// Numbas version: exam_results_page_options
{"name": "Three force body method: Beam with angled load", "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": [["question-resources/diagram_1.png", "/srv/numbas/media/question-resources/diagram_1.png"], ["question-resources/diagram_2.png", "/srv/numbas/media/question-resources/diagram_2.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Three force body method: Beam with angled load", "tags": ["Equilibrium", "equilibrium", "Mechanics", "mechanics", "rigid body", "Rigid Body", "Statics", "statics", "three force body", "Three force body"], "metadata": {"description": "Simple geometry to introduce the three-force-body procedure.", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{geogebra_applet(\"xfpyfgd9\",[['split',&nbsp;split], ['&theta;',theta+'&deg;']])}&nbsp;</p>\n<p>A beam is loaded with a {F} force at a {theta}&deg; angle from the horizontal, as shown. &nbsp;Distance&nbsp;$\\overline{AB}$ is {AB}, and $\\overline{BC}$ is {BC}.</p>\n<p>Use the three-force body method to determine the magnitudes of the reactions at pin $A$ and roller $C$.</p>", "advice": "<p><strong>Given:</strong></p>\n<ul>\n<li>$F$ = {F}</li>\n<li>$\\theta$ = {theta}&deg;</li>\n<li>$\\overline{AB}$ = {AB}</li>\n<li>$\\overline{BC}$ = {BC}</li>\n<li>Force $\\mathbf{C}$ acts straight up, due to the roller.</li>\n</ul>\n<p><strong>Required:&nbsp;</strong></p>\n<ul>\n<li>magnitudes&nbsp;of $\\mathbf{A}$ and $\\mathbf{C}$.</li>\n</ul>\n<p><strong>Procedure:</strong></p>\n<ol>\n<li>Start by drawing a clear diagram representing the situation and locate point \"$x$\" where the lines of action of $\\mathbf{F}$ and $\\mathbf{C}$ intersect. &nbsp;In three-force-bodies, the line of action of $\\mathbf{A}$ must pass through that point too. &nbsp;</li>\n<li>Draw the line of action of $\\mathbf{A}$ and define $\\alpha$.\n<p><img src=\"resources/question-resources/diagram_1.png\" width=\"448\" height=\"345\"/></p>\n</li>\n<li>Find $h$, using: &nbsp;\\[\\tan\\theta = \\frac{h}{\\overline{BC}}\\]</li>\n<li>Find $\\alpha$: &nbsp;\\[\\tan\\alpha&nbsp;=\\frac{h}{(\\overline{AB} + \\overline{BC})}\\]</li>\n<li>Rearrange the forces into a force triangle, tip-to-tail, and label it.\n<p><img src=\"resources/question-resources/diagram_2.png\" width=\"320\" height=\"288\"/></p>\n</li>\n<li>\n<p>Use the law of sines&nbsp;to&nbsp;solve for the unknown magnitudes. \\[ \\frac{F}{\\sin (90 + \\alpha)} = &nbsp; &nbsp;\\frac{A}{\\sin (90&deg; -&nbsp;\\theta)} =&nbsp;\\frac{C}{\\sin (\\theta-\\alpha)}\\]</p>\n</li>\n</ol>", "rulesets": {}, "extensions": ["geogebra", "quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"L": {"name": "L", "group": "inputs", "definition": "qty(random(1..5),'m')", "description": "<p>length of beam</p>\n<p></p>", "templateType": "anything", "can_override": false}, "split": {"name": "split", "group": "inputs", "definition": "random(0.2..0.8#0.5)", "description": "<p>percentage position of point B</p>", "templateType": "anything", "can_override": false}, "AB": {"name": "AB", "group": "Ungrouped variables", "definition": "split l", "description": "<p>segment AB</p>", "templateType": "anything", "can_override": false}, "BC": {"name": "BC", "group": "Ungrouped variables", "definition": "L-AB", "description": "", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "inputs", "definition": "random(15..80#5)", "description": "", "templateType": "anything", "can_override": false}, "F": {"name": "F", "group": "inputs", "definition": "qty(random(25..150#5),'kN')", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "solution", "definition": "tan(radians(theta))BC", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "solution", "definition": "degrees(arctan(scalar(h/L)))", "description": "", "templateType": "anything", "can_override": false}, "K": {"name": "K", "group": "solution", "definition": "F/sin(radians(90+alpha))", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "solution", "definition": "K sin(radians(90-theta))", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "solution", "definition": "K sin(radians(theta-alpha))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["AB", "BC"], "variable_groups": [{"name": "inputs", "variables": ["split", "L", "theta", "F"]}, {"name": "solution", "variables": ["h", "alpha", "K", "A", "C"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$A$ =&nbsp;[[0]]&nbsp;$\\qquad C$ =&nbsp;[[1]]</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": "A", "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": "C", "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/"}]}