// Numbas version: exam_results_page_options {"name": "V-M 5a: Arbitrary parabolic loading", "extensions": ["linear-algebra", "geogebra", "polynomials", "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
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto 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.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf 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%,Shear and bending moment diagram for a beam loaded with an arbitrary parabolic distributed load described with a loading function. Integrate to find reactions and equations for shear and bending moment.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "A simply-supported beam of length $L = \\var {qty(beamlen, units[0])}$ is subjected to a parabolic loading $w\\!(x)$ given by the function:
\n$w\\!(x) = \\simplify[fractionNumbers,canonicalOrder]{{w}}$ [{units[1]} / {units[0]}]
\nThe shear and bending moment diagrams are also shown.
\n{applet}
\nStarted working on maximum shear and moment, but did not finish. Need to solve a cubic equation by writing equation solver. I would like to turn the visibility of the curves on as a hint, but need a signal for that.
", "advice": "Given $w(x)$ and beam length $L$,
\n1. Find load $W= \\int_0^L w(x)\\; dx$
\n$\\begin{align} W & = \\int w\\!(x) \\text{d}x \\\\ & = \\simplify[fractionNumbers,canonicalOrder]{defint({w}, x, 0, {beamlen})} \\\\ &= \\left[\\simplify[fractionNumbers,canonicalOrder]{{intw}}+C_1 \\right]_0^\\var{beamlen}\\\\ &= \\var{siground(qty(load,units[1]),5)} = \\var{siground(qty(abs(load),units[1]),5)} \\var{arrow(-load)}\\end{align}$
\n2. Find $Q_y = \\int_0^L x w(x)\\;dx$
\n$\\begin{align} Q_y &= \\int_0^L x\\ w\\!(x) \\text{d}x\\\\&= \\simplify[fractionNumbers,canonicalOrder]{defint({dqy},x,0,L)}\\\\& = \\left[\\simplify[fractionNumbers,canonicalOrder]{{intdqy}}+C_2 \\right]_0^\\var{beamlen}\\\\ &= \\var{siground(qty(Qy,units[0] + \" \" + units[1]),4)} \\end{align}$
\n3. Find centroid $\\bar{x}=\\frac{Q_y}{W}$
\n$\\bar{x} = \\dfrac{Q_y}{W} = \\dfrac{\\var{siground(Qy,4)}}{\\var{siground(load,4)}} = \\var{siground(qty(xbar,units[0]),4)}$
\n4. Take moments about $A$ and $B$ to find reactions.
\n$\\begin{align}\\sum M_B &= 0 & \\sum M_A &=0 \\\\ R_A L &= \\simplify{{sign(load)} W }(L-\\bar{x}) & + R_B L &= \\simplify{{sign(load)} W }\\bar{x} & \\\\ R_A&= \\var{show(qty(abs(R_A),units[1]))} \\var{arrow(R_A)} & R_B &= \\var{show(qty(abs(R_B),units[1]))} \\var{arrow(R_B)} \\end{align}$
\n5. Integrate $V(x) = \\int w(x)\\; dx$ to get the shear function.
\nNote: Positive values of $w\\!(x)$ indicate downward forces, so the integrations is over $-w\\!(x)$.
\n$\\begin{align} V\\!(x) &= \\int - w\\!(x) dx \\\\&= \\simplify[fractionNumbers, canonicalOrder]{int({-w},x)} \\\\&= \\simplify[fractionNumbers,canonicalOrder]{{v -v[0]}}+C_3 && v\\!(0) = R_A \\therefore C_3 = \\var{show(qty(R_A,\"\"))}\\\\ &= \\simplify[fractionNumbers,canonicalOrder]{{v}} && [\\var{units[1]}] &\\end{align}$
\n6. Integrate $M(x) = \\int V(x)\\; dx$ to get moment function.
\n$\\begin{align} M\\!(x) &= \\int V\\!(x) dx \\\\&= \\simplify[fractionNumbers, canonicalOrder]{int({v},x)}\\\\&= \\simplify[fractionNumbers,canonicalOrder]{{v}}+C_4 && M\\!(0) =0 \\therefore C_4 = 0 \\\\&= \\simplify[fractionNumbers,canonicalOrder]{{m}} && [\\var{units[1]}\\text{-}\\var{units[0]} ]&\\end{align}$
\n\nMaximum moment occurs where $dM/dx = V = 0$
\nEvaluate $M(x)$ at point of maximum bending moment.
\nMaximum shear occurs where $d V /d x = -w(x) = 0$
\nEvaluate $V(x)$ at point of maximum shear.
\n\nTo find maximum shear, determine where $\\simplify{diff(v,x,1)} = -w\\!(x) = 0$ using the quadratic equation.
\n$x_{max} = \\frac{- b \\pm \\sqrt{b^2 - 4 a c}}{2a}$ where, $a= \\var[fractionNumbers]{-w[2]}, b=\\var[fractionNumbers]{-w[1]}$ and $c=\\var[fractionNumbers]{-w[0]}$.
\nAny real roots of $w\\!(x)$ between the beam's endpoints plus the endpoints themselves are locations of local maximums or minimums.
\n{v_extremes}
\n$\\simplify{{show(v_extremes[1])}}$
\nThe maximum of these local maximums is the the one we want
\n$V_{max} = \\var{show(qty(v_max[1], units[1]))}$
\n\n", "rulesets": {}, "extensions": ["geogebra", "linear-algebra", "polynomials", "quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"beamLen": {"name": "beamLen", "group": "Unnamed group", "definition": "random(10..20#2)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Unnamed group", "definition": "random(['ft','lb'],['m','kN'])", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Unnamed group", "definition": "vector(0,random(-4..3) scale )", "description": "Leftmost point on loading curve (x, w(x))
", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Unnamed group", "definition": "vector(beamLen,random(-4..3) scale )", "description": "rightmost point on loading curve (x, w(x))
", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "Unnamed group", "definition": "vector(random(4..beamlen-4), random(-4..4) scale )", "description": "interior point on loading curve (x, w(x))
", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "functions", "definition": "geogebra_file('newVM_6j6k8Vp.ggb',params)", "description": "// Create the worksheet.
// This function returns an object with a container `element` and a `promise` resolving to a GeoGebra applet.
var params = {
material_id: 'r8hqdxsg',
width:560,
height:600
}
var result = Numbas.extensions.geogebra.createGeogebraApplet(params);
\n// Once the applet has loaded, run some commands to manipulate the worksheet.
result.promise.then(function(d) {
var app = d.app;
question.applet = d;
//initialize the dimensions and forces
function setGGBPoint(g_name, n_name = g_name) {
// moves point in GGB to location of Numbas Vector Variable
// g_name = geogebra point, n_name = numbas vector
//var pt = question.scope.evaluate(n_name).value
var pt = scope.getVariable(n_name).value
app.setFixed(g_name,false,false);
app.setCoords(g_name, pt[0], pt[1]);
//app.setFixed(g_name,true,true);
}
function setGGBNumber(g_name, n_name = g_name) {
// Sets number in GGB to a Numbas Variable
var n = scope.getVariable(n_name).value;
app.setValue(g_name,n);
}
var units = question.unwrappedVariables.units
app.setTextValue('units_d', units[0]);
app.setTextValue('units_f', units[1]);
setGGBNumber('beamLen');
setGGBPoint(\"A'\", \"A\");
setGGBPoint(\"B'\", \"B\");
setGGBPoint(\"C'\", \"C\");
app.evalCommand(\"RunClickScript(Rescale)\");
app.setFixed(\"B\",true,true);
app.setVisible(\"A'\", false, false);
app.setVisible(\"B'\", false, false);
app.setVisible(\"C'\", false, false);
app.setVisible('TR',false);
app.setVisible('BL',false);
app.setLabelVisible('TR',true);
app.setLabelStyle('TR',2);
app.setLabelVisible('BL',true);
app.setLabelStyle('BL',2);
app.setCoords('BL',-4,-35);
app.setVisible(\"showR\", false, false);
app.setVisible(\"showV\", false, false);
app.setVisible(\"showM\", false, false);
app.setVisible(\"showMax\", false, false);
app.setValue(\"showR\",false);
app.setValue(\"showV\",false);
app.setValue(\"showM\",false);
app.setValue(\"showMax\",false);
app.setVisible(\"NewProblem\", false, false);
app.setVisible(\"Rescale\", false, false);
app.setVisible(\"textShowSoln\", false, false);
});
// This function returns the result of `createGeogebraApplet` as an object
// with the JME data type 'ggbapplet', which can be substituted into the question's content.
return new Numbas.jme.types.ggbapplet(result);
safe(\"CopyFreeObject(scaleFunction(Max({M_{max},abs(M_{min})})/3 ))\")
\n\"C'\": [definition: \"({b},{h} AxisStepY()/Scale_w)\"],
\nScale_w: [definition: safe('CopyFreeObject(scaleFunction(y(Max(w, 0.0000, beamLen)) / 3))')]
\n\n\n\nvar units = question.unwrappedVariables.units
app.setTextValue('units_d', units[0]);
app.setTextValue('units_f', units[1]);
setGGBNumber('beamLen');
setGGBPoint(\"A'\", \"A\");
setGGBPoint(\"B'\", \"B\");
setGGBPoint(\"C'\", \"C\");
app.evalCommand(\"RunClickScript(Rescale)\");
app.setFixed(\"B\",true,true);
app.setVisible(\"A'\", false, false);
app.setVisible(\"B'\", false, false);
app.setVisible(\"C'\", false, false);
app.setVisible('TR',false);
app.setVisible('BL',false);
app.setLabelVisible('TR',true);
app.setLabelStyle('TR',2);
app.setLabelVisible('BL',true);
app.setLabelStyle('BL',2);
app.setCoords('BL',-4,-35);
app.setVisible(\"showR\", false, false);
app.setVisible(\"showV\", false, false);
app.setVisible(\"showM\", false, false);
app.setVisible(\"showMax\", false, false);
app.setValue(\"showR\",false);
app.setValue(\"showV\",false);
app.setValue(\"showM\",false);
app.setValue(\"showMax\",false);
app.setVisible(\"NewProblem\", false, false);
app.setVisible(\"Rescale\", false, false);
app.setVisible(\"textShowSoln\", false, false);
});
used to solve three simultaneous equations to find C1, C2, C3
\ny = C1 x^2 + C2 x + C3
", "templateType": "anything", "can_override": false}, "w": {"name": "w", "group": "functions", "definition": "polynomial(x,[matrix[2][3], matrix[1][3], matrix[0][3],0,0])", "description": "loading function w(x)
", "templateType": "anything", "can_override": false}, "v": {"name": "v", "group": "functions", "definition": "-polynomial(x, [-R_A, w[0], w[1]/2, w[2]/3])", "description": "This is the shear function V(x) = - \\int w(x) dx
\nConstant C is reaction at x=0
", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "functions", "definition": "polynomial(x,[ 0, v[0], v[1]/2, v[2]/3, v[3]/4])", "description": "", "templateType": "anything", "can_override": false}, "load": {"name": "load", "group": "Reactions", "definition": "eval(intW,beamlen) - eval(intW,0)", "description": "downward force on beam = $\\simplify{defint(w,x,0,{beamlen})$
\n\nPositive = down
", "templateType": "anything", "can_override": false}, "dQy": {"name": "dQy", "group": "Reactions", "definition": "polynomial(x) w", "description": "", "templateType": "anything", "can_override": false}, "intdQy": {"name": "intdQy", "group": "Reactions", "definition": "polynomial(x, [0, dQy[0], dQy[1]/2, dQy[2]/3, dQy[3]/4])", "description": "integral of dQy
", "templateType": "anything", "can_override": false}, "Qy": {"name": "Qy", "group": "Reactions", "definition": "eval(intdqy,beamlen)", "description": "definite integral of x dw from 0 to L
", "templateType": "anything", "can_override": false}, "xBar": {"name": "xBar", "group": "Reactions", "definition": "Qy/load", "description": "", "templateType": "anything", "can_override": false}, "intW": {"name": "intW", "group": "Reactions", "definition": "polynomial(x, [0, w[0], w[1]/2, w[2]/3])", "description": "", "templateType": "anything", "can_override": false}, "R_B": {"name": "R_B", "group": "Reactions", "definition": "xbar load / beamlen", "description": "reaction at B Positive is up
", "templateType": "anything", "can_override": false}, "R_A": {"name": "R_A", "group": "Reactions", "definition": "(beamlen-xbar) load/ beamlen", "description": "", "templateType": "anything", "can_override": false}, "check": {"name": "check", "group": "Reactions", "definition": "withintolerance(R_A+R_B,load,10^10)", "description": "check sometimes has roundoff error.
", "templateType": "anything", "can_override": false}, "roots": {"name": "roots", "group": "maxshear", "definition": "sort(\n if(d>=0, \n filter(x>=0 and x <=beamlen,x,\n let([a: w[2], b: w[1], c: w[0]], \n [(-b + sqrt(d))/(2 a), (-b - sqrt(d))/(2 a)]\n)),[]) + [0,beamlen])", "description": "use quadratic equation to find where w(x) is zero, filter out any roots not on interval, or imaginary.
\nThe maximum shear will occur at one of these points
", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "w[1]^2 - 4 w[2] * w[0]", "description": "descriminant for quadratic equation w(x)
", "templateType": "anything", "can_override": false}, "v_extremes": {"name": "v_extremes", "group": "maxshear", "definition": "map(vector(x,eval(v,x)),x,roots)", "description": "extreme points
\nlist of shear force v(x) at ends and at roots of w(x) -- potential maximums or minimums
", "templateType": "anything", "can_override": false}, "v_max": {"name": "v_max", "group": "maxshear", "definition": "foldl(if(abs(pt[1])>abs(v[1]),pt,v),pt, v, vector(0,0),v_extremes)", "description": "filters the list of v_extremes to find the one with the greatest absolute value of shear
", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "load <> 0 // we really want the load to be non-zero\nand abs(w[2]) > 1/10// and want to be sure it is a quadratic\n", "maxRuns": 100}, "ungrouped_variables": ["d", "debug"], "variable_groups": [{"name": "Unnamed group", "variables": ["A", "B", "C", "scale", "beamLen", "units"]}, {"name": "functions", "variables": ["applet", "params", "matrix", "w", "v", "m"]}, {"name": "Reactions", "variables": ["load", "dQy", "intdQy", "Qy", "xBar", "intW", "R_B", "R_A", "check"]}, {"name": "maxshear", "variables": ["roots", "v_extremes", "v_max"]}], "functions": {"arrow": {"parameters": [["F", "?"]], "type": "anything", "language": "jme", "definition": "if(sign(F) >= 0 ,latex(\"\\\\uparrow\"), latex(\"\\\\downarrow\"))"}, "show": {"parameters": [["A", "?"]], "type": "anything", "language": "jme", "definition": "if(abs(if(type(A)=type(qty(1,'m')),scalar(A),A))<1,\n precround(A,4),siground(A,4))"}}, "preamble": {"js": "question.signals.on('adviceDisplayed',function() {\n try{\n var app = question.scope.variables.applet.app; \n app.setVisible(\"showV\", true,false);\n app.setVisible(\"showM\", true,false);\n app.setValue(\"showV\",true);\n app.setValue(\"showM\",true);\n }\n catch(err){} \n})\n\n\n", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Reactions", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Find the reactions at the end suppports. Use negative values to indicate downward forces.
\n$R_A = $ [[0]] $\\qquad R_B=$ [[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": "qty(R_A,units[1])", "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": "qty(R_B,units[1])", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Shear Function", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Use integration to determine the equation of the shear function $V\\!(x) = \\int -w\\!(x) \\textrm{d} x$
\n$V\\!(x) = \\simplify[fractionNumbers,canonicalOrder]{{v}}$ = {string(v)}
\n$V\\!(x) = $[[0]]
", "gaps": [{"type": "jme", "useCustomName": true, "customName": "$V\\!(x)$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{expr(v)}", "answerSimplification": "fractionNumbers,canonicalOrder", "showPreview": true, "checkingType": "sigfig", "checkingAccuracy": "2", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, "1"], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Bending Moment", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Use integration to find the bending moment function $M(x) =\\int V\\!(x) \\textrm{d}x$.
\n$M\\!(x) = \\simplify[fractionNumbers,canonicalOrder]{{m}}$ = {string(m)}
\n$M\\!(x) = $ [[0]]
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