// Numbas version: finer_feedback_settings {"name": "Frame: A-frame Difficulty 2", "extensions": ["geogebra", "weh", "stats", "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": [{"name": "Frame: A-frame Difficulty 2", "tags": ["Equilibrium", "equilibrium", "frame", "Frame", "Mechanics", "mechanics", "statics", "Statics"], "metadata": {"description": "

An A-frame structure supporting a force or a moment.  One leg is a two force body.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

{geogebra_applet('qe7xhnse',[[\"B\",B],[\"C\",C],['units','\"'+units[1]+'\"']]+ggb_load )}

\n

The A-frame shown supports a {description} as shown.  

\n

Determine the scalar components of the reactions at pins A and C.  

\n

Note: the sign of a scalar component indicates the sense of the force. A positive sense indicates the force points towards the positive end of the corresponding axis. 

\n

\n

", "advice": "

Strategy:

\n

       Draw a free body diagram of the entire frame and each of its legs.  Note that member {if(Fd=0,\"AB\",\"BC\")} is a two-force body and the direction of the line of action of force {if(Fd=0,\"A\",\"C\")} is known;  that means that FBD {if(Fd=0,'III','II')} has three unknowns. FBD I has four unknowns, and FBD {if(Fd=0,'II','III')} has no knowns.  

\n

{geogebra_applet('p6rz9bqx',[[\"B\",B],[\"C\",C]] + ggb_load )}

\n

Known:

\n

$M_E = \\var{display(abs(M_E))}$ $D = \\var{display(abs(F_D))}$

\n

Determine necessary angles:

\n

$\\alpha = \\tan^{-1}\\left(\\frac{\\var{y1}}{\\var{x1}}\\right) = \\var{siground(alpha,4)}$°

\n

$\\beta = \\tan^{-1}\\left(\\frac{\\var{y2}}{\\var{x2}}\\right) = \\var{siground(beta,4)}$°

\n

Start with FBD {if(Fd=0,'III','II')} which has three unknowns, and take moments at point {if(Fd=0,'C','A')} to find force {if(Fd=0,\"A\",\"C\")}

\n
\n

II: $\\Sigma M_A = 0$

\n

$\\simplify{{sign(-fd)} D }  (\\var{y1/2}) + C_x (\\var{y1}) + C_y ( \\var{x1}) = 0$

\n

$\\simplify{{sign(-fd)} D} (\\var{y1/2}) + (C \\cos \\beta)  (\\var{y1}) + (C  \\sin \\beta) (\\var{x1}) = 0$

\n

$ C   = \\dfrac{\\simplify{{sign(fd)} D } (\\var{y1/2}) }{ (\\var{y1}) \\cos \\beta + (\\var{x1}) \\sin \\beta} = \\dfrac{ \\var{ F_D y1 /2 }}{\\var{display(y1 * cos(radians(beta)) + x1 * sin(radians(beta)))}} = \\var{display(magC)}$

\n

$C_x = C \\cos \\beta  = \\var{display(qty(-vecC[0],units[0]))} = \\var{display(abs(qty(vecC[0],units[0])))} \\var{if(vecC[0]>0,latex('\\\\rightarrow'),latex('\\\\leftarrow'))}$

\n

$C_y = C  \\sin \\beta  = \\var{display(qty(vecC[1],units[0]))} =  \\var{display(abs(qty(vecC[1],units[0])))} \\var{if(vecC[1]<0,latex('\\\\downarrow'),latex('\\\\uparrow'))}$ 

\n

\n
\n
\n

II: $\\Sigma M_C = 0$

\n

$\\simplify{M_E }   + A_x (\\var{y2}) + A_y ( \\var{x2}) = 0$

\n

$\\simplify{M_E} + (A \\cos \\alpha)  (\\var{y2}) + (A  \\sin \\alpha) (\\var{x2}) = 0$

\n

$ A = \\dfrac{\\simplify{- M_E }}{ (\\var{y2}) \\cos \\alpha + (\\var{x2}) \\sin \\alpha} = \\dfrac{ \\var{M_E }}{\\var{display(y2 * cos(radians(alpha)) + x2 * sin(radians(alpha)))}} = \\var{display(magA)}$

\n

$A_x = A \\cos \\alpha  = \\var{display(qty(vecA[0],units[0]))} = \\var{display(abs(qty(vecA[0],units[0])))} \\var{if(vecA[0]<0,latex('\\\\leftarrow'),latex('\\\\rightarrow'))}$

\n

$A_y = A  \\sin \\alpha  = \\var{display(qty(vecA[1],units[0]))} =  \\var{display(abs(qty(vecA[1],units[0])))}\\var{if(vecA[1]<0,latex('\\\\downarrow'),latex('\\\\uparrow'))}$

\n

\n
\n

Apply $\\Sigma F_x = 0$ and $\\Sigma F_y=0$ to FBD I to find the reactions at {if(fd=0,'C','A')}.

\n
\n

$\\begin{align} \\Sigma F_x &= 0\\\\ A_x - C_x  &=0\\\\ C_x &= A_x\\\\ &= (\\var{display(qty(vecA[0],units[0]))}) \\\\ &= \\var{display(abs(qty(vecC[0],units[0])))} \\var{if(vecC[0]<0,latex('\\\\leftarrow'),latex('\\\\rightarrow'))} \\end{align}$  

\n

$\\begin{align} \\Sigma F_y &= 0\\\\ C_y +A_y & = 0\\\\ C_y &= - A_y \\\\&= -(\\var{display(qty(vecA[1],units[0]))})\\\\  &=  \\var{display(abs(qty(vecC[1],units[0])))} \\var{if(vecC[1]>0,latex('\\\\downarrow'),latex('\\\\uparrow'))} \\end{align}$ 

\n
\n

\n
\n

$\\begin{align} \\Sigma F_x &= 0\\\\   \\simplify{ A_x  +  {sign(fd)} D } - C_x &= 0\\\\ A_x &= \\simplify{C_x - {sign(fd)} D } \\\\&= \\simplify[!collectNumbers]{({-siground(vecC[0],4)}) + ({-vecD[0]})}\\\\ &= \\simplify{({-siground(vecC[0],4)}) + ({-vecD[0]})}\\\\&= \\var{display(abs(qty(vecA[0],units[0])))} \\var{if(vecA[0]<0,latex('\\\\leftarrow'),latex('\\\\rightarrow'))} \\end{align}$  

\n

$\\begin{align}\\Sigma F_y &= 0\\\\ A_y + C_y &=0\\\\A_y &= -C_y \\\\ &= -( \\var{display(qty(vecC[1],units[0]))}) \\\\ &=  \\var{display(abs(qty(vecA[1],units[0])))} \\var{if(vecA[1]<0,latex('\\\\downarrow'),latex('\\\\uparrow'))} \\end{align}$

\n
", "rulesets": {}, "extensions": ["geogebra", "quantities", "stats", "weh"], "variables": {"me": {"name": "me", "group": "Ungrouped variables", "definition": "load[1]", "description": "

the magnitude of the moment

", "templateType": "anything"}, "beta": {"name": "beta", "group": "magnitudes", "definition": "degrees(angle(vector(-1,0),B-C))", "description": "", "templateType": "anything"}, "w": {"name": "w", "group": "Ungrouped variables", "definition": "0//random(100..500#25)", "description": "", "templateType": "anything"}, "x2": {"name": "x2", "group": "magnitudes", "definition": "qty(abs(b[0]-c[0]),units[1])", "description": "", "templateType": "anything"}, "y1": {"name": "y1", "group": "magnitudes", "definition": "qty(B[1],units[1])", "description": "", "templateType": "anything"}, "magA": {"name": "magA", "group": "magnitudes", "definition": "M_E/(y2 * cos(radians(alpha)) + x2 sin(radians(alpha)))\n\n", "description": "

\n

magnidude of force a in version 1 only

", "templateType": "anything"}, "F_w": {"name": "F_w", "group": "magnitudes", "definition": "qty(w,units[0])", "description": "", "templateType": "anything"}, "y2": {"name": "y2", "group": "magnitudes", "definition": "qty(abs(b[1]-c[1]),units[1])", "description": "", "templateType": "anything"}, "version": {"name": "version", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "

version 0 = force d

\n

version 1 = moment e

", "templateType": "anything"}, "vecA": {"name": "vecA", "group": "vectors", "definition": "[-vecD - scalar(magC) * vector(cos(radians(180-beta)), sin(radians(180-beta))),\nscalar(magA)* vector(cos(radians(alpha)), sin(radians(alpha)))][version]", "description": "

reactions at A for both versions as a vector

", "templateType": "anything"}, "alpha": {"name": "alpha", "group": "magnitudes", "definition": "degrees(angle(vector(1,0),B))", "description": "", "templateType": "anything"}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "random(['N','m'],['lb','ft'])", "description": "", "templateType": "anything"}, "M_E": {"name": "M_E", "group": "magnitudes", "definition": "qty(me,units[0]+\"*\"+units[1])", "description": "", "templateType": "anything"}, "fd": {"name": "fd", "group": "Ungrouped variables", "definition": "Load[0]", "description": "

the magnitude of the force

", "templateType": "anything"}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything"}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "vector(random(3..5),random(3..5))", "description": "

location of pin B

", "templateType": "anything"}, "Load": {"name": "Load", "group": "Ungrouped variables", "definition": "[[random(-500..500#25 except 0),0],\n[0,random(100..2000#100) random(1,-1)]]\n[version]", "description": "

establishes whether force or moment load is active.  Weight at B is always zero in this problem

", "templateType": "anything"}, "ggb_load": {"name": "ggb_load", "group": "Ungrouped variables", "definition": "[['fd',fd],['me',me],['w',0]]", "description": "

This will select either the force or the moment, but not both.  Weight is always zero.

\n

\n

", "templateType": "anything"}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "vector(B[0]+ random(3..5),random(-2..3))", "description": "

Location of pin C.  Pin A is at (0,0)

", "templateType": "anything"}, "vecC": {"name": "vecC", "group": "vectors", "definition": "[scalar(magC) * vector(cos(radians(180-beta)),sin(radians(180-beta))),\n-scalar(magA)* vector(cos(radians(alpha)), sin(radians(alpha)))][version]", "description": "

reactions at C for both versions as a vector

", "templateType": "anything"}, "sigma_f": {"name": "sigma_f", "group": "vectors", "definition": "vecW+vecA+vecC + vecD", "description": "", "templateType": "anything"}, "F_d": {"name": "F_d", "group": "magnitudes", "definition": "qty(fd,units[0])", "description": "", "templateType": "anything"}, "x1": {"name": "x1", "group": "magnitudes", "definition": "qty(B[0],units[1])", "description": "", "templateType": "anything"}, "vecW": {"name": "vecW", "group": "vectors", "definition": "vector(0,-w)", "description": "

always 0 in this problem

", "templateType": "anything"}, "magC": {"name": "magC", "group": "magnitudes", "definition": "(F_D y1 /2)/\n(y1 * cos(radians(beta)) + \nx1 * sin(radians(beta)))\n \n", "description": "

magnitude of reaction in version 0 only

", "templateType": "anything"}, "vecD": {"name": "vecD", "group": "vectors", "definition": "vector(scalar(f_d),0)", "description": "", "templateType": "anything"}, "description": {"name": "description", "group": "magnitudes", "definition": "if(version=0,\n display(abs(F_d)) + \" force $D$ at the midpoint of member AB\",\n display(abs(M_E)) + if(me>0,\" counter-\",\" \") + \"clockwise moment $M_E$ \")", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "B[1]<> C[1] and C[1]<>0", "maxRuns": 100}, "ungrouped_variables": ["B", "C", "fd", "me", "w", "units", "ggb_load", "Load", "version", "debug"], "variable_groups": [{"name": "magnitudes", "variables": ["F_w", "F_d", "M_E", "alpha", "beta", "magA", "magC", "x1", "y1", "x2", "y2", "description"]}, {"name": "vectors", "variables": ["vecW", "vecA", "vecC", "sigma_f", "vecD"]}], "functions": {"display": {"parameters": [["Q", "quantity"]], "type": "string", "language": "jme", "definition": "string(siground(q,4))"}}, "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": "

$A_x = $ [[0]] $A_y = $ [[1]] $C_x = $ [[2]] $C_y = $ [[3]]  

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$A_x$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(vecA[0],units[0])", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$A_y$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(vecA[1],units[0])", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$C_x$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(vecC[0],units[0])", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$C_y$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(vecC[1],units[0])", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "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/"}]}