// Numbas version: exam_results_page_options {"name": "Vector addition: parallelogram rule", "extensions": ["geogebra", "weh", "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.

\n

Accepts '°' and 'deg' as units.

\n

Penalizes if not close enough or no units.

\n

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.

", "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": [{"advice": "

Procedure:

\n
    \n
  1. Draw a neat diagram and label the unknown side and angles.
  2. \n
  3. Determine the angle opposite the unknown force $\\textbf{R}$.
  4. \n
  5. Use law of cosines to determine the magnitude $|\\textbf{R}|$
  6. \n
  7. Use either the law of sines or cosines to determine the other two angles.
  8. \n
  9. Use the angles you have found to determine the direction of force $\\textbf{R}$ from the x-axis.
  10. \n
", "variable_groups": [{"variables": ["FB", "dirB", "Ax", "Ay", "units"], "name": "Inputs"}, {"variables": ["dirA", "A", "B", "R"], "name": "Results"}], "ungrouped_variables": ["thetaA", "thetaB", "thetaR"], "functions": {"loc": {"language": "jme", "parameters": [["A", "vector"], ["B", "vector"], ["C", "vector"]], "definition": "degrees(arccos((abs(A)^2-abs(B)^2-abs(C)^2)/(-2 * abs(B) * abs(C))))", "type": "number"}, "direction": {"language": "javascript", "parameters": [["v", "vector"]], "definition": "return Math.atan2(v[1],v[0])\n", "type": "number"}}, "extensions": ["geogebra", "quantities", "weh"], "variablesTest": {"condition": "abs(dirA- dirB) > 25 and abs(dirA-dirB) < 160 ", "maxRuns": "200"}, "type": "question", "statement": "

Vector Addition: $\\textbf{R}$ = $\\textbf{A}$ + $\\textbf{B}$

\n

Find the magnitude and direction of resultant $\\textbf{R}$ when $A$ = {2 FB} {units} and $B$ = {FB} {units},

\n

a) graphically, using the parallelogram rule and a scaled diagram, and

\n

b) exactly, by using the parallelogram rule and trigonometry.

\n

{geogebra_applet('udgn8s84',[['A_x',Ax],['A_y',Ay],['θ_B',radians(dirB)]])}

", "preamble": {"js": "Numbas.extensions.weh.scope.ggbApplet.then((diagram) => doThings(diagram));\n\nvar doThings = function(applet){\n applet.setVisible('show',false);\n};\n\n\n\n", "css": ""}, "tags": ["mechanics, statics, parallelogram rule, vector addition"], "parts": [{"customMarkingAlgorithm": "\n ", "sortAnswers": false, "scripts": {}, "prompt": "

Graphical Solution

\n
    \n
  1. Use a ruler and protractor, a CAD program, or Geogebra, to carefully draw a neat, labeled, accurately scaled diagram representing the vector addition
    $\\textbf{R}$ = $\\textbf{A}+\\textbf{B}$ using the parallelogram rule.
  2. \n
  3. Based on your scaled diagram,  estimate the magnitude of resultant and its direction of measured from positive x- axis:
  4. \n
\n

$|\\textbf{R}|$ = [[0]]

\n

$\\theta_x$  =  [[1]]

", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true, "marks": 0, "unitTests": [], "gaps": [{"showFeedbackIcon": true, "variableReplacements": [], "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "settings": {"right": "1.0", "C2": "50", "close": "2.0", "C1": "75", "correctAnswer": "qty(abs(R),units)", "C3": "25"}, "unitTests": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "engineering-answer"}, {"showFeedbackIcon": true, "variableReplacements": [], "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "settings": {"tolerance": "5", "expected_answer": "degrees(direction(R))"}, "unitTests": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "angle"}], "variableReplacements": []}, {"customMarkingAlgorithm": "", "sortAnswers": false, "scripts": {"mark": {"order": "after", "script": "numbasGGBApplet0.setVisible('show',true);\nnumbasGGBApplet0.setValue('show',true);"}}, "prompt": "

Trigonometric (Exact) Solution

\n
    \n
  1. Label the three angles inside the triangle $\\theta_A$, $\\theta_B$, and $\\theta_C$ where the subscript is the name of the side opposite.
  2. \n
  3. Use law of cosines/sines to find the following values, exactly. Give all answers to three significant digits.
  4. \n
\n

$\\theta_A$ = [[0]] 

\n

$\\theta_B$ = [[1]]

\n

$\\theta_R$ = [[2]]

\n

$|\\textbf{R}|$ = [[3]] 

\n

", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true, "marks": 0, "unitTests": [], "gaps": [{"showFeedbackIcon": true, "variableReplacements": [], "marks": "2", "scripts": {"mark": {"order": "before", "script": "var ans= numbasGGBApplet0.getValue(\"\u03b8_a\")*180/Math.PI;\nthis.resolved_input_options.correctAnswer= Numbas.math.siground(ans,3); \n"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "settings": {"tolerance": "1", "expected_answer": "thetaA"}, "unitTests": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "angle"}, {"showFeedbackIcon": true, "variableReplacements": [], "marks": "2", "scripts": {"mark": {"order": "before", "script": "var ans= numbasGGBApplet0.getValue(\"\u03b8_b\")*180/Math.PI;\nthis.resolved_input_options.correctAnswer= Numbas.math.siground(ans,3); \n"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "settings": {"tolerance": "1", "expected_answer": "thetaB"}, "unitTests": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "angle"}, {"showFeedbackIcon": true, "variableReplacements": [], "marks": "2", "scripts": {"mark": {"order": "before", "script": "var ans= numbasGGBApplet0.getValue(\"\u03b8_r\")*180/Math.PI;\nthis.resolved_input_options.correctAnswer= Numbas.math.siground(ans,3); \n"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "settings": {"tolerance": "1", "expected_answer": "thetaR"}, "unitTests": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "angle"}, {"showFeedbackIcon": true, "variableReplacements": [], "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "settings": {"right": "0.2", "C2": "50", "close": "1.0", "C1": "75", "correctAnswer": "qty(abs(R),units)", "C3": "25"}, "unitTests": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "engineering-answer"}], "variableReplacements": []}], "rulesets": {}, "variables": {"FB": {"templateType": "anything", "description": "

Magnitude of force B,  Magnitude of A is twice this value.

", "definition": "random(5..100#5)", "group": "Inputs", "name": "FB"}, "R": {"templateType": "anything", "description": "", "definition": "A + B", "group": "Results", "name": "R"}, "dirA": {"templateType": "anything", "description": "

Direction of force A, based on Ax and Ay.

", "definition": "degrees(atan2(Ay,Ax))", "group": "Results", "name": "dirA"}, "Ax": {"templateType": "anything", "description": "", "definition": "random(-4..4 except 0)", "group": "Inputs", "name": "Ax"}, "B": {"templateType": "anything", "description": "

Force B

", "definition": "FB vector(cos(radians(dirB)),sin(radians(dirB)))\n", "group": "Results", "name": "B"}, "thetaA": {"templateType": "anything", "description": "", "definition": "loc(A,B,R)", "group": "Ungrouped variables", "name": "thetaA"}, "units": {"templateType": "anything", "description": "", "definition": "random(['lb','N','kN'])", "group": "Inputs", "name": "units"}, "thetaB": {"templateType": "anything", "description": "", "definition": "loc(B,A,R)", "group": "Ungrouped variables", "name": "thetaB"}, "A": {"templateType": "anything", "description": "

Force A

", "definition": "2 FB vector(cos(radians(dirA)),sin(radians(dirA)))", "group": "Results", "name": "A"}, "dirB": {"templateType": "anything", "description": "", "definition": "(random(0..360#15 except 0..360#45))", "group": "Inputs", "name": "dirB"}, "thetaR": {"templateType": "anything", "description": "", "definition": "loc(R,A,B)", "group": "Ungrouped variables", "name": "thetaR"}, "Ay": {"templateType": "anything", "description": "", "definition": "random(-4..4 except 0)", "group": "Inputs", "name": "Ay"}}, "metadata": {"description": "

Find the sum of two 2-dimensional vectors, graphically and exactly using the parallelogram rule.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "name": "Vector addition: parallelogram rule", "contributors": [{"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}