// Numbas version: finer_feedback_settings
{"name": "Acceleration and weight: apply $F=ma$ and $W=mg$", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["mass1", "g", "weight1", "mass2", "a1", "force1", "mass3", "force2", "decelerate"], "name": "Acceleration and weight: apply $F=ma$ and $W=mg$", "tags": [], "advice": "<p><strong>a)</strong> Use $W=mg = \\var{mass1} \\times \\var{g}$. So the weight is $\\var{mass1*g} \\ \\mathrm{N}$.</p>\n<p><strong>b)</strong> To find the mass we use $W=mg$ rearranged for $m$. This gives $m = \\frac{W}{g} = \\frac{\\var{weight1}}{\\var{g}}$. So the mass is $\\var{precround(weight1/g,3)} \\ \\mathrm{kg}$.</p>\n<p><strong>c)</strong> Use $F=ma$ with $m=\\var{mass2}$ and $a=\\var{a1}$. This gives $F=\\var{mass2} \\times \\var{a1} = \\var{mass2*a1}$. So the force required is $\\var{mass2*a1} \\ \\mathrm{N}$.</p>\n<p><strong>d)</strong> Use $F=ma$ rearranged for $a$. This gives $a = \\frac{F}{m} = \\frac{\\var{force1}}{\\var{mass3}}$. So the acceleration is $a=\\var{precround(force1/mass3,3)} \\ \\mathrm{ms^{-2}}$.</p>\n<p><strong>e)</strong> Use $F=ma$ rearranged for $m$. This gives $m = \\frac{F}{a} = \\frac{\\var{force2}}{\\var{decelerate}}$. So the mass is $m=\\var{precround(force2/decelerate,3)} \\ \\mathrm{kg}$.</p>\n<p></p>", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "<p>Find the weight in Newtons of a box that has mass $\\var{mass1} \\, \\mathrm{kg}$.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "mass1*g", "minValue": "mass1*g", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>If the weight of a particle is $\\var{weight1} \\, \\mathrm{N}$ what is its mass?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "weight1/g", "minValue": "weight1/g", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>Find the force required to accelerate a $\\var{mass2} \\, \\mathrm{kg}$ mass at a rate of $\\var{a1} \\, \\mathrm{ms^{-2}}$.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "mass2*a1", "minValue": "mass2*a1", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p style=\"text-align: left;\">Find the acceleration when a particle of mass $\\var{mass3} \\, \\mathrm{kg}$ is acted on by a resultant force of $\\var{force1} \\, \\mathrm{N}$.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "force1/mass3", "minValue": "force1/mass3", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>A&nbsp;moving object is acted upon by&nbsp;a force of $\\var{force2} \\, \\mathrm{N}$ which causes it to decelerate at a rate of $\\var{decelerate} \\, \\mathrm{ms^{-2}}$. Find the mass of the object.</p>", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "force2/decelerate", "minValue": "force2/decelerate", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>Using $g= 9.8\\ \\mathrm{ms^{-2}}$ answer the following questions to 3 decimal places.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"decelerate": {"definition": "random(0.5..5#0.25)", "templateType": "randrange", "group": "Ungrouped variables", "name": "decelerate", "description": ""}, "mass1": {"definition": "random(1..10#0.25)", "templateType": "randrange", "group": "Ungrouped variables", "name": "mass1", "description": ""}, "mass3": {"definition": "random(200..500#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "mass3", "description": ""}, "g": {"definition": "9.8", "templateType": "number", "group": "Ungrouped variables", "name": "g", "description": "<p>gravity</p>"}, "mass2": {"definition": "random(0.5..7#0.25)", "templateType": "randrange", "group": "Ungrouped variables", "name": "mass2", "description": ""}, "a1": {"definition": "random(0.5..8#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a1", "description": "<p>acceleration</p>"}, "force1": {"definition": "random(80..300#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "force1", "description": "<p>force acting on particle</p>"}, "weight1": {"definition": "random(200..600#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "weight1", "description": ""}, "force2": {"definition": "random(15..60#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "force2", "description": ""}}, "metadata": {"description": "<p>Solving questions using $F=ma$ and $W=mg$.</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/"}]}