// Numbas version: exam_results_page_options
{"name": "Relate impulse to change in momentum", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["football_mass", "football_speed", "squash_mass", "squash_speed", "restitution", "squash_impulse", "squash_second_speed"], "name": "Relate impulse to change in momentum", "tags": [], "advice": "<h4>a)</h4>\n<p>Impulse is change in momentum. The ball begins at rest so initially has a momentum of zero.</p>\n<p>Therefore</p>\n<p>\\begin{align} <br/>I &amp; = \\var{football_mass} \\times\\var{football_speed} - 0, \\\\<br/>&amp; = \\var{siground(football_mass*football_speed,3)} \\, \\mathrm{Ns}. <br/>\\end{align}</p>\n<p>The impulse received by the ball is $ \\var{siground(football_mass*football_speed,3)} \\, \\mathrm{Ns}$.</p>\n<h4>b)</h4>\n<p>Impulse is change in momentum. Therefore we take the rebound direction as being positive and have that&nbsp;</p>\n<p>\\begin{align} <br/>I &amp; = mv - mu, \\\\<br/>\\var{squash_impulse} &nbsp;&amp; = \\var{squash_mass} v - (\\var{squash_mass} \\times \\var{- squash_speed}), \\\\<br/>v &amp; = \\frac{\\var{squash_impulse} + (\\var{squash_mass} \\times \\var{-squash_speed})}{\\var{squash_mass}}, \\\\<br/>&amp; = \\var{siground((squash_impulse + squash_mass*-squash_speed)/squash_mass,3)} \\, \\mathrm{ms^{-1}}. <br/>\\end{align}</p>\n<p>The speed after the ball rebounds is $\\var{siground(squash_second_speed,3)} \\, \\mathrm{ms^{-1}}$.</p>", "rulesets": {}, "parts": [{"precisionType": "sigfig", "prompt": "<p>A football of mass $\\var{football_mass} \\, \\mathrm{kg}$ is at rest before&nbsp;it is kicked.</p>\n<p>What is the impulse received by the ball in $\\mathrm{Ns}$ if its speed is $\\var{football_speed}&nbsp;\\,&nbsp;\\mathrm{ms^{-1}}$ after it is struck?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "football_mass*football_speed", "minValue": "football_mass*football_speed", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "sigfig", "prompt": "<p>A squash ball of mass $\\var{squash_mass} \\, \\mathrm{kg}$ hits a fixed vertical wall at right angles with speed $\\var{squash_speed} \\, \\mathrm{ms^{-1}}$. The ball rebounds at right angles to the wall.</p>\n<p>What is the speed of the ball in $\\mathrm{ms^{-1}}$ just after it has hit the wall, given that the magnitude of the impulse exerted by the wall on the ball is $\\var{squash_impulse} \\, \\mathrm{Ns}$?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "(squash_impulse)/(squash_mass) - squash_speed", "minValue": "(squash_impulse)/(squash_mass) - squash_speed", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>Give your&nbsp;answers to the following questions to 3 significant figures.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "squash_second_speed>0"}, "preamble": {"css": "", "js": ""}, "variables": {"squash_impulse": {"definition": "precround(squash_mass*((1+restitution)*squash_speed),1)", "templateType": "anything", "group": "Ungrouped variables", "name": "squash_impulse", "description": ""}, "squash_mass": {"definition": "random(0.01..1#0.01)", "templateType": "randrange", "group": "Ungrouped variables", "name": "squash_mass", "description": ""}, "football_speed": {"definition": "random(10..50#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "football_speed", "description": ""}, "squash_second_speed": {"definition": "squash_impulse/squash_mass-squash_speed", "templateType": "anything", "group": "Ungrouped variables", "name": "squash_second_speed", "description": ""}, "squash_speed": {"definition": "random(0.5..5#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "squash_speed", "description": ""}, "football_mass": {"definition": "random(0.05..1#0.05)", "templateType": "randrange", "group": "Ungrouped variables", "name": "football_mass", "description": ""}, "restitution": {"definition": "random(0.1..0.9#0.02)", "templateType": "randrange", "group": "Ungrouped variables", "name": "restitution", "description": "<p>coefficient of restitution of the wall</p>"}}, "metadata": {"description": "<p>Finding speeds and impulses&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}]}]}], "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}]}