// Numbas version: exam_results_page_options {"name": "Vector addition of three forces", "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.

Magnitude:  $R =$ [[0]]  Direction: $\\theta =$  [[2]] measured from the [[1]].

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Determine the resultant of three random 2-D vectors.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "preamble": {"css": "", "js": ""}, "ungrouped_variables": [], "variable_groups": [{"name": "Inputs", "variables": ["O", "A", "B", "C", "MA", "MB", "MC", "units"]}, {"name": "Forces", "variables": ["F_A", "F_B", "F_C", "R", "theta", "angle_from_ref", "angle"]}], "advice": "

\n
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1. Find the scalar components of the three forces.
2. \n
3. Add the scalar components of the components to find the scalar components of the resultant.
\\begin{align}R_x &= \\Sigma F_x & R_y &= \\Sigma F_y \\\\R_x &= A_x + B_x + C_x & R_y &= A_y + B_y + C_y \\\\R_x &= (\\var{fmt(F_A[0])}) +(\\var{fmt(F_B[0])}) + (\\var{fmt(F_C[0]) }) & R_y &=( \\var{fmt(F_A[1])}) + (\\var{fmt(F_B[1])} )+(\\var{fmt(F_C[1])})\\\\R_x &= \\var{qty(fmt(R[0]),units)} & R_y &=\\var{qty(fmt(R[1]),units)}\\end{align}
4. \n
5. Draw a triangle representing $\\vec{R}= \\vec{R_x} + \\vec{R_y}$,
6. \n
7. Use the pythagorean theorem and inverse tangent to find the magnitude and direction of $\\textbf{R}.$
\\begin{align}R &= \\sqrt{R_x^2 + R_y^2} = \\var{qty(fmt(abs(R)),units)}& \\theta&=\\arctan{\\left(\\left|\\dfrac{R_y}{R_x}\\right|\\right)} = \\var{fmt(angle)}°\\end{align}
8. \n
", "variables": {"angle_from_ref": {"definition": "let(ang,theta,\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)])\n\n", "group": "Forces", "description": "", "name": "angle_from_ref", "templateType": "anything"}, "C": {"definition": "random([vector(random([4,-4]),random(-4..4)),vector(random(-4..4),random([4,-4]))])", "group": "Inputs", "description": "", "name": "C", "templateType": "anything"}, "angle": {"definition": "degrees(arctan(abs(R[1]/R[0])))", "group": "Forces", "description": "", "name": "angle", "templateType": "anything"}, "B": {"definition": "random([vector(random([4,-4]),random(-4..4)),vector(random(-4..4),random([4,-4]))])", "group": "Inputs", "description": "", "name": "B", "templateType": "anything"}, "F_B": {"definition": "MB B/abs(B)", "group": "Forces", "description": "", "name": "F_B", "templateType": "anything"}, "F_C": {"definition": "MC C/abs(C)\n", "group": "Forces", "description": "", "name": "F_C", "templateType": "anything"}, "MA": {"definition": "random(10..50)\n", "group": "Inputs", "description": "", "name": "MA", "templateType": "anything"}, "R": {"definition": "(F_A+F_B+F_C)", "group": "Forces", "description": "", "name": "R", "templateType": "anything"}, "MC": {"definition": "random(10..50)", "group": "Inputs", "description": "", "name": "MC", "templateType": "anything"}, "units": {"definition": "random(['lb','N','kN'])", "group": "Inputs", "description": "", "name": "units", "templateType": "anything"}, "O": {"definition": "vector(0,0)", "group": "Inputs", "description": "", "name": "O", "templateType": "anything"}, "A": {"definition": "random([vector(random([4,-4]),random(-4..4)),vector(random(-4..4),random([4,-4]))])", "group": "Inputs", "description": "", "name": "A", "templateType": "anything"}, "theta": {"definition": "degrees(atan2(R[1],R[0]))", "group": "Forces", "description": "", "name": "theta", "templateType": "anything"}, "F_A": {"definition": "MA A /abs(A)", "group": "Forces", "description": "", "name": "F_A", "templateType": "anything"}, "MB": {"definition": "random(10..50)", "group": "Inputs", "description": "", "name": "MB", "templateType": "anything"}}, "rulesets": {}, "statement": "

{geogebra_applet('cmq7dk74',[['A',A], ['B',B], ['C',C], ['O',O], ['MA',MA], ['MB',MB], ['MC',MC]])}

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Determine the resultant of the three forces shown.

", "name": "Vector addition of three forces", "tags": ["mechanics", "Mechanics", "statics", "Statics", "Vector addition"], "extensions": ["geogebra", "quantities", "weh"], "functions": {"fmt": {"language": "jme", "type": "number", "parameters": [["v", "number"]], "definition": "siground(v,3)"}}, "variablesTest": {"condition": "A <> B and B <> C and C <> A and\nMA < 10 abs(A) and\nMB < 10 abs(B) and\nMC < 10 abs(C)", "maxRuns": 100}, "type": "question", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}