// Numbas version: finer_feedback_settings
{"name": "Vector addition by summing scalar components", "extensions": ["geogebra", "weh", "quantities"], "custom_part_types": [{"source": {"pk": 24, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/24/edit"}, "name": "Angle quantity", "short_name": "angle-quantity-from-reference", "description": "<p>Angle&nbsp;as a quantity in degrees.</p>", "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": "<p>Will check for correct sign elswhere.</p>", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "<p>Must have correct sign to be close.</p>", "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 &plusmn; 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&deg; and +90&deg;.", "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 &plusmn; 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": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "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": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "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": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "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": "<p>Only marked close if the student actually has the right sign.</p>", "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. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;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.<br />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.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "variable_groups": [{"variables": ["A", "B", "C", "alpha", "FA", "FB", "FC", "units", "debug"], "name": "Inputs"}, {"variables": ["ForceA", "beta", "gamma", "ForceB", "ForceC", "ForceR", "rho", "R", "angle_from_ref"], "name": "Outputs"}], "tags": ["mechanics", "statics", "vector addition"], "name": "Vector addition by summing scalar components", "functions": {"direction": {"parameters": [["v", "vector"]], "language": "javascript", "definition": "return Math.atan2(v[1],v[0])", "type": "number"}}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "<p>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</p>"}, "ungrouped_variables": [], "parts": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "gaps": [{"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(forceA[0],units[1])", "right": "0.2", "C2": "50", "C1": "75", "C3": "25", "close": "1.0"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "engineering-answer", "unitTests": [], "variableReplacements": [], "scripts": {}, "marks": "4"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(forceA[1],units[1])", "right": "0.2", "C2": "50", "C1": "75", "C3": "25", "close": "1.0"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "engineering-answer", "unitTests": [], "variableReplacements": [], "scripts": {}, "marks": "4"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(forceB[0],units[1])", "right": "0.2", "C2": "50", "C1": "75", "C3": "25", "close": "1.0"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "engineering-answer", "unitTests": [], "variableReplacements": [], "scripts": {}, "marks": "4"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(forceB[1],units[1])", "right": "0.2", "C2": "50", "C1": "75", "C3": "25", "close": "1.0"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "engineering-answer", "unitTests": [], "variableReplacements": [], "scripts": {}, "marks": "4"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(forceC[0],units[1])", "right": "0.2", "C2": "50", "C1": "75", "C3": "25", "close": "1.0"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "engineering-answer", "unitTests": [], "variableReplacements": [], "scripts": {}, "marks": "4"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(forceC[1],units[1])", "right": "0.2", "C2": "50", "C1": "75", "C3": "25", "close": "1.0"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "engineering-answer", "unitTests": [], "variableReplacements": [], "scripts": {}, "marks": "4"}], "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "scripts": {}, "type": "gapfill", "prompt": "<p>Find the scalar components of the component forces <strong>A</strong>, <strong>B</strong>, and <strong>C</strong>.&nbsp;</p>\n<p>$A_x =$&nbsp;[[0]]&nbsp; $B_x =$&nbsp;[[2]]&nbsp; $C_x =$&nbsp;[[4]]</p>\n<p>$A_y =$&nbsp;[[1]]&nbsp; $B_y =$&nbsp;[[3]]&nbsp; $C_y =$&nbsp;[[5]]</p>"}, {"variableReplacementStrategy": "originalfirst", "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "gaps": [{"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(ForceR[0],units[1])", "right": "0.2", "C2": "50", "C1": "75", "C3": "25", "close": "1.0"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "engineering-answer", "unitTests": [], "variableReplacements": [], "scripts": {}, "marks": "4"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(ForceR[1],units[1])", "right": "0.2", "C2": "50", "C1": "75", "C3": "25", "close": "1.0"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "engineering-answer", "unitTests": [], "variableReplacements": [], "scripts": {}, "marks": "4"}], "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "scripts": {}, "type": "gapfill", "prompt": "<p>Sum the scalar components to get&nbsp;the scalar components of the resultant <strong>R</strong>.</p>\n<p>$R_x = \\Sigma F_x &nbsp;= A_x + B_x + C_x =$&nbsp;[[0]]&nbsp;</p>\n<p>$R_y = \\Sigma F_y &nbsp;= A_y + B_y + C_y =$ [[1]]&nbsp;&nbsp;</p>"}, {"variableReplacementStrategy": "originalfirst", "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "gaps": [{"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(R,units[1])", "right": "0.2", "C2": "50", "C1": "75", "C3": "25", "close": "1.0"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "engineering-answer", "unitTests": [], "variableReplacements": [], "scripts": {}, "marks": "4"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "settings": {"dummy": "'ignore'"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "drop-down-axis-reference", "unitTests": [], "variableReplacements": [], "scripts": {"mark": {"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') +'.');", "order": "after"}}, "marks": "0"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "settings": {"correct_quantity": "qty(angle_from_ref[0],'deg')", "restrict_angle": true, "C2": "50", "right": "0.2", "C1": "75", "C3": "25", "close": "1.01"}, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "angle-quantity-from-reference", "unitTests": [], "variableReplacements": [], "scripts": {}, "marks": "4"}], "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "scripts": {}, "type": "gapfill", "prompt": "<p>Resolve&nbsp;$R_x$ and $R_y$ to find the magnitude and direction of <strong>R</strong>.</p>\n<p>$R = \\sqrt{{R_x}^2 +{R_y}^2}$ =&nbsp;[[0]]&nbsp;</p>\n<p>&nbsp;$\\theta = \\tan^{-1}\\left(\\left|\\dfrac{R_y}{R_x}\\right| \\right)$ =&nbsp;[[2]]&nbsp; measured from the&nbsp;&nbsp;[[1]]</p>\n<p><span data-jme-visible=\"debug\">{angle_from_ref}</span></p>"}], "variablesTest": {"maxRuns": 100, "condition": "B[0]<>C[0] and B[1]<>C[1] and abs(alpha-beta) >= 15 and abs(gamma-beta) >= 15 and  abs(gamma-alpha) >= 15"}, "variables": {"ForceB": {"name": "ForceB", "description": "<p>Force B as a vector</p>", "definition": "FB *( vector(cos(radians(beta)),sin(radians(beta))))", "templateType": "anything", "group": "Outputs"}, "C": {"name": "C", "description": "<p>Position of point C</p>", "definition": "vector(random(1,-1)random(2..6),random(1,-1)random(2..6))", "templateType": "anything", "group": "Inputs"}, "FC": {"name": "FC", "description": "<p>Magnitude of force C</p>", "definition": "random(10..100#5)", "templateType": "anything", "group": "Inputs"}, "ForceR": {"name": "ForceR", "description": "<p>Resultant as a vector</p>", "definition": "ForceA+ForceB+ForceC", "templateType": "anything", "group": "Outputs"}, "FA": {"name": "FA", "description": "<p>Magnitude of force A</p>", "definition": "random(10..100#5)", "templateType": "anything", "group": "Inputs"}, "beta": {"name": "beta", "description": "<p>Direction of force B</p>", "definition": "degrees(direction(vector(B[0]-A[0],B[1]-A[1])))", "templateType": "anything", "group": "Outputs"}, "R": {"name": "R", "description": "<p>Magnitude of resultant</p>", "definition": "sqrt(ForceR[0]^2+forceR[1]^2)", "templateType": "anything", "group": "Outputs"}, "ForceC": {"name": "ForceC", "description": "<p>Force C as a vector</p>", "definition": "FC *( vector(cos(radians(gamma)),sin(radians(gamma))))", "templateType": "anything", "group": "Outputs"}, "gamma": {"name": "gamma", "description": "<p>Direction of force C in degrees</p>", "definition": "degrees(direction(vector(C[0]-A[0],C[1]-A[1])))", "templateType": "anything", "group": "Outputs"}, "rho": {"name": "rho", "description": "<p style=\"text-align: left;\">direction of resultant</p>", "definition": "degrees(direction(ForceR))", "templateType": "anything", "group": "Outputs"}, "alpha": {"name": "alpha", "description": "<p>direction of force A</p>", "definition": "(random(-80..175#5 except[45,135,-45,80,100]))", "templateType": "anything", "group": "Inputs"}, "FB": {"name": "FB", "description": "<p>Magnitude of Force B</p>", "definition": "random(10..100#10)", "templateType": "anything", "group": "Inputs"}, "B": {"name": "B", "description": "<p>Position of point B</p>", "definition": "vector( random(1,-1) random(4..10),random(1,-1) random(2..5))", "templateType": "anything", "group": "Inputs"}, "A": {"name": "A", "description": "<p>Position of point A</p>", "definition": "vector(0,0)", "templateType": "anything", "group": "Inputs"}, "units": {"name": "units", "description": "", "definition": "random(['ft','lb'],['in','lb'],['cm','N'])", "templateType": "anything", "group": "Inputs"}, "ForceA": {"name": "ForceA", "description": "<p>force A&nbsp;as a vector</p>", "definition": "FA *( vector(cos(radians(alpha)),sin(radians(alpha))))", "templateType": "anything", "group": "Outputs"}, "angle_from_ref": {"name": "angle_from_ref", "description": "", "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)])", "templateType": "anything", "group": "Outputs"}, "debug": {"name": "debug", "description": "", "definition": "false", "templateType": "anything", "group": "Inputs"}}, "extensions": ["geogebra", "quantities", "weh"], "type": "question", "preamble": {"js": "", "css": ""}, "advice": "<p>Vector Addition: &nbsp;</p>\n<p>$R_x = \\Sigma F_x = &nbsp;(\\var{siground(ForceA[0],4)}) &nbsp;+ (\\var{siground(ForceB[0],4)}) +(&nbsp;\\var{siground(ForceC[0],4)}) = \\var{siground(ForceR[0],4)}$&nbsp;{units[1]}</p>\n<p>$R_y = \\Sigma F_y = &nbsp;(\\var{siground(ForceA[1],4)}) &nbsp;+ (\\var{siground(ForceB[1],4)}) +(&nbsp;\\var{siground(ForceC[1],4)}) = \\var{siground(ForceR[1],4)}$&nbsp;{units[1]}</p>\n<p></p>\n<p>$ 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)}$&nbsp;{units[1]}</p>\n<p></p>\n<p>$\\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) &nbsp;= \\var{siground(degrees(arctan(abs(forceR[1])/forceR[0])),4)}&deg; &nbsp;= &nbsp;(\\var{siground(rho,4)}&deg; $ from the positive x-axis.)</p>", "statement": "<p><strong></strong>Three forces act on the bracket at point <em>A</em>: &nbsp; <span style=\"color: green;\"><em>A</em> = {FA} {units[1]}</span>, <span style=\"color: blue;\"><em>B</em>&nbsp;= {FB} {units[1]} </span> and, <span style=\"color: red;\"><em>C&nbsp;</em>= {FC} {units[1]}</span>.</p>\n<p>Find the magnitude and direction of the resultant force&nbsp;<strong>R </strong>by summing scalar components.</p>\n<p>{geogebra_applet('dtf3t2dp', [['A',A],['B',B],['C',C],['F_a',FA],['F_b',FB],['F_c',FC],['&alpha;', alpha],['unit','\"'+units[0]+'\"']])}</p>\n<p></p>\n<p><span data-jme-visible=\"debug\">Force A: {fa} at {alpha} = {forceA}&nbsp;</span></p>\n<p><span data-jme-visible=\"debug\">Force B: {fb} at {beta} = {forceB}</span></p>\n<p><span data-jme-visible=\"debug\">Force C: {fc} at {gamma} = {forceC}</span></p>\n<p><span data-jme-visible=\"debug\">Resultant: {R} at {rho} &nbsp;= {forceR}</span></p>", "contributors": [{"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}