// Numbas version: exam_results_page_options {"name": "Maria's copy of Vector Tip-Toe Method Addtion", "extensions": ["geogebra", "weh", "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 value, 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(\ncompatible(quantity(1, student_units),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 value, 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(\ncompatible(quantity(1, student_units),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.

", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "

Modify the unit portion of the student's answer by

\n

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

\n

2. replacing '-' with ' ' 

\n

3. replacing '°' with ' deg' 

\n

to allow answers like 10 ft-lb and 30°

", "definition": "replace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "

This fixes the student answer for two common errors.  

\n

If student_units are wrong  - replace with correct units

\n

If student_scalar has the wrong sign - replace with right sign

\n

If student makes both errors, only one gets fixed.

", "definition": "switch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "

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

", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.  if correct answer is 100 N and close is ±1%,
99  N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.
If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.
This value would be close if the expected units were provided.  If the correct answer is 100 N, and close is ±1%,
99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "advice": "

Vector Addition:  

\n

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

", "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}°.

\n

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

\n

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

\n

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

\n

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

\n

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
\n

{geogebra_applet('jwussezq ', [['f_a', forceA],['f_b', forceB],['f_c', forceC]])}

\n

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

\n

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

\n

"}], "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/"}]}