// Numbas version: exam_results_page_options {"name": "Maria's copy of Vector addition by summing scalar components", "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.

Three forces act on the bracket at point A:   A = {FA} {units[1]}, B = {FB} {units[1]} and, = {FC} {units[1]}.

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Find the magnitude and direction of the resultant force R by summing scalar components.

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Enter your magnitude quatities and SI units, eg. 500 N

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{geogebra_applet('dtf3t2dp', [['A',A],['B',B],['C',C],['F_a',FA],['F_b',FB],['F_c',FC],['α', alpha],['unit','\"'+units[0]+'\"']])}

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Force A: {fa} at {alpha} = {forceA}

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Force B: {fb} at {beta} = {forceB}

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Force C: {fc} at {gamma} = {forceC}

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Resultant: {R} at {rho}  = {forceR}

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$R_x = \\Sigma F_x = (\\var{siground(ForceA[0],4)}) + (\\var{siground(ForceB[0],4)}) +( \\var{siground(ForceC[0],4)}) = \\var{siground(ForceR[0],4)}$ {units[1]}

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$R_y = \\Sigma F_y = (\\var{siground(ForceA[1],4)}) + (\\var{siground(ForceB[1],4)}) +( \\var{siground(ForceC[1],4)}) = \\var{siground(ForceR[1],4)}$ {units[1]}

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$R=\\sqrt{R_x^2 + R_y^2} = \\sqrt{(\\var{siground(ForceR[0],4)})^2 +(\\var{siground(ForceR[0],4)})^2} = \\var{siground(abs(ForceR),4)}$ {units[1]}

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$\\theta = \\tan^{-1}\\left(\\left|\\frac{R_y}{R_x}\\right| \\right) = \\tan^{-1}\\left(\\left|\\frac{\\var{siground(ForceR[1],4)}}{\\var{siground(ForceR[0],4)}}\\right| \\right) = \\var{siground(degrees(arctan(abs(forceR[1])/forceR[0])),4)}° = (\\var{siground(rho,4)}°$ from the positive x-axis.)

", "extensions": ["geogebra", "quantities", "weh"], "parts": [{"variableReplacementStrategy": "originalfirst", "customName": "", "unitTests": [], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 0, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "prompt": "

Find the scalar components of the component forces A, B, and C

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$A_x =$ [[0]]  $B_x =$ [[2]]  $C_x =$ [[4]]

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$A_y =$ [[1]]  $B_y =$ [[3]]  $C_y =$ [[5]]

Sum the scalar components to get the scalar components of the resultant R.

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$R_x = \\Sigma F_x = A_x + B_x + C_x =$ [[0]]

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$R_y = \\Sigma F_y = A_y + B_y + C_y =$ [[1]]

", "showCorrectAnswer": true, "sortAnswers": false, "type": "gapfill", "useCustomName": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "settings": {"C1": "75", "C2": "50", "correctAnswer": "qty(ForceR[0],units[1])", "C3": "25", "right": "0.2", "close": "1.0"}, "customName": "", "unitTests": [], "showFeedbackIcon": true, "marks": "4", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "type": "engineering-answer", "useCustomName": false, "customMarkingAlgorithm": "", "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "settings": {"C1": "75", "C2": "50", "correctAnswer": "qty(ForceR[1],units[1])", "C3": "25", "right": "0.2", "close": "1.0"}, "customName": "", "unitTests": [], "showFeedbackIcon": true, "marks": "4", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "type": "engineering-answer", "useCustomName": false, "customMarkingAlgorithm": "", "scripts": {}}], "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "customName": "", "unitTests": [], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 0, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "prompt": "

Resolve $R_x$ and $R_y$ to find the magnitude and direction of R.

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$R = \\sqrt{{R_x}^2 +{R_y}^2}$ = [[0]]

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$\\theta = \\tan^{-1}\\left(\\left|\\dfrac{R_y}{R_x}\\right| \\right)$ = [[2]]  measured from the  [[1]]

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{angle_from_ref}

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

"}, "variablesTest": {"condition": "B[0]<>C[0] and B[1]<>C[1] and abs(alpha-beta) >= 15 and abs(gamma-beta) >= 15 and abs(gamma-alpha) >= 15", "maxRuns": 100}, "name": "Maria's copy of Vector addition by summing scalar components", "variables": {"ForceR": {"templateType": "anything", "definition": "ForceA+ForceB+ForceC", "group": "Outputs", "name": "ForceR", "description": "

Resultant as a vector

"}, "units": {"templateType": "anything", "definition": "random(['cm','N'],['cm','N'],['cm','N'])", "group": "Inputs", "name": "units", "description": ""}, "FB": {"templateType": "anything", "definition": "random(10..100#10)", "group": "Inputs", "name": "FB", "description": "

Magnitude of Force B

"}, "beta": {"templateType": "anything", "definition": "degrees(direction(vector(B[0]-A[0],B[1]-A[1])))", "group": "Outputs", "name": "beta", "description": "

Direction of force B

"}, "FC": {"templateType": "anything", "definition": "random(10..100#5)", "group": "Inputs", "name": "FC", "description": "

Magnitude of force C

"}, "A": {"templateType": "anything", "definition": "vector(0,0)", "group": "Inputs", "name": "A", "description": "

Position of point A

"}, "angle_from_ref": {"templateType": "anything", "definition": "let(ang,rho,\n[if(ang>180,ang-360,ang),\nif(ang>270,ang-450,if(ang < -90,ang+270,ang-90)),\nif(ang>0,ang-180,ang+180),\nif(ang>90,ang-270,90+ang)])", "group": "Outputs", "name": "angle_from_ref", "description": ""}, "rho": {"templateType": "anything", "definition": "degrees(direction(ForceR))", "group": "Outputs", "name": "rho", "description": "

direction of resultant

"}, "FA": {"templateType": "anything", "definition": "random(10..100#5)", "group": "Inputs", "name": "FA", "description": "

Magnitude of force A

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

Force C as a vector

"}, "alpha": {"templateType": "anything", "definition": "(random(-80..175#5 except[45,135,-45,80,100]))", "group": "Inputs", "name": "alpha", "description": "

direction of force A

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

Force B as a vector

"}, "C": {"templateType": "anything", "definition": "vector(random(1,-1)random(2..6),random(1,-1)random(2..6))", "group": "Inputs", "name": "C", "description": "

Position of point C

"}, "B": {"templateType": "anything", "definition": "vector( random(1,-1) random(4..10),random(1,-1) random(2..5))", "group": "Inputs", "name": "B", "description": "

Position of point B

"}, "debug": {"templateType": "anything", "definition": "false", "group": "Inputs", "name": "debug", "description": ""}, "gamma": {"templateType": "anything", "definition": "degrees(direction(vector(C[0]-A[0],C[1]-A[1])))", "group": "Outputs", "name": "gamma", "description": "

Direction of force C in degrees

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

force A as a vector

"}, "R": {"templateType": "anything", "definition": "sqrt(ForceR[0]^2+forceR[1]^2)", "group": "Outputs", "name": "R", "description": "

Magnitude of resultant

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