// Numbas version: exam_results_page_options {"name": "Chapter 2 Exercises", "metadata": {"description": "

End of chapter exercises for Engineering Statics: Open and Interactive

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": true, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Vectors", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", ""], "variable_overrides": [[], [], [], [], []], "questions": [{"name": "Rectangular components: P to R", "extensions": ["geogebra", "quantities"], "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.

", "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

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

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.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["Mechanics, statics, forces, rectangular components"], "metadata": {"description": "

Find the rectangular (scalar) components of a force for two coordinates systems.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

Force $\\mathbf{F}$ has a magnitude of {F} acting {theta_for_student}.

{applet()}

fx: {fx} fy: {fy} fx': {fx'} fy': {fy'}

", "advice": "

$\\begin{align} F_x & = F \\cos \\var{theta}° & F_y & = F \\sin \\var{theta}°\\\\
F_{x'} &= F \\cos(\\simplify[!collectNumbers]{{theta}-{alpha}})° & F_{y'} &= F \\sin(\\simplify[!collectNumbers]{{theta}-{alpha}})°\\\\
\\end{align}$

Scalar components are signed numbers and you must attach the sign manually after you calculate the numeric value.

For $x$-components, the scalar component is positive if the $x$ component points right, negative if it points left.
For $y$-components, the scalar component is positive if the $y$ component points up, negative if it points down.
In the general case, a scalar component is positive if points towards the positive end of its corresponding axis.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"theta_for_student": {"name": "theta_for_student", "group": "inputs", "definition": "let(ang,abs(theta),\n if(ang<90,(\n random([ang + '\u00b0 from the horizontal', 90-ang + '\u00b0 from the vertical']),\n random([ang-90 +'\u00b0 from the vertical', 180-ang + '\u00b0 from the horizontal']))))", "description": "

Always less than 90° whereas GGB's theta is -180° -180°

", "templateType": "anything", "can_override": false}, "fx": {"name": "fx", "group": "Ungrouped variables", "definition": "f* cos(radians(theta))", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "inputs", "definition": "random(-170..170#10 except [90,0,-90])", "description": "", "templateType": "anything", "can_override": false}, "fx'": {"name": "fx'", "group": "Ungrouped variables", "definition": "f * cos(radians(theta-alpha))", "description": "", "templateType": "anything", "can_override": false}, "fy": {"name": "fy", "group": "Ungrouped variables", "definition": "f* sin(radians(theta))", "description": "", "templateType": "anything", "can_override": false}, "F": {"name": "F", "group": "inputs", "definition": "quantity(random(25..600#25),units)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "inputs", "definition": "random(['lb', 'N', 'kN'])", "description": "", "templateType": "anything", "can_override": false}, "fy'": {"name": "fy'", "group": "Ungrouped variables", "definition": "f*sin(radians(theta-alpha))", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "inputs", "definition": "random(-80..80#5 except 0)", "description": "

angle of x' axis

", "templateType": "anything", "can_override": false}, "tension": {"name": "tension", "group": "inputs", "definition": "random(true,false)", "description": "

Flag to determine weather force points towards or away from origin.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "not(theta=alpha or theta = alpha + 90 or theta = alpha - 90 or theta = alpha + 180 or theta = alpha-180)", "maxRuns": 100}, "ungrouped_variables": ["fx", "fy", "fx'", "fy'", "debug"], "variable_groups": [{"name": "inputs", "variables": ["F", "theta", "units", "theta_for_student", "alpha", "tension"]}], "functions": {"applet": {"parameters": [], "type": "ggbapplet", "language": "javascript", "definition": "// Create the worksheet. \n// This function returns an object with a container `element` and a `promise` resolving to a GeoGebra applet.\nvar params = {\n //material_id: 'wrhxztvu' prior to 12/4/2022 always has tip at origin\n material_id: 'bdwrwkm4' // slides vector to put tail on origin when 'tension=true'\n};\n\nvar result = Numbas.extensions.geogebra.createGeogebraApplet(params);\n\n// Once the applet has loaded, run some commands to manipulate the worksheet.\nresult.promise.then(function(d) {\n var app = d.app;\n question.applet = d;\n //app.setGridVisible(1, true);\n //app.setAxesVisible(true,false);\n //app.enableShiftDragZoom(false);\n \n function setGGBPoint(name, nname=name) {\n // moves point in GGB to Numbas value\n var x = Numbas.jme.unwrapValue(question.scope.getVariable(nname));\n app.setFixed(name,false,false);\n app.setCoords(name, x, 0);\n app.setFixed(name,true,true);\n }\n\n function setGGBAngle(gname, nname=gname) {\n // Sets angle in GGB to a Numbas Variable given in degrees.\n var v = Math.PI / 180 * Numbas.jme.unwrapValue(question.scope.getVariable(nname));\n app.setValue(gname,v);\n } \n setGGBAngle('\u03b8','theta');\n setGGBAngle('\u03b1','alpha');\n app.setValue('tension',Numbas.jme.unwrapValue(question.scope.getVariable('tension')));\n \n});\n\n// This function returns the result of `createGeogebraApplet` as an object \n// with the JME data type 'ggbapplet', which can be substituted into the question's content.\nreturn new Numbas.jme.types.ggbapplet(result);"}}, "preamble": {"js": "question.signals.on('adviceDisplayed',function() {\n try{\n var app = question.applet.app;\n app.setVisible(\"show1\",true);\n app.setVisible(\"show2\",true);\n app.setValue(\"showAxis2\",true);\n \n }\n catch(err){} \n})\n\n", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "$x$-$y$ coordinate system", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Determine the scalar components of $\\mathbf{F}$ in the $x$ and $y$ directions.

$F_x$ = [[0]] $\\qquad F_y$ = [[1]]

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Fx", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "Fx", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Fy", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "Fy", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "$x'$-$y'$ coordinate system", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

A new coordinate system is created by rotating the $x$ - and $y$ axes {abs(alpha)}° {if(alpha>0,'counter-','')}clockwise.

Determine the scalar components of $\\mathbf{F}$ in the $x'$ and $y'$ directions.

$F_{x'}$ = [[0]] $\\qquad F_{y'}$ = [[1]]

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Fx'", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "fx'", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Fy'", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "fy'", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Rectangular components: R to P", "extensions": ["geogebra", "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.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

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.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["angle from reference", "Mechanics", "mechanics", "r to p", "rectangular components", "Statics", "statics"], "metadata": {"description": "

Find the magnitude and direction of a force given its scalar components.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

Force $\\mathbf{F}$ has scalar components: $F_x$ = {qty(Fx,units)} and $F_y$ = {qty(Fy,units)}.

Find the magnitude and direction of the resultant force $\\mathbf{F}$.

", "advice": "

Sketch the components in the correct directions, and the resultant using the parallelogram rule. Define angle $\\theta$ from the positive or negative $x$-axis, such that $\\theta < 90°$.

{geogebra_applet('vttcphbe',[['Fx',Fx],['Fy',Fy]])}

$F = \\sqrt{F_x^2 + F_y^2}$

$\\theta = \\tan^{-1} \\left ( \\left | \\dfrac{F_y}{F_x} \\right | \\right) $, choose reference axis and direction by inspection.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Fx": {"name": "Fx", "group": "Ungrouped variables", "definition": "random(2..10) random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "F": {"name": "F", "group": "Ungrouped variables", "definition": "vector(Fx,Fy)", "description": "", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Ungrouped variables", "definition": "mod(degrees(atan2(Fy,Fx)),360)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "random('N','lb','kN')", "description": "", "templateType": "anything", "can_override": false}, "Fy": {"name": "Fy", "group": "Ungrouped variables", "definition": "random(2..10) random(1,-1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(F) <> 5", "maxRuns": 100}, "ungrouped_variables": ["Fx", "Fy", "F", "units", "theta"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Magnitude", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Give the magnitude of force $\\mathbf{F}$.

$F$ = [[0]]

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Give the direction of $\\mathbf{F}$ by supplying an angle, between 0° and 90°, measured counter-clockwise or clockwise from the $x$-axis.

$\\theta$ = [[0]] measured [[1]] from the [[2]].

Adjusts all angles to 0 < $\\theta$ < 360.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

90° = -270° = 450°

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.

Normalize expected_answer with mod 360

A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["angle from reference", "mechanics", "statics", "vector addition"], "metadata": {"description": "

Given three vectors with integer components, find the corresponding magnitude and direction.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

Three forces, A, B, and C are drawn to scale of 1 square = {scale} {units[1]}. Find the magnitude and direction of each.

{geogebra_applet('qdbwtfa9', [['fa',FA],['fb',FB],['fc',FC]])}

", "advice": "

For force $\\textbf{A}$

$A = \\sqrt{{A_x}^2 + {A_y}^2} = \\sqrt{\\var{FA[0]}^2 +\\var{FA[1]}^2}$ = {siground(mag_A,4)}

$\\theta_A = \\tan^{-1}\\left(\\left|\\dfrac{A_y}{A_x}\\right|\\right) = \\tan^{-1}\\left(\\left|\\dfrac{\\var{FA[1]}}{\\var{FA[0]}}\\right|\\right) =\\var{siground(degrees(arctan(abs(FA[1]/FA[0]))),4)}°$

and similarly for $\\textbf{B}$ and $\\textbf{C}$.

", "rulesets": {}, "variables": {"FC": {"name": "FC", "group": "Inputs", "definition": "vector(random(-5..5 except 0),random(-5..5 except 0))", "description": "", "templateType": "anything"}, "scale": {"name": "scale", "group": "Inputs", "definition": "random(0.1,0.25,0.5,2,4,5,10,20)", "description": "", "templateType": "anything"}, "ref": {"name": "ref", "group": "Ungrouped variables", "definition": "0", "description": "

placeholder for reference axis

", "templateType": "anything"}, "theta_b": {"name": "theta_b", "group": "Outputs", "definition": "degrees(atan2(FB[1],FB[0]))", "description": "", "templateType": "anything"}, "c_from_ref": {"name": "c_from_ref", "group": "Ungrouped variables", "definition": "let(ang,theta_c,\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", "description": "", "templateType": "anything"}, "theta_a": {"name": "theta_a", "group": "Outputs", "definition": "mod(degrees(atan2(FA[1],FA[0])),360)", "description": "", "templateType": "anything"}, "C1": {"name": "C1", "group": "Inputs", "definition": "vector(5,0)\n", "description": "

Position of point C

", "templateType": "anything"}, "b_from_ref": {"name": "b_from_ref", "group": "Ungrouped variables", "definition": "let(ang,theta_b,\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", "description": "", "templateType": "anything"}, "A1": {"name": "A1", "group": "Inputs", "definition": "vector(-5,0)", "description": "

Position of point A (start point for force A) fixed in this problem

", "templateType": "anything"}, "mag_c": {"name": "mag_c", "group": "Outputs", "definition": "qty(abs(FC),units[1]) scale", "description": "", "templateType": "anything"}, "mag_a": {"name": "mag_a", "group": "Outputs", "definition": "qty(abs(FA),units[1]) scale", "description": "", "templateType": "anything"}, "debug": {"name": "debug", "group": "Inputs", "definition": "false", "description": "", "templateType": "anything"}, "theta_c": {"name": "theta_c", "group": "Outputs", "definition": "degrees(atan2(FC[1],FC[0]))", "description": "", "templateType": "anything"}, "a_from_ref": {"name": "a_from_ref", "group": "Ungrouped variables", "definition": "let(ang,theta_a,\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)])", "description": "", "templateType": "anything"}, "units": {"name": "units", "group": "Inputs", "definition": "random(['ft','lb'],['in','lb'],['cm','N'])", "description": "", "templateType": "anything"}, "FA": {"name": "FA", "group": "Inputs", "definition": "vector(random(-5..5 except 0),random(-5..5))", "description": "", "templateType": "anything"}, "FB": {"name": "FB", "group": "Inputs", "definition": "vector(random(-5..5),random(-5..5 except 0))", "description": "", "templateType": "anything"}, "mag_b": {"name": "mag_b", "group": "Outputs", "definition": "qty(abs(FB),units[1]) scale", "description": "", "templateType": "anything"}, "B1": {"name": "B1", "group": "Inputs", "definition": "vector(0,0)\n", "description": "

Position of point B

", "templateType": "anything"}}, "variablesTest": {"condition": "abs(FA)>=3 and abs(FB)>=3 and abs(FC)>=3", "maxRuns": "100"}, "ungrouped_variables": ["a_from_ref", "b_from_ref", "c_from_ref", "ref"], "variable_groups": [{"name": "Inputs", "variables": ["A1", "FA", "B1", "FB", "C1", "FC", "units", "debug", "scale"]}, {"name": "Outputs", "variables": ["mag_a", "theta_a", "mag_b", "theta_b", "mag_c", "theta_c"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Force A", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_angle: // a qty string corrected to standard angle\n student_angle[2] + student_angle[1] * student_angle[0] + student_units\n\nmagnitude:\n studentAnswer[3]\n\nstudent_angle:\n [mod(matchnumber(studentAnswer[0],['plain','en'])[1],360), // angle\n [1,-1][indices(studentAnswer[1],[true])[0]], // ccw = 1 cw = -1\n [0,90,180,-90][indices(studentAnswer[2],[true])[0]]] // reference axis\n\nstudent_units:\n studentAnswer[0][len(matchnumber(studentAnswer[0],['plain','en'])[0])..len(studentAnswer[0])]\n\ninterpreted_answers:\n [interpreted_angle, studentAnswer[1], studentAnswer[2], studentAnswer[3]]\n\ngap_feedback (Feedback on each of the gaps):\n map(\n try(\n let(\n result, submit_part(gaps[gap_number][\"path\"],answer),\n gap, gaps[gap_number],\n name, gap[\"name\"], \n noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n assert(name=\"\" or len(gaps)=1,feedback(translate('part.gapfill.feedback header',[\"name\": name])));\n concat_feedback(filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]), if(marks>0,result[\"marks\"]/marks,1), noFeedbackIcon);\n result\n ),\n err,\n fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n ),\n [gap_number,answer,index],\n zip([3,0],[studentAnswer[3], interpreted_angle],[1,2])\n )\n\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Find the magnitude and direction of A.

$A$ = [[3]]

$\\theta_A$ = [[0]] measured [[1]] from the [[2]].

magnitude = {siground(mag_A,4)}

direction={theta_A}

", "gaps": [{"type": "angle", "useCustomName": true, "customName": "angle", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(theta_a,'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.2"}}, {"type": "1_n_2", "useCustomName": true, "customName": "dir", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+x axis", "+y axis", "-x axis", "-y axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "engineering-answer", "useCustomName": true, "customName": "Magnitude", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "mag_A", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Force B", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_angle: // a qty string corrected to standard angle\n student_angle[2] + student_angle[1] * student_angle[0] + student_units\n\nmagnitude:\n studentAnswer[3]\n\nstudent_angle:\n [mod(matchnumber(studentAnswer[0],['plain','en'])[1],360), // angle\n [1,-1][indices(studentAnswer[1],[true])[0]], // ccw = 1 cw = -1\n [0,90,180,-90][indices(studentAnswer[2],[true])[0]]] // reference axis\n\nstudent_units:\n studentAnswer[0][len(matchnumber(studentAnswer[0],['plain','en'])[0])..len(studentAnswer[0])]\n\ninterpreted_answers:\n [interpreted_angle, studentAnswer[1], studentAnswer[2], studentAnswer[3]]\n\ngap_feedback (Feedback on each of the gaps):\n map(\n try(\n let(\n result, submit_part(gaps[gap_number][\"path\"],answer),\n gap, gaps[gap_number],\n name, gap[\"name\"], \n noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n assert(name=\"\" or len(gaps)=1,feedback(translate('part.gapfill.feedback header',[\"name\": name])));\n concat_feedback(filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]), if(marks>0,result[\"marks\"]/marks,1), noFeedbackIcon);\n result\n ),\n err,\n fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n ),\n [gap_number,answer,index],\n zip([3,0],[studentAnswer[3], interpreted_angle],[1,2])\n )\n\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Find the magnitude and direction of B.

$B$ = [[3]]

$\\theta_B$ = [[0]] measured [[1]] from the [[2]].

magnitude = {siground(mag_B,4)}

direction={theta_B}

", "gaps": [{"type": "angle", "useCustomName": true, "customName": "angle", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(theta_b,'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.2"}}, {"type": "1_n_2", "useCustomName": true, "customName": "dir", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+x axis", "+y axis", "-x axis", "-y axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "engineering-answer", "useCustomName": true, "customName": "Magnitude", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "mag_B", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Force C", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_angle: // a qty string corrected to standard angle\n student_angle[2] + student_angle[1] * student_angle[0] + student_units\n\nmagnitude:\n studentAnswer[3]\n\nstudent_angle:\n [mod(matchnumber(studentAnswer[0],['plain','en'])[1],360), // angle\n [1,-1][indices(studentAnswer[1],[true])[0]], // ccw = 1 cw = -1\n [0,90,180,-90][indices(studentAnswer[2],[true])[0]]] // reference axis\n\nstudent_units:\n studentAnswer[0][len(matchnumber(studentAnswer[0],['plain','en'])[0])..len(studentAnswer[0])]\n\ninterpreted_answers:\n [interpreted_angle, studentAnswer[1], studentAnswer[2], studentAnswer[3]]\n\ngap_feedback (Feedback on each of the gaps):\n map(\n try(\n let(\n result, submit_part(gaps[gap_number][\"path\"],answer),\n gap, gaps[gap_number],\n name, gap[\"name\"], \n noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n assert(name=\"\" or len(gaps)=1,feedback(translate('part.gapfill.feedback header',[\"name\": name])));\n concat_feedback(filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]), if(marks>0,result[\"marks\"]/marks,1), noFeedbackIcon);\n result\n ),\n err,\n fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n ),\n [gap_number,answer,index],\n zip([3,0],[studentAnswer[3], interpreted_angle],[1,2])\n )\n\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Find the magnitude and direction of C.

$C$ = [[3]]

$\\theta_C$ = [[0]] measured [[1]] from the [[2]].

magnitude = {siground(mag_C,4)}

direction={theta_C} {C_from_ref}

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.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["Mechanics", "mechanics", "Statics", "statics", "Vector addition", "vector addition", "Vector Addition"], "metadata": {"description": "

Given the specifications of two vectors, draw the parallelogram representing their sum, then estimate length of the diagonal.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

Vector $\\mathbf{R}$ has components $\\mathbf{A}$ and $\\mathbf{B}$.

Vector $\\mathbf{A}$ has a magnitude of {qty(round(abs(A)),units)} pointing {alpha}° from the x-axis, and Vector $\\mathbf{B}$ has a magnitude of {qty(round(abs(B)),units)} pointing {beta}° from the x-axis.

Carefully draw to scale a parallelogram with sides $\\mathbf{A}$ and $\\mathbf{B}$, then measure the magnitude of diagonal $\\mathbf{R}$ and the angle $\\theta$ opposite to it.

", "advice": "

{applet}

$\\theta = \\var{theta}$

$R = \\var{qty(precround(abs(R),1),units)}$

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"alpha": {"name": "alpha", "group": "Ungrouped variables", "definition": "random(-80..80#5 except 0)", "description": "

direction of first vector

", "templateType": "anything", "can_override": false}, "beta": {"name": "beta", "group": "Ungrouped variables", "definition": "alpha + included", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "random(4..12) vector(cos(radians(alpha)),sin(radians(alpha)))", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "random(4..12) vector(cos(radians(beta)),sin(radians(beta)))", "description": "", "templateType": "anything", "can_override": false}, "included": {"name": "included", "group": "Ungrouped variables", "definition": "random(30..120#5)", "description": "", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "Ungrouped variables", "definition": "geogebra_applet('p8hbh3rj',[A: A, B: B ])", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "\"kN\"", "description": "", "templateType": "anything", "can_override": false}, "R": {"name": "R", "group": "Ungrouped variables", "definition": "A+B", "description": "

resultant

", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Ungrouped variables", "definition": "qty(180-included, 'deg')", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["alpha", "beta", "A", "B", "included", "applet", "units", "R", "theta"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

$R$ = [[1]] $\\theta$ = [[0]]

", "gaps": [{"type": "angle-quantity-from-reference", "useCustomName": true, "customName": "Angle", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correct_quantity": "theta", "right": "0.2", "restrict_angle": false, "C1": "75", "close": "1.0", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Magnitude", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(abs(R),units)", "right": "2", "close": "10", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Arbitrary components", "extensions": ["geogebra", "quantities"], "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.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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

Determine the oblique components of a vector.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

{applet()}

Determine the scalar components of $\\var{F units}$ force $\\mathbf{F}$ in the $a$- and $b$- directions.

", "advice": "

Procedure:

Carefully draw and label a diagram showing the parallelogram rule vector addition.

Determine the values of any known angles and sides.

Use the law of sines or law of cosines to solve for the unknown values.

You can't use SOHCAHTOA on this triangle unless it is a right triangle.

Note:

A Scalar component is equal to the magnitude of the corresponding vector component, but with a $+$ or $-$ sign to indicate its sense.

Vector Magnitudes are always positive, but a scalar component is positive if it points towards the positive end of the axis, or negative if it points the other way.

The positive end of an axis is the end with the label.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"debug": {"name": "debug", "group": "inputs", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "inputs", "definition": "random(0..360#15)", "description": "

Direction of a axis from x axis. b axis and F are measured from here

", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "inputs", "definition": "qty(1, 'kN')", "description": "", "templateType": "anything", "can_override": false}, "beta": {"name": "beta", "group": "inputs", "definition": "random(0..360#15 except [0,90,270,360])", "description": "

direction of +b axis from a axis

", "templateType": "anything", "can_override": false}, "F_a": {"name": "F_a", "group": "inputs", "definition": "EA( -F / sin(radians(beta)) sin(radians(theta - beta)))", "description": "

Answer to question. Component in \"a\" direction.

", "templateType": "anything", "can_override": false}, "F_b": {"name": "F_b", "group": "inputs", "definition": "EA(F / sin(radians(beta)) sin(radians(180 - theta)))", "description": "

component in \"b\" direction

", "templateType": "anything", "can_override": false}, "F": {"name": "F", "group": "inputs", "definition": "random(100..1500#50)", "description": "

Magnitude of F

", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "inputs", "definition": "random(0..360#15)", "description": "

direction of force from a axis

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "//ensure that components look good on diagram\n\n2.5 > abs(F_a/F) > 0.3 and \n2.5 > abs(F_b/F) > 0.3", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "inputs", "variables": ["alpha", "beta", "theta", "debug", "units", "F", "F_a", "F_b"]}], "functions": {"applet": {"parameters": [], "type": "ggbapplet", "language": "javascript", "definition": "// Create the worksheet. \n// This function returns an object with a container `element` and a `promise` resolving to a GeoGebra applet.\nvar params = {\n material_id: 'rgfr3kj8'\n}\n\nvar result = Numbas.extensions.geogebra.createGeogebraApplet(params);\n\n// Once the applet has loaded, run some commands to manipulate the worksheet.\nresult.promise.then(function(d) {\n var app = d.app;\n question.applet = d;\n \n function setGGBAngle(gname, nname=gname) {\n // Sets angle in GGB to a Numbas Variable given in degrees.\n var v = Numbas.jme.unwrapValue(question.scope.getVariable(nname));\n app.setValue(gname,v * Math.PI / 180);\n } \n\n setGGBAngle(\"ang_a\", \"alpha\");\n setGGBAngle(\"ang_b\", \"beta\");\n setGGBAngle(\"theta\", \"theta\");\n //\n app.setGridVisible(true);\n app.setVisible(\"\u03b8\",false);\n app.setVisible(\"\u03b1\",false);\n app.setVisible(\"debug\",false);\n app.setVisible(\"show\",false);\n app.setValue(\"debug\",false);\n app.setValue(\"show\",false);\n app.setValue(\"mag_F\", Numbas.jme.unwrapValue(question.scope.getVariable(\"F\")));\n \n \n});\n\n// This function returns the result of `createGeogebraApplet` as an object \n// with the JME data type 'ggbapplet', which can be substituted into the question's content.\nreturn new Numbas.jme.types.ggbapplet(result);"}, "EA": {"parameters": [["N", "number"]], "type": "anything", "language": "jme", "definition": "round(n*100)/100"}}, "preamble": {"js": "question.signals.on('adviceDisplayed',function() {\n try{\n var app = question.applet.app;\n \n app.setVisible('show',false);\n app.setValue('show',true);\n app.setLabelVisible('show',false);\n \n }\n catch(err){} \n})\n\n\n", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Components", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

$F_a$ = [[0]] {F_a units} $\\qquad F_b$ = [[1]] {F_b units}

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$F_a$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "F_a units", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$F_b$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "F_b units", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Vector Addition", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["Tip-to-tail method", "Parallelogram rule", "Summing scalar components", "", "", "Description only"], "variable_overrides": [[], [], [], [], [], []], "questions": [{"name": "Vector addition: tip-to-tail method", "extensions": ["geogebra", "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.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

90° = -270° = 450°

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.

Normalize expected_answer with mod 360

A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["angle from reference", "Graphical methods", "Mechanics", "mechanics", "Statics", "statics", "Vector addition", "vector addition", "Vector Addition"], "metadata": {"description": "

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

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

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

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

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

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

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

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

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

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.
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 force $R$ will appear.

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

", "advice": "

Vector Addition:

When the forces have been moved to a tip-to=tail arrangement, the magnitude and direction can be read off the polar diagram.

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

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"FA": {"name": "FA", "group": "Inputs", "definition": "random(20..80#5)", "description": "

Magnitude of force A

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

direction of force A

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

Force C as a vector

", "templateType": "anything", "can_override": false}, "ForceR": {"name": "ForceR", "group": "Outputs", "definition": "ForceA+ForceB+ForceC", "description": "

Resultant as a vector

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

Magnitude of Force B

", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Inputs", "definition": "random(['ft','lb'],['in','lb'],['cm','N'])", "description": "", "templateType": "anything", "can_override": false}, "rho": {"name": "rho", "group": "Outputs", "definition": "degrees(direction(ForceR))", "description": "

direction of resultant

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

Direction of force C in degrees

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

Magnitude of force C

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

force A as a vector

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

Force B as a vector

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

Magnitude of resultant

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

Direction of force B

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(alpha-beta) >= 15 and abs(beta-gamma) >= 15 and abs(gamma-alpha) >= 15 and r <=100 and r > 10", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Inputs", "variables": ["alpha", "gamma", "beta", "FA", "FB", "FC", "units", "debug"]}, {"name": "Outputs", "variables": ["ForceA", "ForceB", "ForceC", "ForceR", "rho", "R"]}], "functions": {"direction": {"parameters": [["v", "vector"]], "type": "number", "language": "javascript", "definition": "return Math.atan2(v[1],v[0])"}}, "preamble": {"js": "", "css": ".red{color:red;}\n.blue{color:blue;}\n.green{color:green;}"}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Magnitude", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

$R$ = [[0]]

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Magnitude", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(R,units[1])", "right": "3", "close": "6", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Direction", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_angle: // a qty string corrected to standard angle\n student_angle[2] + student_angle[1] * student_angle[0] + student_units\n\n\nstudent_angle:\n [mod(matchnumber(studentAnswer[0],['plain','en'])[1],360), // angle\n [1,-1][indices(studentAnswer[1],[true])[0]], // ccw = 1 cw = -1\n [0,90,180,-90][indices(studentAnswer[2],[true])[0]]] // reference axis\n\nstudent_units:\n studentAnswer[0][len(matchnumber(studentAnswer[0],['plain','en'])[0])..len(studentAnswer[0])]\n\ninterpreted_answers:\n [interpreted_angle, studentAnswer[1], studentAnswer[2]]\n\ngap_feedback (Feedback on each of the gaps):\n map(\n try(\n let(\n result, submit_part(gaps[gap_number][\"path\"],answer),\n gap, gaps[gap_number],\n name, gap[\"name\"], \n noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n assert(name=\"\" or len(gaps)=1,feedback(translate('part.gapfill.feedback header',[\"name\": name])));\n concat_feedback(filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]), if(marks>0,result[\"marks\"]/marks,1), noFeedbackIcon);\n result\n ),\n err,\n fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n ),\n [gap_number,answer,index],\n zip([0],[interpreted_angle],[1])\n )\n\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

$\\theta$ = [[0]] measured [[1]] from the [[2]].

", "gaps": [{"type": "angle", "useCustomName": true, "customName": "Direction", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "precround(qty(rho,'deg'),0)", "unit_penalty": "20", "close_penalty": "20", "close_tol": "5", "right_tol": "2"}}, {"type": "1_n_2", "useCustomName": true, "customName": "sign", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+x axis", "+y Axis", "-x Axis", "-y Axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Vector addition: parallelogram rule", "extensions": ["geogebra", "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.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

90° = -270° = 450°

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.

Normalize expected_answer with mod 360

A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["mechanics, statics, parallelogram rule, vector addition"], "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"}, "statement": "

Find the magnitude and direction of resultant $\\mathbf{R}$ when $\\mathbf{A} = \\var{qty(2 FB, units)}$ and $\\mathbf{B} = \\var{qty(FB,units)}$,

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

", "advice": "

Procedure:

Draw a neat diagram and label the unknown side and angles.
Determine the angle opposite the unknown force $\\textbf{R}$.
Use law of cosines to determine the magnitude $|\\textbf{R}|$
Use either the law of sines or cosines to determine the other two angles.
Use the angles you have found to determine the direction of force $\\textbf{R}$ from the x-axis.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"thetaR": {"name": "thetaR", "group": "Ungrouped variables", "definition": "loc(R,A,B)", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Results", "definition": "2 FB vector(cos(radians(dirA)),sin(radians(dirA)))", "description": "

Force A

", "templateType": "anything", "can_override": false}, "R": {"name": "R", "group": "Results", "definition": "A + B", "description": "", "templateType": "anything", "can_override": false}, "thetaA": {"name": "thetaA", "group": "Ungrouped variables", "definition": "loc(A,B,R)", "description": "", "templateType": "anything", "can_override": false}, "FB": {"name": "FB", "group": "Inputs", "definition": "random(5..100#5)", "description": "

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

", "templateType": "anything", "can_override": false}, "Ay": {"name": "Ay", "group": "Inputs", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "thetaB": {"name": "thetaB", "group": "Ungrouped variables", "definition": "loc(B,A,R)", "description": "", "templateType": "anything", "can_override": false}, "dirA": {"name": "dirA", "group": "Results", "definition": "degrees(atan2(Ay,Ax))", "description": "

Direction of force A, based on Ax and Ay.

", "templateType": "anything", "can_override": false}, "Ax": {"name": "Ax", "group": "Inputs", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Inputs", "definition": "random(['lb','N','kN'])", "description": "", "templateType": "anything", "can_override": false}, "dirB": {"name": "dirB", "group": "Inputs", "definition": "(random(0..360#15 except 0..360#45))", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Results", "definition": "FB vector(cos(radians(dirB)),sin(radians(dirB)))\n", "description": "

Force B

", "templateType": "anything", "can_override": false}, "dirR": {"name": "dirR", "group": "Results", "definition": "degrees(atan2(R[1],r[0]))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(dirA- dirB) > 25 and abs(dirA-dirB) < 160 ", "maxRuns": "200"}, "ungrouped_variables": ["thetaA", "thetaB", "thetaR"], "variable_groups": [{"name": "Inputs", "variables": ["FB", "dirB", "Ax", "Ay", "units"]}, {"name": "Results", "variables": ["dirA", "A", "B", "R", "dirR"]}], "functions": {"direction": {"parameters": [["v", "vector"]], "type": "number", "language": "javascript", "definition": "return Math.atan2(v[1],v[0])\n"}, "loc": {"parameters": [["A", "vector"], ["B", "vector"], ["C", "vector"]], "type": "number", "language": "jme", "definition": "degrees(arccos((abs(A)^2-abs(B)^2-abs(C)^2)/(-2 * abs(B) * abs(C))))"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Graphical Solution", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "\n ", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

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

$|\\mathbf{R}|$ = [[0]] $\\qquad \\theta_x$ = [[1]]

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$\\theta_x$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(abs(R),units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "angle", "useCustomName": true, "customName": "$|R|$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(dirR,'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Trigonometric (Exact) Solution", "marks": 0, "scripts": {"mark": {"script": "//numbasGGBApplet0.setVisible('show',true);\n//numbasGGBApplet0.setValue('show',true);", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Label the three angles inside the triangle $\\theta_A$, $\\theta_B$, and $\\theta_R$ where the subscript is the name of the side opposite.
Use law of cosines/sines to find the following values, exactly.

$\\theta_A =$ [[0]] $\\qquad \\theta_B = $[[1]] $\\qquad \\theta_R =$ [[2]] $\\qquad |\\mathbf{R}| =$ [[3]]

", "gaps": [{"type": "angle", "useCustomName": true, "customName": "$\\theta_A$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(thetaA,'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}, {"type": "angle", "useCustomName": true, "customName": "$\\theta_B$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(thetaB,'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}, {"type": "angle", "useCustomName": true, "customName": "$\\theta_C$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(thetaR,'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$|R|$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(abs(R),units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Vector addition by summing scalar components - easy", "extensions": ["geogebra", "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.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

90° = -270° = 450°

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.

Normalize expected_answer with mod 360

A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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": [["question-resources/easy_vectors.ggb", "/srv/numbas/media/question-resources/easy_vectors.ggb"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["angle from reference", "Mechanics", "mechanics", "Scalar components", "Statics", "statics", "Vector addition", "vector addition", "Vector Addition"], "metadata": {"description": "

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.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

Three forces, $\\color{red}{\\mathbf{A}}, \\color{blue}{\\mathbf{B}}\\ \\text{and } \\color{forestgreen}{\\mathbf{C}}$ are drawn to scale of 1 square = {scale} {units[1]}. Find the resultant by summing scalar components.

{applet}

", "advice": "

Note: You an drag the vectors around to arrange them tip-to-tail. The resultant is a vector from the start of the chain to the end.

Vector Addition:

$R_x = \\Sigma F_x = \\simplify[!collectNumbers]{{scale FA[0]}+{scale FB[0]}+{scale FC[0]} ={scale FR[0]}}$ {units[1]}

$R_y = \\Sigma F_y = \\simplify[!collectNumbers]{{scale FA[1]}+{scale FB[1]}+{scale FC[1]} ={scale FR[1]}}$ {units[1]}

$R=\\sqrt{R_x^2 + R_y^2} =\\var{siground(resultant,4)}$

$\\theta = \\tan^{-1}\\left(\\left|\\dfrac{R_y}{R_x}\\right| \\right) = \\var{siground(theta,4)}$°

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"C1": {"name": "C1", "group": "Inputs", "definition": "vector(random(-Z+1..Z-1),random(-Z+1..Z-1))\n", "description": "

Position of point C

", "templateType": "anything", "can_override": false}, "scale": {"name": "scale", "group": "Inputs", "definition": "random(0.1,0.2,0.5,2,4,5,10,20)", "description": "", "templateType": "anything", "can_override": false}, "FA": {"name": "FA", "group": "Inputs", "definition": "A2-A1", "description": "

FA in first or fourth quadrant

", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Outputs", "definition": "degrees(atan2(FR[1],FR[0]))", "description": "", "templateType": "anything", "can_override": false}, "FR": {"name": "FR", "group": "Outputs", "definition": "FA + FB + FC", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Inputs", "definition": "random(['ft','lb'],['in','lb'],['cm','N'])", "description": "", "templateType": "anything", "can_override": false}, "A1": {"name": "A1", "group": "Inputs", "definition": "vector(random(-Z+1..Z-1),random(-Z+1..Z-1))", "description": "

Start point

", "templateType": "anything", "can_override": false}, "FB": {"name": "FB", "group": "Inputs", "definition": "B2-B1", "description": "

in third or 4 quadrant

", "templateType": "anything", "can_override": false}, "FC": {"name": "FC", "group": "Inputs", "definition": "C2-C1", "description": "", "templateType": "anything", "can_override": false}, "B1": {"name": "B1", "group": "Inputs", "definition": "vector(random(-Z+1..Z-1),random(-Z+1..Z-1))\n", "description": "

Position of point B

", "templateType": "anything", "can_override": false}, "resultant": {"name": "resultant", "group": "Outputs", "definition": "qty(abs(FR),units[1]) scale", "description": "", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "Ungrouped variables", "definition": "geogebra_file(\"easy_vectors.ggb\",params)", "description": "", "templateType": "anything", "can_override": false}, "params": {"name": "params", "group": "Ungrouped variables", "definition": "[A1: A1, A2: A2, B1: B1, B2: B2, C1: C1, C2: C2, Z: Z]", "description": "

endponts of vector, Z = xmax = ymax, -Z = xmin = ymin

", "templateType": "anything", "can_override": false}, "Z": {"name": "Z", "group": "Ungrouped variables", "definition": "8\n", "description": "

sets bound of window and max length of (unscaled) resultant FR

", "templateType": "anything", "can_override": false}, "B2": {"name": "B2", "group": "Inputs", "definition": "vector(random(-Z+1..Z-1 except B1[0]),random(-Z+1..Z-1 except B1[1]))", "description": "", "templateType": "anything", "can_override": false}, "C2": {"name": "C2", "group": "Inputs", "definition": "vector(random(-Z+1..Z-1),random(-Z+1..Z-1))", "description": "", "templateType": "anything", "can_override": false}, "A2": {"name": "A2", "group": "Inputs", "definition": "vector(random(-Z+1..Z-1 except A1[0]),random(-Z+1..Z-1 except A1[1]))", "description": "", "templateType": "anything", "can_override": false}, "AB": {"name": "AB", "group": "Ungrouped variables", "definition": "intersect(A1,A2,B1,B2)", "description": "

does FA intersect with FB?

", "templateType": "anything", "can_override": false}, "BC": {"name": "BC", "group": "Ungrouped variables", "definition": "intersect(B1,B2,C1,C2)", "description": "

does FB intersect with FC?

", "templateType": "anything", "can_override": false}, "CA": {"name": "CA", "group": "Ungrouped variables", "definition": "intersect(C1,C2,A1,A2)", "description": "

does FC intersect with FA?

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "2 <= abs(FR) <= Z //resultant not too short or too long\nand abs(FA) >=2 and abs(FB) >= 2 and abs(FC) >= 2 //vectors not too short\nand not(AB) and not(BC) and not (CA) // vectors don't intersect", "maxRuns": "100"}, "ungrouped_variables": ["applet", "params", "Z", "AB", "BC", "CA"], "variable_groups": [{"name": "Inputs", "variables": ["FA", "FB", "FC", "units", "scale", "A1", "B1", "C1", "A2", "B2", "C2"]}, {"name": "Outputs", "variables": ["FR", "theta", "resultant"]}], "functions": {"f": {"parameters": [["pt", "vector"]], "type": "boolean", "language": "jme", "definition": "pt[1]>(FA[1]/FA[0])(pt[0] - A1[0]) + A1[1] //This tests whether the point is above the line of action of force A. using point-slope formula y= m(x-x_1) + y_1 "}, "CCW": {"parameters": [["A", "vector"], ["B", "vector"], ["C", "vector"]], "type": "boolean", "language": "jme", "definition": "(C[1]-A[1]) * (B[0]-A[0]) > (B[1]-A[1]) * (C[0]-A[0])"}, "intersect": {"parameters": [["A", "vector"], ["B", "vector"], ["C", "vector"], ["D", "vector"]], "type": "boolean", "language": "jme", "definition": "// Return true if line segments AB and CD intersect\n// see https://stackoverflow.com/questions/3838329/how-can-i-check-if-two-segments-intersect\nccw(A,C,D) <> ccw(B,C,D) and ccw(A,B,C) <> ccw(A,B,D)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Components of components", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

First, find the scalar components of the three forces.

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

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

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Ax", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(FA[0],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Ay", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(FA[1],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Bx", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(FB[0],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "By", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(FB[1],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Cx", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(FC[0],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Cy", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(FC[1],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Components of resultant", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Then, sum the scalar components to get the scalar components of the resultant $\\mathbf{R}$.

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

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

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Rx", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(FR[0],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Ry", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(FR[1],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Magnitude and direction", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_angle: // a qty string corrected to standard angle\n student_angle[2] + student_angle[1] * student_angle[0] + student_units\n\nmagnitude:\n studentAnswer[3]\n\nstudent_angle:\n [mod(matchnumber(studentAnswer[0],['plain','en'])[1],360), // angle\n [1,-1][indices(studentAnswer[1],[true])[0]], // ccw = 1 cw = -1\n [0,90,180,-90][indices(studentAnswer[2],[true])[0]]] // reference axis\n\nstudent_units:\n studentAnswer[0][len(matchnumber(studentAnswer[0],['plain','en'])[0])..len(studentAnswer[0])]\n\ninterpreted_answers:\n [interpreted_angle, studentAnswer[1], studentAnswer[2], studentAnswer[3]]\n\ngap_feedback (Feedback on each of the gaps):\n map(\n try(\n let(\n result, submit_part(gaps[gap_number][\"path\"],answer),\n gap, gaps[gap_number],\n name, gap[\"name\"], \n noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n assert(name=\"\" or len(gaps)=1,feedback(translate('part.gapfill.feedback header',[\"name\": name])));\n concat_feedback(filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]), if(marks>0,result[\"marks\"]/marks,1), noFeedbackIcon);\n result\n ),\n err,\n fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n ),\n [gap_number,answer,index],\n zip([3,0],[studentAnswer[3], interpreted_angle],[1,2])\n )\n\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Finally, resolve $R_x$ and $R_y$ to find the magnitude and direction of $\\mathbf{R}$.

$R = \\sqrt{{R_x}^2 +{R_y}^2}$ =[[3]]

$\\theta = \\tan^{-1}\\left(\\left|\\dfrac{R_y}{R_x}\\right| \\right)$ = [[0]] measured [[1]] from the [[2]].

", "gaps": [{"type": "angle", "useCustomName": true, "customName": "$\\theta$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(siground(theta,4),'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.2"}}, {"type": "1_n_2", "useCustomName": true, "customName": "dir", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+x axis", "+y axis", "-x axis", "-y axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "engineering-answer", "useCustomName": true, "customName": "$R$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "resultant", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Vector addition of three forces", "extensions": ["geogebra", "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.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

90° = -270° = 450°

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.

Normalize expected_answer with mod 360

A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["angle from reference", "Mechanics", "mechanics", "Statics", "statics", "Vector addition", "vector addition", "Vector Addition"], "metadata": {"description": "

Determine the resultant of three random 2-D vectors.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

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

Determine the resultant of the three forces shown.

", "advice": "

Find the scalar components of the three forces.
Add the scalar components of the components to find the scalar components of the resultant.
$\\begin{align}R_x &= \\Sigma F_x & R_y &= \\Sigma F_y \\\\R_x &= A_x + B_x + C_x & R_y &= A_y + B_y + C_y \\\\R_x &= (\\var{fmt(F_A[0])}) +(\\var{fmt(F_B[0])}) + (\\var{fmt(F_C[0]) }) & R_y &=( \\var{fmt(F_A[1])}) + (\\var{fmt(F_B[1])} )+(\\var{fmt(F_C[1])})\\\\R_x &= \\var{qty(fmt(R[0]),units)} & R_y &=\\var{qty(fmt(R[1]),units)}\\end{align}$
Draw a triangle representing $\\textbf{R}= \\textbf{R}_x + \\textbf{R}_y$,
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}$

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$R$ = [[3]]

$\\theta_R$ = [[0]] measured [[1]] from the [[2]].

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A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["Mechanics", "mechanics", "Statics", "statics", "Vector addition", "vector addition", "Vector Addition"], "metadata": {"description": "

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

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

Three forces act on the bracket at point $A$ as shown: $\\color{darkgreen}{ \\mathbf{A} = \\var{FA}\\ \\var{units[1]}}$, $\\color{blue}{\\mathbf{B} = \\var{FB}\\ \\var{units[1]}}$ and, $\\color{red}{\\mathbf{C} = \\var{FC}\\ \\var{units[1]}}$.

Find the magnitude and direction of the resultant force $\\mathbf{R}$ by summing scalar components.

{geogebra_applet('btgqdpqx', [['A',A],['B',B],['C',C],['α', radians(mod(alpha,360))]])}

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

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

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

Resultant: {R} at {rho} = {forceR}

", "advice": "

Vector Addition:

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

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

$ 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]}

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

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Magnitude of force C

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

Position of point A

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Position of point C

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Position of point B

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Magnitude of force A

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Resultant as a vector

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Magnitude of resultant

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Force C as a vector

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Magnitude of Force B

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

direction of resultant

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

Direction of force B

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force A as a vector

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Direction of force C in degrees

", "templateType": "anything", "can_override": false}, "ForceB": {"name": "ForceB", "group": "Outputs", "definition": "precround(FB *( vector(cos(radians(beta)),sin(radians(beta)))),4)", "description": "

Force B as a vector

", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Inputs", "definition": "random(['ft','lb'],['in','lb'],['cm','N'])", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Inputs", "definition": "random(0..360#5)", "description": "

direction of force A

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(mod(beta,180) - mod(gamma,180)) > 30 and\nabs(mod(beta,180) - mod(alpha,180)) > 30 and\nabs(mod(alpha,180) - mod(gamma,180)) > 30 and\nquadrant(B) <> quadrant(C)\n", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Inputs", "variables": ["A", "B", "C", "alpha", "FA", "FB", "FC", "units", "debug"]}, {"name": "Outputs", "variables": ["ForceA", "beta", "gamma", "ForceB", "ForceC", "ForceR", "rho", "R", "angle_from_ref"]}], "functions": {"direction": {"parameters": [["v", "vector"]], "type": "number", "language": "javascript", "definition": "return Math.atan2(v[1],v[0])"}, "quadrant": {"parameters": [["pt", "vector"]], "type": "anything", "language": "jme", "definition": "let(a,mod(degrees(atan2(pt[1],pt[0])),360),if(a< 90, 1, if(a < 180, 2, (if(a < 270, 3,4)))))"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Components of Components", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

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

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

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

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

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

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

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

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

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "R", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(R,units[1])", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Direction", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "mark:\n if(iscorrect, set_credit(1,\"Correct. \"), set_credit(0, correct_angle))\n\ntarget_angle (the correct angle):\n scalar(gaps[0][\"settings\"][\"correctAnswer\"])\n\nreference (student choice of reference axis: 0,90,180,-90 ):\n answers[2]\n\nanswers0:\n answers[2]\n\nsign (student choice of directions: 1, -1):\n answers[1]\n\nstudent_angle (student input as as standard angle):\n reference + sign * scalar(answers[0])\n\ncorrect_angle:\n \"Correct answer: \" + precround((target_angle-reference)/sign,2) + \"\u00b0 for your selections.\"\n\nisCorrect:\n resultsequal(cos(radians(student_angle)),cos(radians(target_angle)),\"absdiff\", radians(0.1)) and\n resultsequal(sin(radians(student_angle)),sin(radians(target_angle)),\"absdiff\", radians(0.1))\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

$\\theta = \\tan^{-1}\\left(\\left|\\dfrac{R_y}{R_x}\\right| \\right) =$ [[0]]

measured [[1]] from the [[2]].

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "angle", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(rho,\"deg\")", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "1_n_2", "useCustomName": true, "customName": "dir", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_answer:\n [1,-1][indices( studentAnswer,[true])[0]]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_answer:\n [0,90,180,-90][indices(studentAnswer,[true])[0]]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["Positive x axis", "Positive y axis", "Negative x axis", "Negative y axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Vector Addition: no diagram", "extensions": ["quantities", "weh"], "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.

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.

A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["Mechanics", "mechanics", "Statics", "statics", "vector addition", "Vector Addition", "Vector addition"], "metadata": {"description": "

Sum three force vectors based on a written description of the situation.

", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "

Given: Three forces act on particle $P$.

Force $\\textbf{A}$ has a magnitude of {qty(A,unit)} and acts {theta}° CCW from the {dirA[0]}.
Force $\\textbf{B}$ has a magnitude of {qty(B,unit)} and acts along a ray from point $P$ with a slope of $\\dfrac{\\var{rise}}{\\var{run}}$.
Force $\\textbf{C}$ has a magnitude of {qty(C,unit)} and acts straight {dirC[0]}.

", "advice": "

Given

$\\mathbf{A}$ = {A} {unit} at {alpha}°

$\\mathbf{B}$ = {B} {unit} at {precround(beta,2)}°

$\\mathbf{C}$ = {C} {unit} at {gamma}°

Find Scalar Components

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

	$F_x$	$F_y$
$\\mathbf{A}$	{precround(Ax,2)} {unit}	{precround(Ay,2)} {unit}
$\\mathbf{B}$	{precround(Bx,2)} {unit}	{precround(By,2)} {unit}
$\\mathbf{C}$	{precround(Cx,2)} {unit}	{precround(Cy,2)} {unit}

Find rectangular components of the Resultant

$R_x = A_x + B_x +C_x = \\var{precround(Rx,2)}$ {unit}

$R_y = A_y + B_y +C_y = \\var{precround(Ry,2)}$ {unit}

Find the Magnitude of the Resultant

$R = \\sqrt{{R_x}^2 + {R_y}^2} = \\var{precround(R,2)}$ {unit}

Find the Direction of the Resultant

The angle in a right triangle with sides of length $R_x$ and $R_y$ is

$\\alpha = \\arctan{\\left|\\dfrac{R_y}{R_x}\\right|} = \\var{siground(degrees(arctan(abs(Ry/Rx))),4)}$°

Since $R_x = \\var{siground(qty(Rx,unit),3)}$ and $R_y = \\var{siground(qty(Ry,unit),3)}$ force $\\textbf{R}$ points {if(Rx > 0, \"right\", \"left\")} and {if(Ry > 0, \"up\", \"down\")}, therefore the angle between $\\textbf{R}$ and the positive $x$ axis is:

$\\theta = \\var{(if(Rx>0,if(Ry > 0, \"$\\\\alpha$\",\"$-\\\\alpha$\"),if(Ry > 0, \"$180°-\\\\alpha$\", \"$-180° + \\\\alpha$\")))} = \\var{siground(theta_r,4)} $°

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Magnitude of force A

", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "random(30..80#10)", "description": "", "templateType": "anything", "can_override": false}, "unit": {"name": "unit", "group": "Ungrouped variables", "definition": "random(['N','lb'])", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "random(10..60#5)", "description": "", "templateType": "anything", "can_override": false}, "dirC": {"name": "dirC", "group": "Ungrouped variables", "definition": "random(['left',180],['right',0],['up',90],['down',270])", "description": "

Description and angle for direction of B

", "templateType": "anything", "can_override": false}, "rise": {"name": "rise", "group": "Ungrouped variables", "definition": "random([-1,-3,-4,1,3,4])", "description": "", "templateType": "anything", "can_override": false}, "run": {"name": "run", "group": "Ungrouped variables", "definition": "random([-1,-3,-4,1,3,4])", "description": "", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Ungrouped variables", "definition": "random([30,60])", "description": "", "templateType": "anything", "can_override": false}, "dirA": {"name": "dirA", "group": "Ungrouped variables", "definition": "random([\n [\"positive $x$ axis\",0+theta],\n [\"positive $y$ axis\",90+theta],\n [\"negative $x$ axis\",180+theta],\n [\"negative $y$ axis\",270+theta]])\n \n \n ", "description": "

Description and angle for direction of A

", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Ungrouped variables", "definition": "dirA[1]", "description": "", "templateType": "anything", "can_override": false}, "beta": {"name": "beta", "group": "Ungrouped variables", "definition": "degrees(atan2(rise,run))", "description": "", "templateType": "anything", "can_override": false}, "gamma": {"name": "gamma", "group": "Ungrouped variables", "definition": "dirC[1]", "description": "", "templateType": "anything", "can_override": false}, "ax": {"name": "ax", "group": "answers", "definition": "A cos(radians(alpha))", "description": "", "templateType": "anything", "can_override": false}, "bx": {"name": "bx", "group": "answers", "definition": "B cos(radians(beta))", "description": "", "templateType": "anything", "can_override": false}, "cx": {"name": "cx", "group": "answers", "definition": "precround(C cos(radians(gamma)),6)", "description": "", "templateType": "anything", "can_override": false}, "ay": {"name": "ay", "group": "answers", "definition": "A sin(radians(alpha))", "description": "", "templateType": "anything", "can_override": false}, "by": {"name": "by", "group": "answers", "definition": "B sin(radians(beta))", "description": "", "templateType": "anything", "can_override": false}, "cy": {"name": "cy", "group": "answers", "definition": "precround(C sin(radians(gamma)),5)", "description": "

precround to avoid precision errors 0 != 0.00000000000000213

", "templateType": "anything", "can_override": false}, "rx": {"name": "rx", "group": "answers", "definition": "ax+bx+cx", "description": "", "templateType": "anything", "can_override": false}, "ry": {"name": "ry", "group": "answers", "definition": "ay+by+cy", "description": "", "templateType": "anything", "can_override": false}, "R": {"name": "R", "group": "answers", "definition": "sqrt(rx^2+ry^2)", "description": "", "templateType": "anything", "can_override": false}, "theta_R": {"name": "theta_R", "group": "answers", "definition": "degrees(atan2(ry,rx))", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(rise) <> abs(run) and\nRx <>0 and\nRy <>0", "maxRuns": 100}, "ungrouped_variables": ["A", "B", "unit", "C", "rise", "run", "theta", "dirA", "dirC", "alpha", "beta", "gamma", "debug"], "variable_groups": [{"name": "answers", "variables": ["ax", "bx", "cx", "ay", "by", "cy", "rx", "ry", "R", "theta_R"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Find Rectangular Components", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Draw a neat, scaled, labeled diagram representing particle $P$ and the three forces acting on it.
Find the scalar components of $\\textbf{A}, \\textbf{B}$, and $\\textbf{C}$. Remember, scalar components use a sign to indicate direction along their line of action.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Force	$x$	$y$
$\\textbf{A}$	[[0]]	[[1]]
$\\textbf{B}$	[[2]]	[[3]]
$\\textbf{C}$	[[4]]	[[5]]

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

	x	y
A	{precround(Ax,2)} {unit}	{precround(Ay,2)} {unit}
B	{precround(Bx,2)} {unit}	{precround(By,2)} {unit}
C	{precround(Cx,2)} {unit}	{precround(Cy,2)} {unit}
R	{precround(Rx,2)} {unit}	{precround(Ry,2)} {unit}

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Draw a neat, labeled, scaled digram representing the tip-to-tail vector addition $\\textbf{R} = \\textbf{A} + \\textbf{B} + \\textbf{C}$.
Add the three vectors to find the scalar components of the resultant.
$\\qquad R_x =$ [[0]] $R_y = $ [[1]]
Find the magnitude of the resultant $\\textbf{R}$ and the angle it makes with the positive $x$-axis.
$\\qquad R=$ [[2]] $\\theta =$ [[3]] $(-180° \\le \\theta \\le 180°)$

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Angle as a quantity in degrees.

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": 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.

Accepts '°' and 'deg' as units.

Penalizes if not close enough or no units.

90° = -270° = 450°

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.

Normalize expected_answer with mod 360

A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.

Modify the unit portion of the student's answer by

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

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to allow answers like 10 ft-lb and 30°

This fixes the student answer for two common errors.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If student makes both errors, only one gets fixed.

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": [["question-resources/easy_vectors.ggb", "/srv/numbas/media/question-resources/easy_vectors.ggb"]]}