", "name": "gamma", "templateType": "anything", "group": "Inputs", "description": "

Direction of force C in degrees

"}, "rho": {"definition": "degrees(direction(ForceR))", "name": "rho", "templateType": "anything", "group": "Outputs", "description": "

direction of resultant

"}, "ForceC": {"definition": "FC *( vector(cos(radians(gamma)),sin(radians(gamma))))", "name": "ForceC", "templateType": "anything", "group": "Outputs", "description": "

Force C as a vector

"}, "ref": {"definition": "0", "name": "ref", "templateType": "anything", "group": "Outputs", "description": ""}, "units": {"definition": "random(['ft','lb'],['in','lb'],['cm','N'])", "name": "units", "templateType": "anything", "group": "Inputs", "description": ""}, "FA": {"definition": "random(20..80#5)", "name": "FA", "templateType": "anything", "group": "Inputs", "description": "

Magnitude of force A

"}, "debug": {"definition": "false", "name": "debug", "templateType": "anything", "group": "Inputs", "description": ""}, "angle_from_ref": {"definition": "[if(rho>180,rho-360,rho),\nif(rho>270,rho-450,rho-90),\nrho-180,\nif(rho>90,rho-270,90+rho)]\n\n", "name": "angle_from_ref", "templateType": "anything", "group": "Outputs", "description": ""}, "ForceR": {"definition": "ForceA+ForceB+ForceC", "name": "ForceR", "templateType": "anything", "group": "Outputs", "description": "

Resultant as a vector

"}, "ForceB": {"definition": "FB *( vector(cos(radians(beta)),sin(radians(beta))))", "name": "ForceB", "templateType": "anything", "group": "Outputs", "description": "

Force B as a vector

"}, "R": {"definition": "abs(ForceR)", "name": "R", "templateType": "anything", "group": "Outputs", "description": "

Magnitude of resultant

"}, "FC": {"definition": "random(20..80#5)", "name": "FC", "templateType": "anything", "group": "Inputs", "description": "

Magnitude of force C

"}}, "parts": [{"showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "extendBaseMarkingAlgorithm": true, "sortAnswers": false, "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"settings": {"C2": "50", "right": "2", "correctAnswer": "qty(R,units[1])", "C3": "25", "C1": "75", "close": "4"}, "showFeedbackIcon": true, "showCorrectAnswer": true, "scripts": {}, "type": "engineering-answer", "variableReplacementStrategy": "originalfirst", "marks": "4", "extendBaseMarkingAlgorithm": true, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacements": []}, {"settings": {"dummy": "'ignore'"}, "showFeedbackIcon": true, "showCorrectAnswer": true, "scripts": {"mark": {"order": "after", "script": "index = Numbas.jme.unwrapValue(this.studentAnswerAsJME());\nangles = Numbas.jme.unwrapValue(Numbas.exam.currentQuestion.scope.getVariable('angle_from_ref'));\nans = angles[index]+' deg';\nthis.parentPart.gaps[2].settings.correct_quantity.value=Qty(ans);\nthis.markingComment(\"For your axis, the direction is \" + ans +'.');"}}, "type": "drop-down-axis-reference", "variableReplacementStrategy": "originalfirst", "marks": "0", "extendBaseMarkingAlgorithm": true, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacements": []}, {"settings": {"C2": "50", "restrict_angle": false, "right": "2", "C1": "75", "C3": "25", "correct_quantity": "qty(angle_from_ref[ref],'deg')", "close": "4"}, "showFeedbackIcon": true, "showCorrectAnswer": true, "scripts": {}, "type": "angle-quantity-from-reference", "variableReplacementStrategy": "alwaysreplace", "marks": "4", "extendBaseMarkingAlgorithm": true, "unitTests": [], "customMarkingAlgorithm": "", "variableReplacements": [{"must_go_first": false, "variable": "ref", "part": "p0g1"}]}], "marks": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "prompt": "
\n
1. Move the tips of forces A, B, and C in this diagram to the correct magnitudes and directions. When this has been done correctly the dotted vector will become solid.
2. \n
3. Pick up vectors A, B and C  by their tails, and move them into a tip to tail arrangement. When this has been correctly done the resultant R will appear.
4. \n
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{geogebra_applet('jwussezq ', [['f_a', forceA],['f_b', forceB],['f_c', forceC]])}

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Based on this diagram, estimate the magnitude R  and direction of the resultant.

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R = [[0]] @ [[2]] measured from the [[1]].

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"}], "type": "question", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Johnny Yi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2810/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Johnny Yi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2810/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}