// Numbas version: finer_feedback_settings {"name": "Centroid by integration: upper and lower bounds are functions", "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

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": "Centroid by integration: upper and lower bounds are functions", "tags": ["centroid", "integration", "Mechanics", "mechanics", "Statics", "statics"], "metadata": {"description": "

Use integration to find the centroid of an area bounded by a parabola, a sloping line, and the y-axis.

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

{applet()}

Determine the coordinates of the centroid of the shaded area bounded by the $y$-axis, a parabola passing throught the origin and point $A$, and a straight line passing through points $A$ and $B$.

Given: $A = ( \\var{A[0]}, \\var{A[1]} ), B = (0, \\var{b}) $

", "advice": "

Bounding Functions

Parabola: $f(x) = k x^2$

at $x=\\var{A[0]}, f(x)=\\var{A[1]}$ , so $k = \\dfrac{\\var{A[1]}}{\\var{A[0]}^2}$

so, $f(x) = \\var[fractionNumbers]{A[1]/A[0]^2} x^2$

Line: $g(x) = m x + b$

where $m = \\dfrac{(\\var{A[1]}-\\var{b})}{\\var{x}}$, and $b = \\var{b}$

so, g(x) = $\\var[fractionNumbers]{(A[1]-b) /x} x + \\var{b}$

Strip Properties for Vertical strips

$dA = [g(x) - f(x)]\\; dx =\\left(\\simplify[all]{- {A[1]}/{A[0]}^2} x^2 +\\simplify{({A[1]}-{b}) /{x}} x + \\simplify{{b}} \\right )\\; dx $

$\\bar{x}_{el} = x$

$\\bar{y}_{el} = \\dfrac{g(x) + f(x)}{2} $

Integrals

$A = \\int_0^\\var{x}\\; dA = \\var{siground(area,4)} \\text{ units}^2$

$Q_y = \\int_0^\\var{x} \\bar{x}_{el} \\; dA = \\var{siground(Qy,4)} \\text{ units}^3$

$Q_x = \\int_0^\\var{x} \\bar{y}_{el} \\; dA = \\var{siground(Qx,4)}\\text{ units}^3$

Centroid

$\\bar{x} = \\dfrac{Q_y}{A} = \\var{siground(xbar,4)}$ units

$\\bar{y} = \\dfrac{Q_x}{A} = \\var{siground(ybar,4)}$ units

", "rulesets": {}, "extensions": ["geogebra", "quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"A": {"name": "A", "group": "Ungrouped variables", "definition": "vector(random(1..10),random(3..12))", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(0..10)", "description": "

y component of point B

", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "A[1]/A[0]^2", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "(A[1]-b)/A[0]", "description": "

slope

", "templateType": "anything", "can_override": false}, "area": {"name": "area", "group": "Unnamed group", "definition": "- k x^3/3 + m x^2/2 + b x", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "A[0]", "description": "", "templateType": "anything", "can_override": false}, "Qy": {"name": "Qy", "group": "Unnamed group", "definition": "- k x^4/4 + m x^3/3 + b x^2/2", "description": "", "templateType": "anything", "can_override": false}, "xbar": {"name": "xbar", "group": "Unnamed group", "definition": "Qy/area", "description": "", "templateType": "anything", "can_override": false}, "Qx": {"name": "Qx", "group": "Unnamed group", "definition": "(-k^2 x^5/5 + m^2 x^3/3 + m b x^2 + b^2 x)/2", "description": "", "templateType": "anything", "can_override": false}, "ybar": {"name": "ybar", "group": "Unnamed group", "definition": "Qx/area", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "m <> 0 // don't want the line to be horizontal", "maxRuns": 100}, "ungrouped_variables": ["A", "b", "k", "m", "x"], "variable_groups": [{"name": "Unnamed group", "variables": ["area", "Qy", "xbar", "Qx", "ybar"]}], "functions": {"g": {"parameters": [["x", "number"]], "type": "number", "language": "jme", "definition": " m x + by"}, "applet": {"parameters": [], "type": "ggbapplet", "language": "javascript", "definition": "//{geogebra_applet('cpf7gyej',['A': A, 'by': b, \"C\": [visible: false, label_style: 3]])}\n// Create the worksheet. \n// This function returns an object with a container `element` and a `promise` resolving to a GeoGebra applet.\nvar params = {\n material_id: 'cpf7gyej'\n}\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 \n //initialize the dimensions and forces\n \n function setGGBPoint(g_name, n_name = g_name) {\n // moves point in GGB to location of Numbas Vector Variable\n // g_name = geogebra point, n_name = numbas vector\n \n //var pt = question.scope.evaluate(n_name).value\n var pt = scope.getVariable(n_name).value\n app.setFixed(g_name,false,false);\n app.setCoords(g_name, pt[0], pt[1]);\n app.setFixed(g_name,true,true);\n }\n \n function setGGBNumber(gname, nname=gname) {\n // Sets number in GGB to a Numbas Variable\n var n = question.scope.evaluate(nname).value;\n app.setValue(gname,n);\n }\n \n setGGBPoint(\"A\");\n setGGBNumber(\"by\", \"b\");\n app.setVisible(\"C\",false);// centroid\n\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": "question.signals.on('adviceDisplayed',function() {\n try{\n var app = question.applet.app;\n app.setVisible(\"C\", true,false);\n }\n catch(err){} \n \n})\n\n\n\n", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "centroid", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

$\\bar{x} = $ [[0]] units

$\\bar{y} = $ [[1]] units

", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "xbar", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(xbar,'')", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "ybar", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(ybar,'')", "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/"}]}