// Numbas version: exam_results_page_options {"name": "Distributed Loads: trapezoidal loading", "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": "
A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "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": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "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": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "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": "Only marked close if the student actually has the right sign.
", "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. if correct answer is 100 N and close is ±1%,Find the reactions of a simply-supported beam with a trapazoidal distributed load.
", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "{geogebra_applet('xgjx2s8s',[['a', a 10/L], ['b', b 10/L],['c', c 10/L],['showfbd','false']])}
\n$\\var{qty(L,unit[0])}$ long beam $AB$ is subjected to a distributed load which
\nDetermine the reactions at $A$ and $B$.
", "advice": "{geogebra_applet('xgjx2s8s',[['a', a 10/L], ['b', b 10/L],['c', c 10/L],['showfbd','true']])}
\n$\\begin{align}\\\\ W_R &= \\var{QWR} & x_R &= \\var{QxR} \\\\ W_T &= \\var{QWT} &x_T &= \\var{QxT}\\end{align}$
\n$\\begin{align}\\\\ \\Sigma M_A &= 0 \\\\W_R x_r + W_T x_T &= B L \\\\ B &= \\frac{W_R x_r + W_T x_T}{L} \\\\&= \\var{QRB} \\\\ \\\\ \\Sigma F_y &= 0 \\\\ A + B &= W_T + W_R \\\\ A &= W_T + W_R - B \\\\ &= \\var{QRA} \\end{align}$
\nhorizontal location of the starts of the triangular load.
\ncould be on the left or right of point B
", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(0..L)", "description": "horizontal position of point between triangle and rectangle. l
", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(0..L)", "description": "horizontal location of the end of the rectangular load.
\ncould be on the left or right of point B
", "templateType": "anything"}, "w": {"name": "w", "group": "Ungrouped variables", "definition": "random(50..150#10)", "description": "Max value of loading in [force/distance]
", "templateType": "anything"}, "WT": {"name": "WT", "group": "solution", "definition": "abs(a-b) w /2", "description": "weight of the triangular load
", "templateType": "anything"}, "WR": {"name": "WR", "group": "solution", "definition": "abs(b-c) w", "description": "weight of the rectangular load
", "templateType": "anything"}, "WTot": {"name": "WTot", "group": "solution", "definition": "WT+WR", "description": "Total weight of load
", "templateType": "anything"}, "xR": {"name": "xR", "group": "solution", "definition": "(b+c)/2", "description": "location of centroid of rect
", "templateType": "anything"}, "xT": {"name": "xT", "group": "solution", "definition": "b + (a-b)/3", "description": "Centroid of triangle
", "templateType": "anything"}, "L": {"name": "L", "group": "Ungrouped variables", "definition": "random([10,12,16,20])", "description": "length of beam
", "templateType": "anything"}, "unit": {"name": "unit", "group": "Ungrouped variables", "definition": "random([['ft','lb'],['m','kN']])", "description": "", "templateType": "anything"}, "RB": {"name": "RB", "group": "solution", "definition": "(WR xR + WT xT)/ L", "description": "", "templateType": "anything"}, "RA": {"name": "RA", "group": "solution", "definition": "(WT * (L-xT) + WR * (L-xR ))/ L", "description": "", "templateType": "anything"}, "check": {"name": "check", "group": "solution", "definition": "RA + RB = Wtot", "description": "", "templateType": "anything"}, "QxR": {"name": "QxR", "group": "quantities", "definition": "quantity(xR,unit[0])", "description": "", "templateType": "anything"}, "QxT": {"name": "QxT", "group": "quantities", "definition": "qty(precround(xT,2),unit[0])", "description": "", "templateType": "anything"}, "Qw": {"name": "Qw", "group": "quantities", "definition": "qty(w,unit[1] + \"/\" + unit[0])", "description": "", "templateType": "anything"}, "QWr": {"name": "QWr", "group": "quantities", "definition": "qty(Wr,unit[1])", "description": "", "templateType": "anything"}, "QWt": {"name": "QWt", "group": "quantities", "definition": "qty(Wt,unit[1])", "description": "", "templateType": "anything"}, "QRA": {"name": "QRA", "group": "quantities", "definition": "qty(precround(RA,2),unit[1])", "description": "", "templateType": "anything"}, "QRB": {"name": "QRB", "group": "quantities", "definition": "qty(precround(RB,2),unit[1])", "description": "", "templateType": "anything"}, "QA": {"name": "QA", "group": "quantities", "definition": "qty(A,unit[0])", "description": "", "templateType": "anything"}, "QB": {"name": "QB", "group": "quantities", "definition": "qty(B,unit[0])", "description": "", "templateType": "anything"}, "QC": {"name": "QC", "group": "quantities", "definition": "qty(C,unit[0])", "description": "", "templateType": "anything"}, "Q0": {"name": "Q0", "group": "quantities", "definition": "qty(0,unit[1] + \"/\" + unit[0])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "b > min(a,c) and b < max(a,c) and abs(a-b) L/10 > 1 and abs(b-c) L/10 > 1", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "w", "L", "unit"], "variable_groups": [{"name": "solution", "variables": ["WT", "WR", "WTot", "xR", "xT", "RB", "RA", "check"]}, {"name": "quantities", "variables": ["QxR", "QxT", "Qw", "QWr", "QWt", "QRA", "QRB", "QA", "QB", "QC", "Q0"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Find Reactions", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$A = $ [[0]] $B = $ [[1]]
", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "A", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "{QRA}", "right": "0.2", "close": "1.0", "C1": "80", "C2": "80", "C3": "65"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "B", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "{QRB}", "right": "0.2", "close": "1.0", "C1": "80", "C2": "80", "C3": "65"}}], "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/"}]}