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{"name": "Find weight of particle under gravity, and acceleration given force", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["m", "F"], "name": "Find weight of particle under gravity, and acceleration given force", "tags": [], "advice": "<h4>a)</h4>\n<p>The weight of a particle in Newtons is given by&nbsp;</p>\n<p>\\begin{align} W &amp; = mg \\\\<br/>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&amp; = \\var{m} \\times 9.8 \\\\<br/>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&amp; = \\var{m*9.8}, \\end{align}</p>\n<p>where $g$ is the force due to gravity acting on an object.&nbsp;The particle weighs $\\var{precround(m*9.8,3)} \\, \\mathrm{N}$.</p>\n<h4>b)</h4>\n<p>We can use the relationship $F=ma$ to find the acceleration $a$.</p>\n<p>\\begin{align} F &amp; = ma \\\\<br/>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;\\var{F} &nbsp; &nbsp;&amp; = \\var{m} \\times a \\\\<br/>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;a &amp; = \\var{precround(F/m,3)}. \\end{align}<br/>The acceleration is $\\var{precround(F/m,3)} \\, \\mathrm{ms}^{-2}$.</p>", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "<p>Find the weight in Newtons of this particle.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "m*9.8", "minValue": "m*9.8", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>Find the acceleration in $\\mathrm{ms^{-2}}$ of the particle when it is acted on by a resultant force of $\\var{F}\\ \\mathrm{N}$. Give your answer to 3 decimal places.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "F/m", "minValue": "F/m", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>Consider a particle of mass $\\var{m} \\, \\mathrm{kg}$. The acceleration due to gravity is $9.8 \\, \\mathrm{ms^{-2}}$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"m": {"definition": "random(5..15#0.25)", "templateType": "randrange", "group": "Ungrouped variables", "name": "m", "description": "<p>particles mass</p>"}, "F": {"definition": "random(1..15#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "F", "description": "<p>Force&nbsp;</p>"}}, "metadata": {"description": "<p>Find the weight of a particle when the mass and acceleration due to gravity is known. Using $F=ma$ to find the acceleration of the particle when it is acted on by a resultant force.</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/"}]}