// Numbas version: exam_results_page_options
{"name": "Equilibrium of a rigid body: Car on a hill", "extensions": ["geogebra", "weh", "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": "<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": [{"name": "Equilibrium of a rigid body: Car on a hill", "tags": ["Equilibrium", "equilibrium", "Mechanics", "mechanics", "Rigid Body", "rigid body", "Statics", "statics", "three force body", "Three force body"], "metadata": {"description": "<p>Classic problem of a vehicle parked on an incline. &nbsp;Best solved by rotating the coordinate system.</p>\n<p>Image Credit:&nbsp;https://svgsilh.com/image/34325.html &nbsp;CC-0</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{geogebra_applet('w4xb6n95',['alpha':&nbsp;radians(alpha), 'fbd': [visible: false] ])}</p>\n<p>A car is parked on a {alpha}&deg;&nbsp;slope, with the rear wheels locked by the parking brake.&nbsp;&nbsp;Find the components&nbsp;of the forces acting on each of the front and rear wheels, parallel and perpendicular to the roadbed.</p>\n<div>\n<p style=\"padding-left: 30px;\"><strong>Vehicle Specifications</strong></p>\n<table style=\"margin-left: 30px; float: left;\">\n<tbody>\n<tr>\n<td>Wheelbase</td>\n<td>$L = $ {wb} mm</td>\n</tr>\n<tr>\n<td>Curb weight</td>\n<td>$m = $ {m} kg</td>\n</tr>\n<tr>\n<td>Center of Gravity</td>\n<td>$d = $ {d} mm<br/>$h = $ {h} mm</td>\n</tr>\n</tbody>\n</table>\n</div>", "advice": "<p style=\"float: right; padding: 5px;\">{geogebra_applet('w4xb6n95',['alpha':&nbsp;radians(alpha), 'fbd': [definition: 'true', visible: true] ])}</p>\n<p>First, draw a free body diagram of the vehicle. &nbsp;</p>\n<p>For convenience, let the <em>x</em>- and <em>y-</em> directions be parallel and perpendicular to the roadbed and define $\\alpha$ as the&nbsp;the angle the road makes with the horizontal.&nbsp;Note that $\\alpha$ is also the&nbsp;angle between the&nbsp;weight and the y-direction. Treat the front wheels like a roller, the rear wheels like a rough surface.</p>\n<p style=\"padding-left: 30px;\">$\\alpha = \\var{alpha}&deg;$</p>\n<p>Define $L$ as the distance between the front and rear wheels:</p>\n<p style=\"padding-left: 30px;\">$L= \\var{qty(wb,'mm')}$</p>\n<p>Note that the curb 'weight' is actually a mass, so let:</p>\n<p style=\"padding-left: 30px;\">$\\begin{align}W &amp;= m g\\\\ &amp;= (\\var{qty(m,'kg')}) \\cdot (\\var{qty(g, 'm/s^2')}) =\\var{show(w)}\\\\ W_x&amp; = W \\sin \\alpha = \\var{show(w_x)}\\\\W_y&amp; = W \\cos \\alpha = \\var{show(w_y)}\\end{align}$</p>\n<p>Apply the equations of equilibrium, starting with the sum of the moments about either A or B, since two unknown&nbsp;forces&nbsp;intersect there.</p>\n<p style=\"padding-left: 30px;\">$\\begin{align}\\Sigma M_A &amp;= 0\\\\&nbsp;&nbsp;B_y&nbsp;(L)&nbsp;&amp;= W_y(d)&nbsp;+ W_x&nbsp;&nbsp;(h)\\\\ B_y &amp;= &nbsp;W \\left(\\dfrac{d \\cos \\alpha + h \\sin \\alpha}{L}\\right)\\\\&amp;= \\var{show(B_y)}\\\\\\\\ \\Sigma F_x &amp;= 0\\\\ B_x &amp;= W_x\\\\ B_x &amp;= \\var{show(w_x)}\\\\\\\\ \\Sigma F_y &amp;= 0\\\\A + B_y &amp;=&nbsp;W_y \\\\A &amp;= W_y-B_y\\\\&amp;=\\var{show(A)}\\end{align}$</p>\n<p>Since there are two front wheels and two rear wheels, the forces acting on each wheel are&nbsp;half of these values:</p>\n<p style=\"padding-left: 30px;\">$A_{||} = 0 \\text{ N} \\qquad A_\\perp = A/2 = \\var{show(A/2)} \\qquad&nbsp;B_{||} = B_x/2 = &nbsp;\\var{show(B_x/2)} \\qquad&nbsp;B_\\perp = B_y/2 = \\var{show(B_y/2)}$</p>", "rulesets": {}, "extensions": ["geogebra", "quantities", "weh"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"B_x": {"name": "B_x", "group": "answers", "definition": "w_x", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "round(random(90..110) d /100)", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "answers", "definition": "w_y-b_y", "description": "", "templateType": "anything", "can_override": false}, "w_y": {"name": "w_y", "group": "answers", "definition": "W cos(radians(alpha))", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "round(random(0.25..0.35#0.01)wb)", "description": "", "templateType": "anything", "can_override": false}, "B_y": {"name": "B_y", "group": "answers", "definition": "(w_x h + w_y d)/wb", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(1200..1400)", "description": "<p>curb weight in kg</p>", "templateType": "anything", "can_override": false}, "W": {"name": "W", "group": "answers", "definition": "m g ", "description": "<p>weight of vechicle</p>", "templateType": "anything", "can_override": false}, "w_x": {"name": "w_x", "group": "answers", "definition": "W sin(radians(alpha))", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "9.81", "description": "", "templateType": "anything", "can_override": false}, "wb": {"name": "wb", "group": "Ungrouped variables", "definition": "random(2450..2580)", "description": "<p>wheelbase in mm</p>", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Ungrouped variables", "definition": "random([10,15,20,25,30])", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "['N','mm']", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "answers", "definition": "false", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["alpha", "m", "wb", "units", "d", "h", "g"], "variable_groups": [{"name": "answers", "variables": ["w_y", "A", "w_x", "B_x", "B_y", "W", "debug"]}], "functions": {"show": {"parameters": [["f", "number"]], "type": "number", "language": "jme", "definition": "siground(qty(f,'N'),4)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"mark": {"script": "//numbasGGBApplet0.setValue('fbd',true)\n//numbasGGBApplet0.setVisible('fbd',true)", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$A_{||} =$ &nbsp;[[0]]&nbsp; &nbsp;$\\qquad A_\\perp = $&nbsp;[[3]]&nbsp;<span data-jme-visible=\"debug\"> $0 B_{\\perp} = &nbsp; \\var{qty(A/2 ,'N')}$</span></p>\n<p>$B_{||}&nbsp;=$ &nbsp;[[1]]&nbsp; &nbsp;$\\qquad B_\\perp = $&nbsp;[[2]]&nbsp; <span data-jme-visible=\"debug\">$B_{||}= \\var{qty(B_x/2,'N')} B_{\\perp} = &nbsp; \\var{qty(B_y/2,'N')}$</span></p>", "gaps": [{"type": "engineering-answer", "useCustomName": false, "customName": "", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(0, 'N')", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": false, "customName": "", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(B_x/2,'N')", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": false, "customName": "", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(B_y/2,'N')", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": false, "customName": "", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(A/2 ,'N')", "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/"}]}