// Numbas version: exam_results_page_options
{"name": "Moment of a force about a point", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<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": "Moment of a force about a point", "tags": ["2-D", "2-d", "Mechanics", "mechanics", "Moment", "moment", "Perpendicular distance", "perpendicular distance", "Statics", "statics"], "metadata": {"description": "<p>Determine the moment of a force about a point by using $M= F d_\\perp$ or $M = F_\\perp d$.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{applet}</p>\n<p><span data-jme-visible=\"version=0\">A $\\var{scalar(f)}$ lb force $\\mathbf{F}$ is applied to the control rod $AB$ as shown. Knowing that the length of the rod is $\\var{d}$ and that $\\alpha$ is {alpha}&deg;, determine the component&nbsp;of $\\mathbf{F}$&nbsp;perpendicular to rod $AB$<em>&nbsp;</em>and the magnitude of the moment produced.</span></p>\n<p></p>\n<p><span data-jme-visible=\"version=1\">A $\\var{scalar(f)}$ lb force $\\mathbf{F}$&nbsp;is applied to the control rod&nbsp;$AB$&nbsp;as shown. Knowing that the length of the rod is $\\var{d}$ and that $\\alpha$ is {alpha}&deg;, determine the perpendicular distance from the line of action of force $\\mathbf{F}$&nbsp;to point $B$<em>,&nbsp;</em>and&nbsp;the magnitude of the moment produced.</span></p>\n<p></p>\n<p><span data-jme-visible=\"version=2\">Force $\\mathbf{F}$&nbsp;is applied to the $\\var{d}$ long control rod&nbsp;$AB$&nbsp;at angle $\\alpha$ =&nbsp;{alpha}&deg; as shown. &nbsp;Knowing that it&nbsp;creates a {siground(scalar(M),4)} in lb {direction} moment about point <em>B</em>, determine the perpendicular distance from the line of action of force $\\mathbf{F}$&nbsp;to point $B$, and the magnitude of force $\\mathbf{F}$.</span></p>\n<p></p>\n<p><span data-jme-visible=\"version=3\">A {scalar(f)} lb force $\\mathbf{F}$ is applied to control rod&nbsp;$AB$&nbsp;at angle $\\alpha$ = {alpha}&deg; as shown. Knowing that it creates a {siground(scalar(M),4)} in lb {direction} moment about point&nbsp;$B$&nbsp;, determine the length of the control rod, and the component of $\\mathbf{F}$&nbsp;in a direction perpendicular to&nbsp;$AB$&nbsp;.</span></p>\n<p></p>\n<p><span data-jme-visible=\"version=4\">A {scalar(f)} lb force $\\mathbf{F}$&nbsp;is applied to the {scalar(d)}&nbsp;inch long control rod&nbsp;$AB$&nbsp;as shown. Knowing that it creates a {siground(scalar(M),4)} in lb {direction} moment about point&nbsp;$B$&nbsp;, determine angle $\\alpha$ and the perpendicular distance between the line of action of force $\\mathbf{F}$&nbsp;and point&nbsp;$B$&nbsp;.</span></p>\n<div data-jme-visible=\"debug\">\n<p>F: {F} D:{D} $\\alpha$: {alpha} $F_\\perp$: {fperp} $d_\\perp$: {dperp} M: {M}</p>\n</div>\n<p></p>\n<p></p>\n<p><strong></strong></p>", "advice": "<p>{advice}</p>\n<p><strong>Method 1</strong></p>\n<ol>\n<li>Draw the line of action of the force.</li>\n<li>Make a triangle including the perpendicular distance $d_\\perp.$</li>\n<li>Use geometry to find an angle in the triangle.</li>\n<li>Use trig to find the value of the perpendicular distance.</li>\n<li>Apply equation $M=F d_\\perp = F(d sin \\alpha) $ &nbsp;to solve for the unknown quantity.</li>\n</ol>\n<p><strong>Method 2</strong></p>\n<ol>\n<li>Use geometry to find the angle between the force and the control rod.</li>\n<li>Identify and solve for the component of force $F$&nbsp;perpendicular to the control rod, $F_\\perp$ &nbsp;.</li>\n<li>Apply equation $M = F_\\perp d = (F sin \\alpha) d $ to solve for the unknown quantity. &nbsp;</li>\n</ol>", "rulesets": {}, "extensions": ["geogebra", "quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"alpha'": {"name": "alpha'", "group": "Inputs", "definition": "random(-150..150#5 except [0,5,10,90,-5,-10,-90])", "description": "<p>angle of force with respect to the bar.</p>", "templateType": "anything", "can_override": false}, "Fperp": {"name": "Fperp", "group": "results", "definition": "M/D", "description": "<p>The perpendicular component of the force.</p>", "templateType": "anything", "can_override": false}, "version": {"name": "version", "group": "display", "definition": "random(0..4)", "description": "<p>which question version?</p>", "templateType": "anything", "can_override": false}, "direction": {"name": "direction", "group": "results", "definition": "if(alpha'<180,'clockwise','counterclockwise')", "description": "", "templateType": "anything", "can_override": false}, "Dperp": {"name": "Dperp", "group": "results", "definition": "M/F", "description": "<p>The perpendicular distance.</p>", "templateType": "anything", "can_override": false}, "F": {"name": "F", "group": "Inputs", "definition": "siground(qty(random(10..150)*random(0.1,0.5,1),'lb'),4)", "description": "<p>Magnitude of the force.</p>", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "display", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "beta": {"name": "beta", "group": "display", "definition": "if(beta'>90,180-beta',beta')", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "display", "definition": "if(abs(alpha')>90,(180-abs(alpha')),abs(alpha'))", "description": "<p>Angle alpha as shown on the diagram, always less than 90&deg;.</p>", "templateType": "anything", "can_override": false}, "answers": {"name": "answers", "group": "display", "definition": "[['$F_\\\\perp$', Fperp ,  '$M$', M],\n\n['$d_\\\\perp$',  Dperp, '$M$', M ],\n\n['$d_\\\\perp$',Dperp, '$F$', F],\n\n['$\\\\ell$', D, '$F_\\\\perp$', Fperp],\n\n['$\\\\alpha$',qty(alpha,'deg'), '$d_\\\\perp$',Dperp]]\n", "description": "<p>labels, gap answer, and units</p>", "templateType": "anything", "can_override": false}, "beta'": {"name": "beta'", "group": "Inputs", "definition": "random(20..160#10 except 90)", "description": "<p>angle of bar from positive x axis</p>", "templateType": "anything", "can_override": false}, "M": {"name": "M", "group": "results", "definition": "siground(sin(radians(alpha)),5) * ( F * D )", "description": "<p>The magnitude of the moment</p>", "templateType": "anything", "can_override": false}, "D": {"name": "D", "group": "Inputs", "definition": "qty(random(6..30#2),'in')", "description": "<p>Length of the bar AB.</p>", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "ggb", "definition": "geogebra_applet('tvby7hmg', params)", "description": "", "templateType": "anything", "can_override": false}, "params": {"name": "params", "group": "ggb", "definition": "['\u03b1\\'': radians(alpha'), '\u03b2\\'': radians(beta'), \nshow1: [visible: false], show2: [visible: false]]", "description": "", "templateType": "anything", "can_override": false}, "advice": {"name": "advice", "group": "ggb", "definition": "showAdvice(geogebra_applet('tvby7hmg', params))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Inputs", "variables": ["beta'", "alpha'", "D", "F"]}, {"name": "results", "variables": ["M", "Fperp", "Dperp", "direction"]}, {"name": "display", "variables": ["alpha", "beta", "version", "answers", "debug"]}, {"name": "ggb", "variables": ["applet", "params", "advice"]}], "functions": {"showAdvice": {"parameters": [["app", "ggbapplet"]], "type": "anything", "language": "javascript", "definition": "// see https://wiki.geogebra.org/en/Reference:GeoGebra_Apps_API for other commands\n\napp.promise.then(function(d) {\n   d.app.setVisible('show1', true);\n   d.app.setVisible('show2', true);\n   d.app.setValue('show1', true);\n   d.app.setCaption('\u03b1', '$%v$');\n});\nreturn new Numbas.jme.types.ggbapplet(app);\n"}}, "preamble": {"js": "//question.signals.on('adviceDisplayed',function() {\n\n//try{\n//   var app = question.scope.variables.applet.app; \n//   app.setVisible('show1', true);\n//   app.setVisible('show2', true);\n//   app.setValue('show1', true);\n//   app.setCaption('\u03b1', '$%v$');\n//  }\n//  catch(err){}  \n//})\n\n\n", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Answers", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{answers[version][0]} =&nbsp;[[0]] &nbsp;$\\qquad$&nbsp;{answers[version][2]} =&nbsp;[[1]]</p>\n<p></p>\n<p></p>\n<p><span data-jme-visible=\"debug\">{answers[version][1]}</span></p>\n<p><span data-jme-visible=\"debug\">{answers[version][3]}</span></p>", "gaps": [{"type": "engineering-answer", "useCustomName": false, "customName": "", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "answers[version][1]", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": false, "customName": "", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "answers[version][3]", "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/"}]}