// Numbas version: exam_results_page_options {"name": "Particle Equilibrium: Use slopes to find components", "extensions": ["linear-algebra", "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

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": [{"name": "Particle Equilibrium: Use slopes to find components", "tags": ["Equilibrium", "equilibrium", "Mechanics", "mechanics", "Particle", "particle", "Statics", "statics"], "metadata": {"description": "

Two dimensional particle equilibrium problem. Advice shows how to use how to use slope triangles to find sines and cosines, rather than finding the angle and using that.

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

{applet1(\"G\", 300)}

A $\\var{qty(F,\"N\")}$ force $F$ is applied in the direction shown to a small ring, which is held in equilibrium by two inextensible ropes attached to fixed points $A$ and $B$.

", "advice": "

1. Draw FBD of the Particle

{applet1(\"D\", 250)}

2. Determine slope triangles from geometry.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Force	Rise	Run	Hypotenuse
$F$	$\\var{dyF}$	$\\var{dxF}$	$\\sqrt{\\var{rF2}}$
$A$	$\\var{dyA}$	$\\var{dxA}$	$\\sqrt{\\var{rA2}}$
$B$	$\\var{dyB}$	$\\var{dxB}$	$\\sqrt{\\var{rB2}}$

3. Determine scalar components in terms of $A$, $B$, and $F$ from slopes and given $F = \\var{qty(F,'N')}$

$\\begin{align}
F_x &= \\left(\\frac{\\var{dxF}}{\\sqrt{\\var{rF2}}}\\right) F = \\var{precround(qty(vecF[0], 'N'),4)} & F_y &= \\left(\\frac{\\var{dyF}}{\\sqrt{\\var{rF2}}}\\right) F = \\var{precround(qty(vecF[1], 'N'),4)}\\\\
A_x &= \\left(\\frac{\\var{dxA}}{\\sqrt{\\var{rA2}}}\\right) A = \\var{precround(cos(radians(alpha)),3)} A & A_y &= \\left(\\frac{\\var{dyA}}{\\sqrt{\\var{rA2}}}\\right) A = \\var{precround(sin(radians(alpha)),3)} A\\\\
B_x &= \\left(\\frac{\\var{dxB}}{\\sqrt{\\var{rB2}}}\\right) B = \\var{precround(cos(radians(beta )),3)} B & B_y &= \\left(\\frac{\\var{dyB}}{\\sqrt{\\var{rB2}}}\\right) B = \\var{precround(sin(radians(beta )),3)} B
\\end{align}$

4. Set up two equations of equilibrium.

$\\begin{align}
\\Sigma F_x &= 0 & \\Sigma F_y &= 0\\\\
A_x + B_x + F_x &=0& A_y + B_y +F_y &=0\\\\
\\simplify[!noLeadingMinus]{{precround(cos(radians(alpha)),3)} A + {precround(cos(radians(beta)),3)} B} & =\\var{precround(qty(- vecF[0], 'N'),4)} &
\\simplify[!noLeadingMinus]{{precround(sin(radians(alpha)),3)} A + {precround(sin(radians(beta)),3)} B} & =\\var{precround(qty(- vecF[1], 'N'),4)}\\\\
\\end{align}$

5. Solve simultaneously to get:

$\\begin{align}
A &= \\var{siground(qty(abs(FA),'N'),4)} & B &= \\var{siground(qty(abs(FB),'N'),4)}
\\end{align}$

", "rulesets": {}, "extensions": ["geogebra", "linear-algebra", "quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"applet": {"name": "applet", "group": "Ungrouped variables", "definition": "geogebra_applet('saaa7mqd')", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "random(vector(random(0,10), random(0..-10)), vector(random(0..10), random(0,-10)))", "description": "

Grid top left at (0,0) bottom right at(10,-10)

", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "random(vector(random(0,10), random(0..-10)), vector(random(0..10), random(0,-10)))", "description": "", "templateType": "anything", "can_override": false}, "P": {"name": "P", "group": "Ungrouped variables", "definition": "vector(random(3..7),random(-3..-7))", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "angles", "definition": "degrees(atan2(A[1]-P[1], A[0]-P[0]))", "description": "

Direction of Force A will only point in quadrant 2 or 4

", "templateType": "anything", "can_override": false}, "beta": {"name": "beta", "group": "angles", "definition": "degrees(atan2(B[1]-P[1], B[0]-P[0]))", "description": "

Direction of force B will only point in quadrant 1 or 2

", "templateType": "anything", "can_override": false}, "F": {"name": "F", "group": "Ungrouped variables", "definition": "random(50..600#25)", "description": "", "templateType": "anything", "can_override": false}, "FA": {"name": "FA", "group": "Ungrouped variables", "definition": "soln[0][2]", "description": "", "templateType": "anything", "can_override": false}, "FB": {"name": "FB", "group": "Ungrouped variables", "definition": "soln[1][2]", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "random(vector(random(0,10), random(0..-10)), vector(random(0..10), random(0,-10)))", "description": "", "templateType": "anything", "can_override": false}, "phi": {"name": "phi", "group": "angles", "definition": "degrees(atan2(C[1]-P[1], C[0]-P[0]))", "description": "

Direction of force F (will only point in quadrant 3 or 4)

", "templateType": "anything", "can_override": false}, "soln": {"name": "soln", "group": "Ungrouped variables", "definition": "reduced_row_echelon_form( \nmatrix([cos(radians(alpha)),cos(radians(beta)),- F cos(radians(phi))],\n [sin(radians(alpha)),sin(radians(beta)),- F sin(radians(phi))]))", "description": "", "templateType": "anything", "can_override": false}, "vecA": {"name": "vecA", "group": "Ungrouped variables", "definition": "vector(cos(radians(alpha)),sin(radians(alpha))) FA", "description": "", "templateType": "anything", "can_override": false}, "vecB": {"name": "vecB", "group": "Ungrouped variables", "definition": "vector(cos(radians(beta)),sin(radians(beta))) FB", "description": "", "templateType": "anything", "can_override": false}, "vecF": {"name": "vecF", "group": "Ungrouped variables", "definition": "siground(vector(cos(radians(phi)),sin(radians(phi))) F,4)", "description": "", "templateType": "anything", "can_override": false}, "Check": {"name": "Check", "group": "Ungrouped variables", "definition": "vecA + vecB + vecF", "description": "", "templateType": "anything", "can_override": false}, "dxA": {"name": "dxA", "group": "angles", "definition": "(A[0]-P[0])", "description": "

run for force A

", "templateType": "anything", "can_override": false}, "dyA": {"name": "dyA", "group": "angles", "definition": "(A[1]-P[1])", "description": "

Rise for force A

", "templateType": "anything", "can_override": false}, "dxB": {"name": "dxB", "group": "angles", "definition": "(B[0]-P[0])", "description": "", "templateType": "anything", "can_override": false}, "dyB": {"name": "dyB", "group": "angles", "definition": "(B[1]-P[1])", "description": "", "templateType": "anything", "can_override": false}, "dxF": {"name": "dxF", "group": "angles", "definition": "(C[0]-P[0])", "description": "", "templateType": "anything", "can_override": false}, "dyF": {"name": "dyF", "group": "angles", "definition": "(C[1]-P[1])", "description": "", "templateType": "anything", "can_override": false}, "rA2": {"name": "rA2", "group": "angles", "definition": "(dxA^2+dyA^2)", "description": "", "templateType": "anything", "can_override": false}, "rB2": {"name": "rB2", "group": "angles", "definition": "(dxB^2+dyB^2)", "description": "", "templateType": "anything", "can_override": false}, "rF2": {"name": "rF2", "group": "angles", "definition": "(dxF^2+dyF^2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "//avoid forces on same line of action\ntan(radians(alpha)) <> tan(radians(beta)) and\ntan(radians(beta)) <> tan(radians(phi)) and\ntan(radians(phi)) <> tan(radians(alpha)) and\nFA > 0 and FB > 0 and // only tension please\nFA < 50 F and FB < 50F // and not too big", "maxRuns": 100}, "ungrouped_variables": ["applet", "A", "B", "P", "C", "F", "FA", "FB", "soln", "vecA", "vecB", "vecF", "Check"], "variable_groups": [{"name": "angles", "variables": ["alpha", "beta", "phi", "dxA", "dyA", "dxB", "dyB", "dxF", "dyF", "rA2", "rB2", "rF2"]}], "functions": {"applet1": {"parameters": [["perspective", "string"], ["width", "number"]], "type": "anything", "language": "javascript", "definition": "// Create the worksheet. \n// This function returns an object with a container `element` and a `promise` resolving to a GeoGebra applet.\n\nvar params = {\n material_id: 'saaa7mqd'\n};\nvar result = Numbas.extensions.geogebra.createGeogebraApplet(params);\n\n// Once the applet has loaded, run some commands to manipulate the worksheet.\nresult.promise.then(function(d) {\n var app = d.app;\n question.applet = d;\n app.setPerspective(perspective);\n app.setWidth(width);\n app.setHeight(width);\n //app.setAxesVisible(true,false);\n //app.enableShiftDragZoom(false);\n\n function setGGBPoint(name, nname = name) {\n // moves point in GGB to Numbas value\n var x = Numbas.jme.unwrapValue(question.scope.getVariable(nname));\n app.setFixed(name, false, false); //fixed and selection allowed\n app.setCoords(name, x[0], x[1]);\n app.setFixed(name, true, false);\n }\n\n setGGBPoint('A');\n setGGBPoint('B');\n setGGBPoint('C');\n setGGBPoint('P');\n function setGGBAngle(gname, nname = gname) {\n // Sets angle in GGB to a Numbas Variable given in degrees.\n var v = Math.PI / 180 * Numbas.jme.unwrapValue(question.scope.getVariable(nname));\n app.setValue(gname, v);\n }\n\n //setGGBAngle('\u03b8','theta');\n //setGGBAngle('\u03b1','alpha');\n //app.setValue('tension',Numbas.jme.unwrapValue(question.scope.getVariable('tension')));\n\n});\n\n// This function returns the result of `createGeogebraApplet` as an object \n// with the JME data type 'ggbapplet', which can be substituted into the question's content.\nreturn new Numbas.jme.types.ggbapplet(result);\n"}}, "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": "

Determine the tensions in the two ropes.

$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": "siground(qty(FA,\"N\"),3)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"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": "siground(qty(FB,\"N\"),3)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}