// Numbas version: exam_results_page_options
{"name": "Mass resting on a rough plane", "extensions": [], "custom_part_types": [], "resources": [["question-resources/statics6.png", "/srv/numbas/media/question-resources/statics6.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["g", "mass", "theta", "R", "mu"], "name": "Mass resting on a rough plane", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>We can draw a diagram showing the weight, normal reaction $R$ and the force of friction, $F$.</p>\n<p><img src=\"resources/question-resources/statics6.png\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>Here $\\theta = \\var{theta}^{\\circ}$ and $m = \\var{mass}$.&nbsp;</p>\n<h4>a)</h4>\n<p>To find the normal reaction, $R$, we resolve perpendicular to the plane.</p>\n<p>\\begin{align} <br/>R - mg \\cos \\theta &amp; = 0, \\\\<br/>R &amp; = mg \\cos \\theta, \\\\<br/>&amp; = \\var{mass} \\times 9.8 \\cos (\\var{theta}^{\\circ}), \\\\<br/>&amp; = \\var{precround(mass*9.8*cos(radians(theta)),3)} \\ \\mathrm{N}. <br/>\\end{align}</p>\n<h4>b)</h4>\n<p>To find the coefficient of friction we can resolve parallel to the plane and use our 3d.p. value of $R$ from part a) and the fact that friction is limiting ($F = \\mu R$) as we are in equilibrium.</p>\n<p>\\begin{align} <br/>F - mg \\sin \\theta &amp; = 0, \\\\<br/>F &amp; = mg \\sin \\theta, \\\\<br/>\\mu R &amp; = mg \\sin \\theta, \\\\[0.5em]<br/>\\mu &amp; = \\frac{mg \\sin \\theta}{R}, \\\\[0.5em]<br/>&amp; = \\frac{ \\var{mass} \\times 9.8 \\sin (\\var{theta}^{\\circ})}{\\var{R}}, \\\\[0.5em]<br/>&amp; = \\var{precround( (mass*9.8*sin(radians(theta)))/R,3)}. <br/>\\end{align}</p>", "rulesets": {}, "parts": [{"prompt": "<p>Find the normal reaction, $R$, between the ball and the plane, in $\\mathrm{N}$.</p>\n<p>$R = $&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "mass*g*cos(radians(theta))", "strictPrecision": false, "minValue": "mass*g*cos(radians(theta))", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "3", "scripts": {}, "marks": 1, "showPrecisionHint": true, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Using the value of $R$ from part <strong>a)</strong> find the coeffiecient of friction, $\\mu$, between the ball and the plane.</p>\n<p>$\\mu = $&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "mu", "strictPrecision": false, "minValue": "mu", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "3", "scripts": {}, "marks": 1, "showPrecisionHint": true, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>A ball of mass $\\var{mass} \\ \\mathrm{kg}$ rests in limiting equilibrium on a rough plane inclined at $\\var{theta}^{\\circ}$ above the horizontal.</p>\n<p>Suppose that the acceleration due to gravity is $g= 9.8 \\mathrm{ms^{-2}}$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"mu": {"definition": "(mass*g*sin(radians(theta)))/R", "templateType": "anything", "group": "Ungrouped variables", "name": "mu", "description": ""}, "theta": {"definition": "random(10..44#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "theta", "description": ""}, "R": {"definition": "precround(mass*g*cos(radians(theta)),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "R", "description": "<p>the normal reaction R, 3d.p</p>"}, "mass": {"definition": "random(2..8#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "mass", "description": ""}, "g": {"definition": "9.8", "templateType": "number", "group": "Ungrouped variables", "name": "g", "description": ""}}, "metadata": {"description": "<p>A mass is resting on a rough plane. Given the angle of the plane and the mass of the object, find the normal reaction force&nbsp;and hence the coefficient of friction.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}]}