// Numbas version: exam_results_page_options
{"name": "Keith's copy of Frame: A-frame Difficulty 1", "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": [{"metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "<p>An A-frame structure supporting a load at the top. &nbsp;Simple because both legs are two force bodies.</p>"}, "parts": [{"marks": 0, "type": "gapfill", "showCorrectAnswer": true, "gaps": [{"marks": "4", "type": "engineering-answer", "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "settings": {"C3": "25", "close": "1.0", "correctAnswer": "qty(vecA[0],units[0])", "C2": "50", "right": "0.2", "C1": "75"}, "unitTests": [], "variableReplacements": [], "customMarkingAlgorithm": "", "customName": "", "showFeedbackIcon": true, "useCustomName": false}, {"marks": "4", "type": "engineering-answer", "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "settings": {"C3": "25", "close": "1.0", "correctAnswer": "qty(vecA[1],units[0])", "C2": "50", "right": "0.2", "C1": "75"}, "unitTests": [], "variableReplacements": [], "customMarkingAlgorithm": "", "customName": "", "showFeedbackIcon": true, "useCustomName": false}, {"marks": "4", "type": "engineering-answer", "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "settings": {"C3": "25", "close": "1.0", "correctAnswer": "qty(vecC[0],units[0])", "C2": "50", "right": "0.2", "C1": "75"}, "unitTests": [], "variableReplacements": [], "customMarkingAlgorithm": "", "customName": "", "showFeedbackIcon": true, "useCustomName": false}, {"marks": "4", "type": "engineering-answer", "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "settings": {"C3": "25", "close": "1.0", "correctAnswer": "qty(vecC[1],units[0])", "C2": "50", "right": "0.2", "C1": "75"}, "unitTests": [], "variableReplacements": [], "customMarkingAlgorithm": "", "customName": "", "showFeedbackIcon": true, "useCustomName": false}], "scripts": {}, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "variableReplacements": [], "customMarkingAlgorithm": "", "sortAnswers": false, "customName": "", "showFeedbackIcon": true, "prompt": "<p>$A_x = $&nbsp;[[0]] &nbsp; $A_y = $&nbsp;[[1]] &nbsp;<span data-jme-visible=\"debug\">{vecA}</span></p>\n<p>$C_x = $&nbsp;[[2]] &nbsp; $C_y = $&nbsp;[[3]] &nbsp;<span data-jme-visible=\"debug\">{vecC}</span></p>"}], "name": "Keith's copy of Frame: A-frame Difficulty 1", "variablesTest": {"maxRuns": 100, "condition": "B[1]<> C[1] and B[0] <> B[1] and C[0] <> C[1]"}, "functions": {"display": {"parameters": [["Q", "quantity"]], "type": "string", "language": "jme", "definition": "string(siground(q,4))"}}, "variables": {"C": {"name": "C", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "vector(B[0]+ random(3..5),random(-2..3))"}, "x1": {"name": "x1", "templateType": "anything", "group": "magnitudes", "description": "", "definition": "qty(B[0],units[1])"}, "w": {"name": "w", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "random(100..500#25)"}, "beta": {"name": "beta", "templateType": "anything", "group": "magnitudes", "description": "", "definition": "degrees(angle(vector(-1,0),B-C))"}, "vecW": {"name": "vecW", "templateType": "anything", "group": "vectors", "description": "", "definition": "vector(0,-w)"}, "y1": {"name": "y1", "templateType": "anything", "group": "magnitudes", "description": "", "definition": "qty(B[1],units[1])"}, "y2": {"name": "y2", "templateType": "anything", "group": "magnitudes", "description": "", "definition": "qty(abs(b[1]-c[1]),units[1])"}, "sigma_f": {"name": "sigma_f", "templateType": "anything", "group": "vectors", "description": "", "definition": "vecW+vecA+vecC"}, "fd": {"name": "fd", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "0//random(-250..250#50 except 0)"}, "F_w": {"name": "F_w", "templateType": "anything", "group": "magnitudes", "description": "", "definition": "qty(w,units[0])"}, "debug": {"name": "debug", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "false"}, "ggb_load": {"name": "ggb_load", "templateType": "anything", "group": "Ungrouped variables", "description": "<p style=\"text-align: left;\">Below this will select either the force or the moment, but not both.</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\">random(<br /> [['fd',fd], ['me', 0]],<br /> [['me',me], ['fd', 0]]<br />) + [['w',0]]</p>", "definition": "[['me', 0],['fd', 0],['w',-w]]"}, "me": {"name": "me", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "0//random(-1000..1000#100 except 0)"}, "vecC": {"name": "vecC", "templateType": "anything", "group": "vectors", "description": "", "definition": "siground(scalar(magC) *\nvector(cos(radians(180-beta)),\n       sin(radians(180-beta))),4)"}, "vecA": {"name": "vecA", "templateType": "anything", "group": "vectors", "description": "", "definition": "siground(scalar(magA)*\nvector(cos(radians(alpha)),\n  sin(radians(alpha))),4)"}, "B": {"name": "B", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "vector(random(3..5),random(3..5))"}, "magC": {"name": "magC", "templateType": "anything", "group": "magnitudes", "description": "", "definition": "F_w cos(radians(alpha))/sin(radians(alpha+beta))"}, "x2": {"name": "x2", "templateType": "anything", "group": "magnitudes", "description": "", "definition": "qty(abs(b[0]-c[0]),units[1])"}, "magA": {"name": "magA", "templateType": "anything", "group": "magnitudes", "description": "", "definition": "F_w cos(radians(beta))/sin(radians(alpha+beta))"}, "units": {"name": "units", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "random(['N','m'],['lb','ft'])"}, "alpha": {"name": "alpha", "templateType": "anything", "group": "magnitudes", "description": "", "definition": "degrees(angle(vector(1,0),B))"}}, "preamble": {"js": "", "css": ""}, "rulesets": {}, "ungrouped_variables": ["B", "C", "fd", "me", "w", "units", "ggb_load", "debug"], "advice": "<p>{geogebra_applet('uyjv6v8r',[[\"B\",B],[\"C\",C]] + ggb_load )}</p>\n<p><strong></strong></p>\n<p><strong>Strategy:</strong></p>\n<p style=\"padding-left: 30px;\">Note that members <em>AB</em> and <em>BC</em> are two-force bodies and both act on pin <em>B</em>&nbsp;in known directions. &nbsp;Draw a free body diagram of the two members and of the forces acting on pin at <em>B,&nbsp;</em>and solve it for the magnitudes of <em>A</em> and <em>C</em> using the equilibrium equation method or the force-triangle method</p>\n<p><strong>Known:</strong></p>\n<p style=\"padding-left: 30px;\">$W$ = {F_w}</p>\n<p><strong>Determine necessary angles:</strong></p>\n<p style=\"padding-left: 30px;\">$\\alpha = \\tan^{-1}\\left(\\frac{\\var{y1}}{\\var{x1}}\\right) = \\var{siground(alpha,4)}$&deg;</p>\n<p style=\"padding-left: 30px;\">$\\beta = \\tan^{-1}\\left(\\frac{\\var{y2}}{\\var{x2}}\\right) = \\var{siground(beta,4)}$&deg;</p>\n<p><strong>Using the law of sines&nbsp;to&nbsp;solve for forces <em>A</em>&nbsp;and <em>C</em>:</strong></p>\n<p style=\"padding-left: 30px;\">$\\dfrac{W}{\\sin(\\alpha+\\beta)} = \\dfrac{AB}{\\sin(90&deg;-\\alpha)} = \\dfrac{CB}{\\sin(90&deg;-\\beta)}$</p>\n<p style=\"padding-left: 30px;\">$A = W \\dfrac{\\cos(\\alpha)}{\\sin(\\alpha+\\beta)}$ = {display(magA)} $\\nearrow$</p>\n<p style=\"padding-left: 30px;\">$C&nbsp;= W \\dfrac{\\cos(\\beta)}{\\sin(\\alpha+\\beta)}$ = {display(magC)} &nbsp;$\\nwarrow$</p>\n<p><strong>Find the scalar components of the forces at pins <em>A</em> and <em>C</em>.</strong></p>\n<p style=\"padding-left: 30px;\"><i></i>Note: Scalar components have a sign which indicates direction: positive values indicate $\\uparrow$&nbsp;&nbsp;or $\\rightarrow$, negative indicate $\\downarrow$&nbsp;or $\\leftarrow$.</p>\n<p style=\"padding-left: 30px;\">$\\begin{align} A_x = A \\cos(\\alpha) &amp;= \\var{qty(vecA[0],units[0])}&amp; &amp;C_x = C&nbsp;\\cos(\\beta) = \\var{qty(vecC[0],units[0])} \\\\ &nbsp;A_y = A \\sin(\\alpha) &amp;= \\var{qty(vecA[1],units[0])} &nbsp;&amp;&amp; &nbsp; &nbsp; &nbsp;C_y = C&nbsp;\\sin(\\beta) = \\var{qty(vecC[1],units[0])} \\end{align}$</p>\n<p><strong>Check</strong></p>\n<p style=\"padding-left: 30px;\">You can use the equations of equilibrium to verify that&nbsp;these answers put point $B$ in equilibrium.</p>\n<p style=\"padding-left: 30px;\">$\\begin{align}A_x &nbsp;&amp;\\stackrel{?}{=}C_x&nbsp; &amp;A_y + C_y &amp;\\stackrel{?}{=}W\\\\ \\var{vecA[0]} &amp;=&nbsp;\\var{-vecC[0]} \\quad \\checkmark&nbsp;&amp; \\var{vecA[1]} + \\var{vecC[1]} &nbsp;&amp;= \\var{W} \\quad \\checkmark\\\\ \\end{align}$</p>", "variable_groups": [{"name": "magnitudes", "variables": ["F_w", "alpha", "beta", "magA", "magC", "x1", "y1", "x2", "y2"]}, {"name": "vectors", "variables": ["vecW", "vecA", "vecC", "sigma_f"]}], "tags": ["equilibrium", "Equilibrium", "frame", "Frame", "mechanics", "Mechanics", "Statics", "statics"], "statement": "<p>{geogebra_applet('qe7xhnse',[[\"B\",B],[\"C\",C],['units','\"'+units[1]+'\"']]+ggb_load&nbsp;)}</p>\n<p>The A-frame shown supports a {F_w} load as shown. &nbsp;Determine the scalar components of the reactions at pins&nbsp;<em>A</em> and <em>C.</em></p>\n<p><strong></strong></p>", "extensions": ["geogebra", "quantities", "weh"], "type": "question", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Keith Tarnowski", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3425/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Keith Tarnowski", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3425/"}]}