Angle as a quantity in degrees.
", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['correct_quantity'])", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\ncorrect_scalar:\nscalar(correct_quantity)\n \n\ncorrect_quantity:\nsettings['correct_quantity']\n\ncorrect_units:\nunits(correct_quantity)\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\njoin(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_quantity),\nmsg,\nfeedback(msg);false)\n\nstudent_quantity:\nswitch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)\n\nangle_in_range:\nif(settings['restrict_angle'], abs(student_scalar) <= 90, true)\n\nright:\nwithinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])\n\nclose:\nwithinTolerance(student_scalar, correct_scalar, settings['close'])", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)"}, {"name": "correct_scalar", "description": "", "definition": "scalar(correct_quantity)\n "}, {"name": "correct_quantity", "description": "", "definition": "settings['correct_quantity']"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "", "definition": "join(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_quantity),\nmsg,\nfeedback(msg);false)"}, {"name": "student_quantity", "description": "", "definition": "switch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity)"}, {"name": "angle_in_range", "description": "", "definition": "if(settings['restrict_angle'], abs(student_scalar) <= 90, true)"}, {"name": "right", "description": "Will check for correct sign elswhere.
", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "Must have correct sign to be close.
", "definition": "withinTolerance(student_scalar, correct_scalar, settings['close'])\n"}], "settings": [{"name": "correct_quantity", "label": "Correct Angle as quantity ", "help_url": "", "hint": "", "input_type": "code", "default_value": "qty(45,'deg')", "evaluate": true}, {"name": "right", "label": "Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within ± this amount from the correct value.", "input_type": "code", "default_value": "0.1", "evaluate": true}, {"name": "restrict_angle", "label": "Less than 90\u00b0", "help_url": "", "hint": "When checked, angle must be between -90° and +90°.", "input_type": "checkbox", "default_value": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.", "input_type": "percent", "default_value": "75"}, {"name": "close", "label": " Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within ± this amount from the correct value.", "input_type": "code", "default_value": "0.5", "evaluate": true}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value without units.", "input_type": "percent", "default_value": "25"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto 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.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf 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%,Find the scalar components of the component forces A, B, and C.
\n$A_x =$ [[0]] $B_x =$ [[2]] $C_x =$ [[4]]
\n$A_y =$ [[1]] $B_y =$ [[3]] $C_y =$ [[5]]
", "marks": 0, "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "engineering-answer", "settings": {"correctAnswer": "qty(ForceR[0],units[1])", "C3": "25", "right": "0.2", "close": "1.0", "C2": "50", "C1": "75"}, "customMarkingAlgorithm": "", "marks": "2", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "engineering-answer", "settings": {"correctAnswer": "qty(ForceR[1],units[1])", "C3": "25", "right": "0.2", "close": "1.0", "C2": "50", "C1": "75"}, "customMarkingAlgorithm": "", "marks": "2", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}], "showCorrectAnswer": true, "type": "gapfill", "sortAnswers": false, "customMarkingAlgorithm": "", "prompt": "Sum the scalar components to get the scalar components of the resultant R.
\n$R_x = \\Sigma F_x = A_x + B_x + C_x =$ [[0]]
\n$R_y = \\Sigma F_y = A_y + B_y + C_y =$ [[1]]
", "marks": 0, "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "engineering-answer", "settings": {"correctAnswer": "qty(R,units[1])", "C3": "25", "right": "0.2", "close": "1.0", "C2": "50", "C1": "75"}, "customMarkingAlgorithm": "", "marks": "2", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {"mark": {"order": "after", "script": "index = Numbas.jme.unwrapValue(this.studentAnswerAsJME());\nangles = Numbas.jme.unwrapValue(Numbas.exam.currentQuestion.scope.getVariable('angle_from_ref'));\nans = Qty(angles[index],'deg');\nthis.parentPart.gaps[2].settings.correct_quantity.value= ans;\nthis.markingComment(\"For your axis, the direction is \" + ans.toPrec('0.1 deg') +'.');"}}, "showCorrectAnswer": true, "type": "drop-down-axis-reference", "settings": {"dummy": "'ignore'"}, "customMarkingAlgorithm": "", "marks": "0", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "angle-quantity-from-reference", "settings": {"correct_quantity": "qty(angle_from_ref[0],'deg')", "C3": "25", "restrict_angle": true, "right": "0.2", "close": "1.01", "C2": "50", "C1": "75"}, "customMarkingAlgorithm": "", "marks": "2", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}], "showCorrectAnswer": true, "type": "gapfill", "sortAnswers": false, "customMarkingAlgorithm": "", "prompt": "Resolve $R_x$ and $R_y$ to find the magnitude and direction of R.
\n$R = \\sqrt{{R_x}^2 +{R_y}^2}$ = [[0]]
\n$\\theta = \\tan^{-1}\\left(\\left|\\dfrac{R_y}{R_x}\\right| \\right)$ = [[2]] measured from the [[1]]
\n{angle_from_ref}
", "marks": 0, "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}], "variables": {"angle_from_ref": {"definition": "let(ang,rho,\n[if(ang>180,ang-360,ang),\nif(ang>270,ang-450,if(ang < -90,ang+270,ang-90)),\nif(ang>0,ang-180,ang+180),\nif(ang>90,ang-270,90+ang)])", "description": "", "templateType": "anything", "group": "Outputs", "name": "angle_from_ref"}, "FA": {"definition": "random(10..100#5)", "description": "Magnitude of force A
", "templateType": "anything", "group": "Inputs", "name": "FA"}, "units": {"definition": "random(['cm','N'],['cm','N'],['cm','N'])", "description": "", "templateType": "anything", "group": "Inputs", "name": "units"}, "alpha": {"definition": "(random(-80..175#5 except[45,135,-45,80,100]))", "description": "direction of force A
", "templateType": "anything", "group": "Inputs", "name": "alpha"}, "ForceR": {"definition": "ForceA+ForceB+ForceC", "description": "Resultant as a vector
", "templateType": "anything", "group": "Outputs", "name": "ForceR"}, "A": {"definition": "vector(0,0)", "description": "Position of point A
", "templateType": "anything", "group": "Inputs", "name": "A"}, "gamma": {"definition": "degrees(direction(vector(C[0]-A[0],C[1]-A[1])))", "description": "Direction of force C in degrees
", "templateType": "anything", "group": "Outputs", "name": "gamma"}, "C": {"definition": "vector(random(1,-1)random(2..6),random(1,-1)random(2..6))", "description": "Position of point C
", "templateType": "anything", "group": "Inputs", "name": "C"}, "ForceB": {"definition": "FB *( vector(cos(radians(beta)),sin(radians(beta))))", "description": "Force B as a vector
", "templateType": "anything", "group": "Outputs", "name": "ForceB"}, "ForceA": {"definition": "FA *( vector(cos(radians(alpha)),sin(radians(alpha))))", "description": "force A as a vector
", "templateType": "anything", "group": "Outputs", "name": "ForceA"}, "beta": {"definition": "degrees(direction(vector(B[0]-A[0],B[1]-A[1])))", "description": "Direction of force B
", "templateType": "anything", "group": "Outputs", "name": "beta"}, "FC": {"definition": "random(10..100#5)", "description": "Magnitude of force C
", "templateType": "anything", "group": "Inputs", "name": "FC"}, "B": {"definition": "vector( random(1,-1) random(4..10),random(1,-1) random(2..5))", "description": "Position of point B
", "templateType": "anything", "group": "Inputs", "name": "B"}, "ForceC": {"definition": "FC *( vector(cos(radians(gamma)),sin(radians(gamma))))", "description": "Force C as a vector
", "templateType": "anything", "group": "Outputs", "name": "ForceC"}, "FB": {"definition": "random(10..100#10)", "description": "Magnitude of Force B
", "templateType": "anything", "group": "Inputs", "name": "FB"}, "R": {"definition": "sqrt(ForceR[0]^2+forceR[1]^2)", "description": "Magnitude of resultant
", "templateType": "anything", "group": "Outputs", "name": "R"}, "debug": {"definition": "false", "description": "", "templateType": "anything", "group": "Inputs", "name": "debug"}, "rho": {"definition": "degrees(direction(ForceR))", "description": "direction of resultant
", "templateType": "anything", "group": "Outputs", "name": "rho"}}, "advice": "Vector Addition:
\n$R_x = \\Sigma F_x = (\\var{siground(ForceA[0],4)}) + (\\var{siground(ForceB[0],4)}) +( \\var{siground(ForceC[0],4)}) = \\var{siground(ForceR[0],4)}$ {units[1]}
\n$R_y = \\Sigma F_y = (\\var{siground(ForceA[1],4)}) + (\\var{siground(ForceB[1],4)}) +( \\var{siground(ForceC[1],4)}) = \\var{siground(ForceR[1],4)}$ {units[1]}
\n\n$ R=\\sqrt{R_x^2 + R_y^2} = \\sqrt{(\\var{siground(ForceR[0],4)})^2 +(\\var{siground(ForceR[0],4)})^2} = \\var{siground(abs(ForceR),4)}$ {units[1]}
\n\n$\\theta = \\tan^{-1}\\left(\\left|\\frac{R_y}{R_x}\\right| \\right) = \\tan^{-1}\\left(\\left|\\frac{\\var{siground(ForceR[1],4)}}{\\var{siground(ForceR[0],4)}}\\right| \\right) = \\var{siground(degrees(arctan(abs(forceR[1])/forceR[0])),4)}° = (\\var{siground(rho,4)}° $ from the positive x-axis.)
", "statement": "Three forces act on the bracket at point A: A = {FA} {units[1]}, B = {FB} {units[1]} and, C = {FC} {units[1]}.
\n(The diagram may take a moment or two to load - give it chance)
\nFind the magnitude and direction of the resultant force R by summing scalar components.
\nEnter your magnitude quatities in SI units, eg. 500 N and give 2 d.p.
\n{geogebra_applet('dtf3t2dp', [['A',A],['B',B],['C',C],['F_a',FA],['F_b',FB],['F_c',FC],['α', alpha],['unit','\"'+units[0]+'\"']])}
\n\nForce A: {fa} at {alpha} = {forceA}
\nForce B: {fb} at {beta} = {forceB}
\nForce C: {fc} at {gamma} = {forceC}
\nResultant: {R} at {rho} = {forceR}
", "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"}, "type": "question", "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}