// Numbas version: finer_feedback_settings {"name": "Vector Quiz", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-shuffled", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], [], []], "questions": [{"name": "Rachel's copy of Parallelogram Rule", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 24, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/24/edit"}, "name": "Angle quantity", "short_name": "angle-quantity-from-reference", "description": "

Angle as a quantity in degrees.

", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['correct_quantity'])", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, 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(\nkind(quantity(1, student_units))= kind(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 angle, 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(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)"}, {"name": "student_quantity", "description": "", "definition": "switch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity)"}, {"name": "angle_in_range", "description": "", "definition": "if(settings['restrict_angle'], abs(student_scalar) <= 90, true)"}, {"name": "right", "description": "

Will check for correct sign elswhere.

", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "

Must have correct sign to be close.

", "definition": "withinTolerance(student_scalar, correct_scalar, settings['close'])\n"}], "settings": [{"name": "correct_quantity", "label": "Correct Angle as quantity ", "help_url": "", "hint": "", "input_type": "code", "default_value": "qty(45,'deg')", "evaluate": true}, {"name": "right", "label": "Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within ± this amount from the correct value.", "input_type": "code", "default_value": "0.1", "evaluate": true}, {"name": "restrict_angle", "label": "Less than 90\u00b0", "help_url": "", "hint": "When checked, angle must be between -90° and +90°.", "input_type": "checkbox", "default_value": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.", "input_type": "percent", "default_value": "75"}, {"name": "close", "label": " Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within ± this amount from the correct value.", "input_type": "code", "default_value": "0.5", "evaluate": true}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value without units.", "input_type": "percent", "default_value": "25"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "

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

", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n\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)"}, {"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/"}, {"name": "Rachel Store", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/31776/"}], "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 vector components $\\mathbf{A}$ and $\\mathbf{B}$ where $\\mathbf{A}$ has a magnitude of {qty(round(abs(A)),units)} and points {alpha}° from the positive x-axis, and $\\mathbf{B}$ has a magnitude of {qty(round(abs(B)),units)} pointing {beta}° from positive the x-axis.

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

", "advice": "

{applet}

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "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": ".GeoGebraFrame {border-width: 0px !important; background-color: var(--background-color) !important;}"}, "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": "precround(qty(abs(R),units),1)", "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, "j": false}, "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: 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°

", "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", "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", "type": "question"}, {"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": "

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

Forces $\\mathbf{A}$ and $\\mathbf{B}$ point in the directions shown and have magnitudes $A = \\var{qty(2 FB, units)}$ and $B = \\var{qty(FB,units)}$.

Graphical Solution: Using a ruler and protractor, carefully draw a neat, labeled, accurately scaled parallelogram representing the vector addition $\\mathbf{R} = \\mathbf{A}+\\mathbf{B}$. Based on your scaled diagram, estimate the magnitude of resultant and its direction from positive $x$-axis.

Exact Solution: Let the three angles inside the triangle be called $\\theta_A$, $\\theta_B$, and $\\theta_R$, where the subscripts are the names of the sides opposite, and then use trigonometry to find the angles and the magnitude of the resultant exactly.

", "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, "j": false}, "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": "Inputs", "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}, "ang": {"name": "ang", "group": "Ungrouped variables", "definition": "(a)-> precround(qty(a, \"deg\"),1)", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "true", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(dirA- dirB) > 25 and abs(dirA-dirB) < 160 ", "maxRuns": "200"}, "ungrouped_variables": ["thetaA", "thetaB", "thetaR", "ang", "debug"], "variable_groups": [{"name": "Inputs", "variables": ["FB", "dirB", "Ax", "Ay", "dirA", "units"]}, {"name": "Results", "variables": ["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": "

$|\\mathbf{R}|$ = [[1]]

$\\theta_x$ = [[0]]

", "gaps": [{"type": "angle", "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": {"expected_answer": "ang(dirR)", "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": "precround(qty(abs(R),units),0)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "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": "

$\\theta_A =$ [[0]]

$\\theta_B = $[[1]]

$\\theta_R =$ [[2]]

$|\\mathbf{R}| =$ [[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": "ang(thetaA)", "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": "ang(thetaB)", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.1"}}, {"type": "angle", "useCustomName": true, "customName": "$\\theta_R$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "ang(thetaR)", "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": "Parallelogram Rule: Pull Stake", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 24, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/24/edit"}, "name": "Angle quantity", "short_name": "angle-quantity-from-reference", "description": "

Angle as a quantity in degrees.

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": ["question-resources/triangle_j1bJHMI.svg"], "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", "parallelogram rule", "Statics", "statics", "Vector addition", "vector addition", "Vector Addition"], "metadata": {"description": "

Use the parallelogram rule to solve a force triangle.

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

Two forces are used to pull a stake from the ground as shown.

{geogebra_applet('keqyzya4',[theta: theta + \"°\", textA: '\"' + A + \"\\\\text\\{ \" + units + '\\}\"',textB: '\"' + B + \"\\\\text\\{ \" + units + '\\}\"'])}

Use the parallelogram rule and trigonometry to find the angle $\\alpha$ which makes the resultant of the two forces vertical, and the corresponding magnitude of the resultant.

", "advice": "

1. Draw a triangle or parallellogram representing the situation, and let

$ A = \\var{qty(A,units)}$, $ B = \\var{qty(B,units)}$ and $\\theta =\\var{theta}°$.

(diagram not to scale)

2. Use Law of Sines to find angle $\\alpha$.

$\\dfrac{B}{\\sin \\alpha} = \\dfrac{A}{\\sin\\theta}$

$\\dfrac{\\var{B}}{\\sin \\alpha} = \\dfrac{\\var{A}}{\\sin (\\var{theta}°)}$

$\\alpha = \\var{precround(alpha,1)}°$

3. Find remaining angle in triangle

$\\phi = 180° - \\alpha - \\beta = \\var{precround(phi,1)} °$

4. Use Law of Cosines to find $R$.

$R^2 =A^2 + B^2 - 2 A B \\cos \\phi$

$R^2 = \\var{A}^2 + \\var{B}^2 - 2 A B \\cos \\var{precround(phi,1)}°$

$ R = \\var{precround(qty(R,units),2)}$

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"applet": {"name": "applet", "group": "Ungrouped variables", "definition": "geogebra_applet('keqyzya4',[theta: theta + \"\u00b0\", \n textA: '\"' + A + \"\\\\text\\{ \" + units + '\\}\"',\n textB: '\"' + B + \"\\\\text\\{ \" + units + '\\}\"'])", "description": "

not used because this method doesn't resume correctly

", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Ungrouped variables", "definition": "random(25..55) ", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "random(10..60#5)", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "random(10..60#5)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "\"lb\"", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Unnamed group", "definition": "degrees(arcsin(B/A sin(radians(theta))))", "description": "", "templateType": "anything", "can_override": false}, "R": {"name": "R", "group": "Unnamed group", "definition": "A cos(radians(alpha)) + B cos(radians(theta))", "description": "", "templateType": "anything", "can_override": false}, "phi": {"name": "phi", "group": "Unnamed group", "definition": "180-alpha-theta", "description": "", "templateType": "anything", "can_override": false}, "R'": {"name": "R'", "group": "Unnamed group", "definition": "sqrt(A^2 + B^2 - 2 A B cos(radians(phi)))", "description": "

Check using law of cosines

", "templateType": "anything", "can_override": false}, "check": {"name": "check", "group": "Unnamed group", "definition": "R=R'", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "A<>B and\nB/A sin(radians(theta)) < 1", "maxRuns": 100}, "ungrouped_variables": ["applet", "theta", "A", "B", "units"], "variable_groups": [{"name": "Unnamed group", "variables": ["alpha", "R", "phi", "R'", "check"]}], "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": "

$\\alpha = $ [[0]]

$R = $ [[1]]

", "gaps": [{"type": "angle-quantity-from-reference", "useCustomName": true, "customName": "$\\alpha$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correct_quantity": "precround(qty(alpha,'deg'),2)", "right": "0.2", "restrict_angle": true, "C1": "75", "close": "1.0", "C2": "50", "C3": "25"}}, {"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": "qty(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"], "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, "j": false}, "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)\ngeogebra_applet(\"ehwmftxq\",params)", "description": "

for testing only delete later

", "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", "BC", "AB", "CA"], "variable_groups": [{"name": "Inputs", "variables": ["FA", "FB", "FC", "units", "scale", "B1", "A1", "C1", "B2", "A2", "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, "showBlankOption": true, "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, "showBlankOption": true, "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}$

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"C": {"name": "C", "group": "Inputs", "definition": "random([vector(random([4,-4]),random(-4..4)),vector(random(-4..4),random([4,-4]))])", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Inputs", "definition": "random([vector(random([4,-4]),random(-4..4)),vector(random(-4..4),random([4,-4]))])", "description": "", "templateType": "anything", "can_override": false}, "F_B": {"name": "F_B", "group": "Forces", "definition": "MB B/abs(B)", "description": "", "templateType": "anything", "can_override": false}, "F_C": {"name": "F_C", "group": "Forces", "definition": "MC C/abs(C)\n", "description": "", "templateType": "anything", "can_override": false}, "MA": {"name": "MA", "group": "Inputs", "definition": "random(10..50)\n", "description": "", "templateType": "anything", "can_override": false}, "R": {"name": "R", "group": "Forces", "definition": "(F_A+F_B+F_C)", "description": "", "templateType": "anything", "can_override": false}, "MC": {"name": "MC", "group": "Inputs", "definition": "random(10..50)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Inputs", "definition": "random(['lb','N','kN'])", "description": "", "templateType": "anything", "can_override": false}, "O": {"name": "O", "group": "Inputs", "definition": "vector(0,0)", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Inputs", "definition": "random([vector(random([4,-4]),random(-4..4)),vector(random(-4..4),random([4,-4]))])", "description": "", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Forces", "definition": "degrees(atan2(R[1],R[0]))", "description": "", "templateType": "anything", "can_override": false}, "F_A": {"name": "F_A", "group": "Forces", "definition": "MA A /abs(A)", "description": "", "templateType": "anything", "can_override": false}, "MB": {"name": "MB", "group": "Inputs", "definition": "random(10..50)", "description": "", "templateType": "anything", "can_override": false}, "R_mag": {"name": "R_mag", "group": "Forces", "definition": "qty(abs(R),units)", "description": "", "templateType": "anything", "can_override": false}, "angle": {"name": "angle", "group": "Forces", "definition": "abs(degrees(arctan(R[1]/R[0])))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "A <> B and B <> C and C <> A and\nMA < 10 abs(A) and\nMB < 10 abs(B) and\nMC < 10 abs(C)", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Inputs", "variables": ["O", "A", "B", "C", "MA", "MB", "MC", "units"]}, {"name": "Forces", "variables": ["F_A", "F_B", "F_C", "R", "theta", "R_mag", "angle"]}], "functions": {"fmt": {"parameters": [["v", "number"]], "type": "number", "language": "jme", "definition": "siground(v,3)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Answers", "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": "

$R$ = [[3]]

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

", "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": "precround(qty(theta,'deg'),1)", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.2"}}, {"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, "showBlankOption": true, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Reference", "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, "showBlankOption": true, "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": "R_mag", "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: no diagram", "extensions": ["quantities"], "custom_part_types": [{"source": {"pk": 24, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/24/edit"}, "name": "Angle quantity", "short_name": "angle-quantity-from-reference", "description": "

Angle as a quantity in degrees.

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%,
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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

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Description and angle for direction of B

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Description and angle for direction of A

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precround to avoid precision errors 0 != 0.00000000000000213

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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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$\\boldsymbol{\\hat{a}}=($[[0]]$,$[[1]]$,$[[2]]$)$. (Enter your answers to 3d.p.)

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Find a unit vector $\\boldsymbol{\\hat{a}}$, which is parallel to $\\boldsymbol{u}=\\pmatrix{\\var{u[0]},\\var{u[1]},\\var{u[2]}}$.

", "tags": ["checked2015", "vector", "Vector"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Find the unit vector parallel to a given vector.

Interim calculations in Advice should be presented in enough accuracy to ensure that the final calculations are to 3dps.

"}, "advice": "

Note that in this advice, the full calculator display is used in the calculation of each step; any rounding is purely for display clarity.

There is only one unit vector parallel to a vector $\\boldsymbol{u}=\\pmatrix{u_1,u_2,u_3}$, namely the unit vector $\\boldsymbol{\\hat{u}}=\\boldsymbol{u}/\\lvert\\boldsymbol{u}\\rvert$, where $\\lvert\\boldsymbol{u}\\rvert=\\sqrt{u_1^2+u_2^2+u_3^2}$.

In this question $\\lvert\\boldsymbol{u}\\rvert=\\sqrt{(\\var{u[0]})^2+(\\var{u[1]})^2+(\\var{u[2]})^2}=\\var{precround(lenu,3)}$, and so $\\boldsymbol{\\hat{a}}=\\boldsymbol{\\hat{u}}=\\frac{1}{\\var{precround(lenu,3)}}\\pmatrix{\\var{u[0]},\\var{u[1]},\\var{u[2]}}=\\pmatrix{\\var{unitu[0]},\\var{unitu[1]},\\var{unitu[2]}}$ to 3d.p.

There is also an anti-parallel unit vector $-\\boldsymbol{\\hat{u}}=\\pmatrix{\\var{-unitu[0]},\\var{-unitu[1]},\\var{-unitu[2]}}$.

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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"], ["question-resources/triangle_j1bJHMI.svg", "/srv/numbas/media/question-resources/triangle_j1bJHMI.svg"]]}