// Numbas version: exam_results_page_options {"name": "Equivalent System: two parallel forces", "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": "

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

1. replacing \"ohms\" with \"ohm\" case insensitive

2. replacing '-' with ' '

3. replacing '°' with ' deg'

to 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.

If student_units are wrong - replace with correct units

If student_scalar has the wrong sign - replace with right sign

If 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%,
99 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.
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.
This value would be close if the expected units were provided. If the correct answer is 100 N, and close is ±1%,
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": [{"rulesets": {}, "variable_groups": [{"variables": ["R", "xbar"], "name": "Unnamed group"}], "tags": ["equivalent system", "mechanics", "moment", "statics"], "name": "Equivalent System: two parallel forces", "functions": {"dist": {"parameters": [["d", "number"]], "language": "jme", "definition": "siground(qty(d,units[0]),4)", "type": "quantity"}, "force": {"parameters": [["F", "number"]], "language": "jme", "definition": "siground(qty(f,units[1]),4)", "type": "quantity"}}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "

Replace two parallel forces with an equivalent single force

"}, "ungrouped_variables": ["L", "d", "ratio", "A", "B", "units"], "parts": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "gaps": [{"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "settings": {"correctAnswer": "Force(R)", "right": "0.2", "C2": "50", "C1": "75", "C3": "25", "close": "1.0"}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "engineering-answer", "variableReplacements": [], "scripts": {}, "marks": "4"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "settings": {"correctAnswer": "dist(xbar)", "right": "0.2", "C2": "50", "C1": "75", "C3": "25", "close": "1.0"}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "engineering-answer", "variableReplacements": [], "scripts": {}, "marks": "4"}], "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "scripts": {"mark": {"script": "numbasGGBApplet0.setVisible('show',true)", "order": "instead"}}, "type": "gapfill", "prompt": "

$R$ = [[0]] $\\qquad \\bar{x} = $ [[1]]

"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"B": {"description": "", "definition": "ratio A\n", "templateType": "anything", "name": "B", "group": "Ungrouped variables"}, "xbar": {"description": "", "definition": "(A *(L - d L) + B L)/R", "templateType": "anything", "name": "xbar", "group": "Unnamed group"}, "R": {"description": "", "definition": "A + B", "templateType": "anything", "name": "R", "group": "Unnamed group"}, "A": {"description": "", "definition": "random(10..100#5)", "templateType": "anything", "name": "A", "group": "Ungrouped variables"}, "units": {"description": "", "definition": "['m', 'kN']", "templateType": "anything", "name": "units", "group": "Ungrouped variables"}, "ratio": {"description": "

ratio of magnitude of force B to magnitude of force A

", "definition": "random(0.5..2#0.1)\n", "templateType": "anything", "name": "ratio", "group": "Ungrouped variables"}, "L": {"description": "", "definition": "random(8,10,12)", "templateType": "anything", "name": "L", "group": "Ungrouped variables"}, "d": {"description": "

ratio of distance between A and B to length.

", "definition": "random(0.3..0.8#0.05)", "templateType": "anything", "name": "d", "group": "Ungrouped variables"}}, "extensions": ["geogebra", "quantities", "weh"], "type": "question", "preamble": {"js": "", "css": ""}, "advice": "

Since both forces are vertical, the resultant force with also be vertical, with a magnitude

$\\begin{align} R &= A + B \\\\&= \\var{A} + \\var{B}\\\\ &= \\var{force(R)}\\end{align}$

The equivalent force R must produce the same moment about any point as the orignal system of forces did. Chosing the left end of the beam as the moment center, and equating moments, gives:

$\\begin{align} M_2 &= M_1\\\\ R\\, \\bar{x} &= A \\,(L - d) + B\\, (L)\\\\ \\bar{x} & = \\dfrac{\\var{force(A)}\\cdot \\var{dist(L - d L)} +\\var{force(B)}\\,\\cdot \\var{dist(L)}} {\\var{force(R)}} \\\\ &= \\var{dist(xbar)} \\end{align}$

", "statement": "

{geogebra_applet('drbgytkc',[['d',d],['ratio',ratio]])}

A {L} {units[0]} long cantilever beam is loaded with vertical forces $A = \\var{force(A)}$ and $B = \\var{force(B)},$ separated by a distance $d$ = {d L} {units[0]}, as shown.

Replace the two forces with a single equivalent force R and determine the distance $\\bar{x}$ from the left end of the beam to the line of action of R.

", "contributors": [{"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}