// Numbas version: exam_results_page_options {"name": "Xiaodan's copy of", "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

\n

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

\n

2. replacing '-' with ' ' 

\n

3. replacing '°' with ' deg' 

\n

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.  

\n

If student_units are wrong  - replace with correct units

\n

If student_scalar has the wrong sign - replace with right sign

\n

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": [{"tags": ["Equilibrium", "equilibrium", "mechanics", "Mechanics", "moments", "statics", "Statics"], "functions": {"format": {"parameters": [["q", "quantity"]], "definition": "string(siground(q,4))", "type": "quantity", "language": "jme"}}, "rulesets": {}, "variable_groups": [{"variables": ["A", "B", "D", "alpha", "F", "units", "debug"], "name": "Inputs"}, {"variables": ["F_hat", "F_y", "d_AB", "M_F", "beta", "rise", "run", "T_hat", "r_ad", "d_perp_t", "d_x", "d_y"], "name": "Outputs"}], "ungrouped_variables": ["T"], "parts": [{"variableReplacementStrategy": "originalfirst", "marks": 0, "unitTests": [], "gaps": [{"variableReplacementStrategy": "originalfirst", "marks": "5", "unitTests": [], "type": "engineering-answer", "showCorrectAnswer": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "settings": {"C2": "50", "correctAnswer": "M_F", "right": "0.2", "close": "1.0", "C3": "25", "C1": "75"}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "scripts": {}}], "showCorrectAnswer": true, "sortAnswers": false, "prompt": "

Determine the moment that the force $\\textbf{F}$ produces about point $A$.

\n

$M_F =$ [[0]] {M_F}

", "extendBaseMarkingAlgorithm": true, "type": "gapfill", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "variableReplacements": [], "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "marks": 0, "unitTests": [], "gaps": [{"variableReplacementStrategy": "originalfirst", "marks": "5", "unitTests": [], "type": "engineering-answer", "showCorrectAnswer": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "settings": {"C2": "50", "correctAnswer": "T", "right": "0.2", "close": "1.0", "C3": "25", "C1": "75"}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "scripts": {}}], "showCorrectAnswer": true, "sortAnswers": false, "prompt": "

Determine the tension required to hold the bracket in position.

\n

$T$ = [[0]] {format(T)}

", "extendBaseMarkingAlgorithm": true, "type": "gapfill", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "variableReplacements": [], "scripts": {}}], "variablesTest": {"condition": "B[0]<>D[0] and B[1]<>D[1] and \nA[0]<>D[0] and A[1]<>D[1] and \nabs(rise) <> abs(run)", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "

Find the tension in a rope necessary to prevent a bracket from rotating by applying $\\Sigma M = 0$.

"}, "type": "question", "statement": "

An L shaped bracket is supported by a frictionless pin at $A$ and a cable between points $B$ and $D$. 

\n

Determine the tension in the cable required for equilibrium when a {F} force $\\textbf{F}$ is applied to the bracket as shown.

\n

{geogebra_applet('phznbxbe', [['A',A],['B',B],['D',D],['α', alpha + '°'],['unit','\"'+units[0]+'\"']])}

\n

", "variables": {"T_hat": {"group": "Outputs", "description": "", "definition": "vector(run,rise,0)/abs(vector(rise,run,0))", "name": "T_hat", "templateType": "anything"}, "F": {"group": "Inputs", "description": "

Magnitude of force A

", "definition": "qty(random(10..100#5),units[1])", "name": "F", "templateType": "anything"}, "d_x": {"group": "Outputs", "description": "", "definition": "qty(abs(A[0]-B[0]),units[0])", "name": "d_x", "templateType": "anything"}, "T": {"group": "Ungrouped variables", "description": "", "definition": "M_F/d_perp_t", "name": "T", "templateType": "anything"}, "d_perp_t": {"group": "Outputs", "description": "", "definition": "qty(abs(cross(T_hat,r_ad)[2]),units[0])", "name": "d_perp_t", "templateType": "anything"}, "F_y": {"group": "Outputs", "description": "", "definition": "F sin(radians(alpha))", "name": "F_y", "templateType": "anything"}, "A": {"group": "Inputs", "description": "

Position of point A

", "definition": "vector(0,0)", "name": "A", "templateType": "anything"}, "beta": {"group": "Outputs", "description": "", "definition": "siground(degrees(atan2(rise,run)),6)", "name": "beta", "templateType": "anything"}, "debug": {"group": "Inputs", "description": "", "definition": "false", "name": "debug", "templateType": "anything"}, "F_hat": {"group": "Outputs", "description": "

force A as a vector

", "definition": "( vector(cos(radians(alpha)),sin(radians(alpha)),0))", "name": "F_hat", "templateType": "anything"}, "r_ad": {"group": "Outputs", "description": "", "definition": "D-A + vector(0,0,0)", "name": "r_ad", "templateType": "anything"}, "D": {"group": "Inputs", "description": "

Position of point C

", "definition": "B + vector(random(1,-1)random(2..5),random(1,-1)random(2..5))", "name": "D", "templateType": "anything"}, "d_AB": {"group": "Outputs", "description": "", "definition": "qty(abs(B[0]),units[0])", "name": "d_AB", "templateType": "anything"}, "M_F": {"group": "Outputs", "description": "", "definition": "siground(abs(F_y) d_AB,5)", "name": "M_F", "templateType": "anything"}, "units": {"group": "Inputs", "description": "", "definition": "random(['ft','lb'],['in','lb'],['cm','N'])", "name": "units", "templateType": "anything"}, "rise": {"group": "Outputs", "description": "", "definition": "d[1]-b[1]", "name": "rise", "templateType": "anything"}, "run": {"group": "Outputs", "description": "", "definition": "d[0]-b[0]", "name": "run", "templateType": "anything"}, "alpha": {"group": "Inputs", "description": "

direction of force A

", "definition": "random(-80..80#10 except 0)", "name": "alpha", "templateType": "anything"}, "B": {"group": "Inputs", "description": "

Position of point B

", "definition": "vector(random(1,-1) random(5..12),random(1,-1) random(4..10))", "name": "B", "templateType": "anything"}, "d_y": {"group": "Outputs", "description": "", "definition": "qty(abs(A[1]-B[1]),units[0])", "name": "d_y", "templateType": "anything"}}, "advice": "

Since the object is in equilibrium $\\Sigma M_A = 0$ implies that the opposing moments must have equal magnitudes.  This is the principle we use to solve the problem. At the start we know the magnitude of $\\textbf{F}$ and the geometry of the system.

\n

1. Begin by drawing a sketch, defining your symbols and determining geometric values.  

\n

Let $\\alpha$ be the angle force $\\textbf{F}$ makes with the horizontal and $\\beta$ be the angle the cable makes with the horizontal.

\n

$\\alpha = \\var{abs(alpha)}°$,   $\\beta = \\var{siground(if(abs(beta)>90, 180-abs(beta), abs(beta)),4)}°$

\n

Let $d_x$ and $d_y$ represent the horizontal and vertical distances from $A$ to $B$.

\n

$d_x = \\var{d_x}$,   $d_y = \\var{d_y}$  

\n

2. Develop expressions for the moments about point $A$ caused by the force $\\textbf{F}$ and the cable. The moment caused by force can be found completely, but the moment caused by the cable tension can only be expressed as a function of the unknown tension $T$.

\n

\n

$M_F = F_y \\cdot d_x =  F \\sin \\alpha \\cdot d_x $

\n

$M_T = T_x \\cdot d_y \\pm T_y \\cdot d_x =   (T \\cos \\beta) \\, d_y \\pm (T \\sin \\beta) \\, d_x =   T (\\var{scalar(d_y)} \\cos \\beta   \\pm \\var{scalar(d_x)} \\sin \\beta) $

\n

When calculating the moment due to the cable $M_T$, if the two component moments act in the same direction, add the terms.  If they twist in opposite directions, take their difference.  Either way, make the final result positive, because we're comparing magnitudes.

\n

3. After substituting the known values and simplifying, equate the moments to get:

\n

$M_T = M_F$

\n

$ T (\\var{format(d_perp_t)}) = \\var{format(M_F)} $

\n

$T = \\dfrac{\\var{format(M_F)}}{\\var{format(d_perp_t)}}= \\var{format(T)} $

\n

", "extensions": ["geogebra", "quantities", "weh"], "name": "Xiaodan's copy of", "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/"}]}