// Numbas version: exam_results_page_options
{"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": "<p>Adjusts all angles to 0 &lt; $\\theta$ &lt; 360.</p>\n<p>Accepts '&deg;' and 'deg' as units.</p>\n<p>Penalizes if not close enough or no units.</p>\n<p>90&deg; = -270&deg; = 450&deg;</p>", "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": "<p>Retuns the scalar part of students answer (which is a quantity) as a number.</p>", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "<p>Normalize angle with mod 360</p>", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "<p>matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"</p>", "definition": "studentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]"}, {"name": "interpreted_unit", "description": "<p>Allows student to use degree symbol or 'deg' for units.</p>", "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": "<p>Normalize expected_answer with mod 360</p>", "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. &nbsp;&nbsp;", "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. &nbsp;", "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": "<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": [["question-resources/easy_vectors.ggb", "/srv/numbas/media/question-resources/easy_vectors.ggb"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Vector addition by summing scalar components - easy", "tags": ["angle from reference", "Mechanics", "mechanics", "Scalar components", "Statics", "statics", "Vector addition", "vector addition", "Vector Addition"], "metadata": {"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>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p><strong></strong>Three forces, $\\color{red}{\\mathbf{A}}, \\color{blue}{\\mathbf{B}}\\ \\text{and } \\color{forestgreen}{\\mathbf{C}}$&nbsp;are drawn&nbsp;to scale of 1 square = {scale} {units[1]}. &nbsp;Find the resultant by summing scalar components.</p>\n<p>{applet}</p>", "advice": "<p>Note: &nbsp;You an drag the vectors around to arrange them tip-to-tail. &nbsp;The resultant is a vector from the start of the chain to the end.</p>\n<p>Vector Addition: &nbsp;</p>\n<p>$R_x = \\Sigma F_x = \\simplify[!collectNumbers]{{scale FA[0]}+{scale FB[0]}+{scale FC[0]} ={scale FR[0]}}$ {units[1]}</p>\n<p>$R_y = \\Sigma F_y = \\simplify[!collectNumbers]{{scale FA[1]}+{scale FB[1]}+{scale FC[1]} ={scale FR[1]}}$ {units[1]}</p>\n<p>$R=\\sqrt{R_x^2 + R_y^2} =\\var{siground(resultant,4)}$&nbsp;</p>\n<p>$\\theta = \\tan^{-1}\\left(\\left|\\dfrac{R_y}{R_x}\\right| \\right) = \\var{siground(theta,4)}$&deg;</p>\n<p></p>", "rulesets": {}, "extensions": ["geogebra", "quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"C1": {"name": "C1", "group": "Inputs", "definition": "vector(random(-Z+1..Z-1),random(-Z+1..Z-1))\n", "description": "<p>Position of point C</p>", "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": "<p>FA in first or fourth quadrant</p>", "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": "<p>Start point</p>", "templateType": "anything", "can_override": false}, "FB": {"name": "FB", "group": "Inputs", "definition": "B2-B1", "description": "<p>in third or 4 quadrant</p>", "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": "<p>Position of point B</p>", "templateType": "anything", "can_override": false}, "resultant": {"name": "resultant", "group": "Outputs", "definition": "qty(abs(FR),units[1]) scale", "description": "", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "Ungrouped variables", "definition": "geogebra_file(\"easy_vectors.ggb\",params)", "description": "", "templateType": "anything", "can_override": false}, "params": {"name": "params", "group": "Ungrouped variables", "definition": "[A1: A1, A2: A2, B1: B1, B2: B2, C1: C1, C2: C2, Z: Z]", "description": "<p>endponts of vector, &nbsp;Z = xmax = ymax, -Z = xmin = ymin</p>", "templateType": "anything", "can_override": false}, "Z": {"name": "Z", "group": "Ungrouped variables", "definition": "8\n", "description": "<p>sets bound of window and max length of (unscaled) resultant FR</p>", "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": "<p>does FA intersect with FB?</p>", "templateType": "anything", "can_override": false}, "BC": {"name": "BC", "group": "Ungrouped variables", "definition": "intersect(B1,B2,C1,C2)", "description": "<p>does FB intersect with FC?</p>", "templateType": "anything", "can_override": false}, "CA": {"name": "CA", "group": "Ungrouped variables", "definition": "intersect(C1,C2,A1,A2)", "description": "<p>does FC intersect with FA?</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "2 <= abs(FR) <= Z //resultant not too short or too long\nand abs(FA) >=2 and abs(FB) >= 2 and abs(FC) >= 2 //vectors not too short\nand not(AB) and not(BC) and not (CA) // vectors don't intersect", "maxRuns": "100"}, "ungrouped_variables": ["applet", "params", "Z", "AB", "BC", "CA"], "variable_groups": [{"name": "Inputs", "variables": ["FA", "FB", "FC", "units", "scale", "A1", "B1", "C1", "A2", "B2", "C2"]}, {"name": "Outputs", "variables": ["FR", "theta", "resultant"]}], "functions": {"f": {"parameters": [["pt", "vector"]], "type": "boolean", "language": "jme", "definition": "pt[1]>(FA[1]/FA[0])(pt[0] - A1[0]) + A1[1]  //This tests whether the point is above the line of action of force A. using point-slope formula y= m(x-x_1) + y_1 "}, "CCW": {"parameters": [["A", "vector"], ["B", "vector"], ["C", "vector"]], "type": "boolean", "language": "jme", "definition": "(C[1]-A[1]) * (B[0]-A[0]) > (B[1]-A[1]) * (C[0]-A[0])"}, "intersect": {"parameters": [["A", "vector"], ["B", "vector"], ["C", "vector"], ["D", "vector"]], "type": "boolean", "language": "jme", "definition": "// Return true if line segments AB and CD intersect\n// see https://stackoverflow.com/questions/3838329/how-can-i-check-if-two-segments-intersect\nccw(A,C,D) <> ccw(B,C,D) and ccw(A,B,C) <> ccw(A,B,D)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Components of components", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>First, find the scalar components of the&nbsp;three forces.&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>", "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": "<p>Then, sum the scalar components to get the scalar components of the resultant $\\mathbf{R}$.</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>", "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": "<p>Finally, resolve&nbsp;$R_x$ and $R_y$ to find the magnitude and direction of $\\mathbf{R}$.</p>\n<p>$R = \\sqrt{{R_x}^2 +{R_y}^2}$ =[[3]]</p>\n<p>&nbsp;$\\theta = \\tan^{-1}\\left(\\left|\\dfrac{R_y}{R_x}\\right| \\right)$ = [[0]]&nbsp; measured [[1]]&nbsp;from the [[2]].</p>\n<p></p>", "gaps": [{"type": "angle", "useCustomName": true, "customName": "$\\theta$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "qty(siground(theta,4),'deg')", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.2"}}, {"type": "1_n_2", "useCustomName": true, "customName": "dir", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+x axis", "+y axis", "-x axis", "-y axis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "engineering-answer", "useCustomName": true, "customName": "$R$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "resultant", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}