// Numbas version: exam_results_page_options
{"name": "Simon's copy of Block sliding down a slope", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Simon's copy of Block sliding down a slope", "variablesTest": {"maxRuns": 100, "condition": "mu<1"}, "tags": [], "parts": [{"showCorrectAnswer": true, "prompt": "<p>Find the normal reaction, $R \\ \\mathrm{N}$ between the block and the plane, to 3 decimal places.</p>", "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "mustBeReduced": false, "marks": 1, "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "minValue": "R", "allowFractions": false, "correctAnswerFraction": false, "maxValue": "R", "customMarkingAlgorithm": "", "type": "numberentry"}, {"precision": "3", "prompt": "<p>Using $R$ find the coefficient of friction, $\\mu$, between the block&nbsp;and the plane, to 3 decimal places.</p>", "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "precisionType": "dp", "variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "showPrecisionHint": false, "correctAnswerFraction": false, "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "showCorrectAnswer": true, "minValue": "mu", "strictPrecision": false, "extendBaseMarkingAlgorithm": true, "maxValue": "mu", "scripts": {}, "allowFractions": false, "mustBeReduced": false, "customMarkingAlgorithm": ""}, {"precision": "3", "prompt": "<p>Suppose that the block hits the bottom of the slope at a speed of $\\var{v}\\mathrm{ms^{-1}}$. To 3 decimal places, how far in metres ($\\mathrm{m}$)&nbsp;has the block slid from its initial position?</p>", "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "precisionType": "dp", "variableReplacements": [], "unitTests": [], "showFeedbackIcon": true, "showPrecisionHint": false, "correctAnswerFraction": false, "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "showCorrectAnswer": true, "minValue": "v^2/(2*a)", "strictPrecision": false, "extendBaseMarkingAlgorithm": true, "maxValue": "v^2/(2*a)", "scripts": {}, "allowFractions": false, "mustBeReduced": false, "customMarkingAlgorithm": ""}], "variable_groups": [], "ungrouped_variables": ["mass", "theta", "a", "R", "mu", "v", "s", "slide_distance"], "variables": {"mu": {"name": "mu", "group": "Ungrouped variables", "templateType": "anything", "description": "<p>The coefficient of&nbsp;friction between the block and the plane.</p>", "definition": "(mass*9.8*cos(radians(90-theta))-mass*a)/R"}, "a": {"name": "a", "group": "Ungrouped variables", "templateType": "randrange", "description": "<p>The acceleration of the block down the slope.</p>", "definition": "random(2..4.5#0.25)"}, "mass": {"name": "mass", "group": "Ungrouped variables", "templateType": "randrange", "description": "<p>The mass of the block.</p>", "definition": "random(0.25..10#0.25)"}, "R": {"name": "R", "group": "Ungrouped variables", "templateType": "anything", "description": "<p>The normal reaction force&nbsp;of the plane on the block, rounded to 3 d.p.</p>", "definition": "precround(mass*9.8*cos(radians(theta)),3)"}, "v": {"name": "v", "group": "Ungrouped variables", "templateType": "randrange", "description": "", "definition": "random(0.5..5#0.25)"}, "slide_distance": {"name": "slide_distance", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "(v^2)/(2a)"}, "theta": {"name": "theta", "group": "Ungrouped variables", "templateType": "randrange", "description": "<p>The angle of the slope.</p>", "definition": "random(30..50#1)"}, "s": {"name": "s", "group": "Ungrouped variables", "templateType": "anything", "description": "<p>The distance the block slides before it reaches the given velocity.</p>", "definition": "v^2/(2*a)"}}, "metadata": {"description": "<p>A block of given mass is sliding down the plane, with given acceleration. Find the normal reaction force, the coefficient of friction, and the distance travelled before reaching a given speed.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"css": "", "js": ""}, "statement": "<p>A block of mass $\\var{mass}\\mathrm{kg}$ slides down a rough plane which is inclined at an angle $\\theta = \\var{theta}^{\\circ}$ to the horizontal. The mass begins at rest and accelerates at $\\var{a}\\mathrm{ms^{-2}}$.</p>\n<p>The acceleration due to gravity is $g=9.8\\mathrm{ms^{-2}}.$</p>", "functions": {}, "rulesets": {}, "advice": "<h4>a)</h4>\n<p>To find the normal reaction force $R$, we resolve the forces 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{R} \\ \\mathrm{N}.<br/>\\end{align}</p>\n<h4>b)</h4>\n<p>To find the coefficient of friction, $\\mu$, we resolve parallel to the plane and use our $R$ value from part <strong>a)</strong>.</p>\n<p>\\begin{align} <br/>mg \\cos (90^{\\circ} - \\theta) - \\mu R &amp; = ma, \\\\<br/>\\mu &amp; = \\frac{mg \\cos(90^{\\circ} - \\theta) - ma}{R}, \\\\<br/>&amp; = \\frac{ (\\var{mass} \\times 9.8) \\cos (\\var{90 - theta}^{\\circ}) - (\\var{mass} \\times \\var{a})}{\\var{R}}, \\\\<br/>&amp; = \\var{precround(mu,3)}. \\end{align}</p>\n<p>The coefficient of friction between the block and the plane is $\\var{precround(mu,3)}$.</p>\n<h4>c)</h4>\n<p>This question can be solved using the SUVAT equations.</p>\n<p>We know&nbsp;that the block was initially at rest, so $u = 0$.</p>\n<p>The acceleration $a = \\var{a}$.</p>\n<p>The final velocity $v = \\var{v}$.</p>\n<p>We can use the equation $v^2 = u^2 + 2as$, and solve for the distance, $s$.</p>\n<p>\\begin{align} <br/>v^2 &amp; = u^2 + 2 as, \\\\<br/>\\var{v}^2 &amp; = 0 + (2 \\times \\var{a}s), \\\\<br/>s &amp; = \\simplify[]{{v^2}/(2*{a})}, \\\\<br/>&amp; = \\var{precround(slide_distance,3)}\\mathrm{m}. \\end{align}</p>\n<p>The block slid $\\var{precround(v^2/(2*a),3)}\\mathrm{m}$ down the slope before reaching the given speed.</p>", "extensions": [], "type": "question", "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/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "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/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}