// Numbas version: finer_feedback_settings
{"name": "Ball in a box ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["mass", "a", "g", "decelerate"], "name": "Ball in a box ", "tags": [], "advice": "<h4>a)</h4>\n<p>We resolve $F=ma$ in the upwards positive direction as acceleration is acting vertically upwards, the normal reaction, $R \\ \\mathrm{N}$, will act in the opposite direction to the weight of the ball.</p>\n<p>\\begin{align} <br/>F &amp; = ma \\\\<br/>R - mg &amp;= ma \\\\<br/>R &amp; = mg + ma \\\\<br/>&amp; = \\left(\\var{mass}\\times \\var{g}\\right) + \\left(\\var{mass} \\times \\var{a}\\right) \\\\<br/>&amp; = \\var{precround(mass*g + mass*a,3)}. <br/>\\end{align}</p>\n<p>The normal reaction on the ball has magnitude $\\var{precround(mass*g + mass*a,3)} \\ \\mathrm{N}$.</p>\n<h4>b)&nbsp;</h4>\n<p>We resolve $F=ma$ in the upwards positive direction. The normal reaction force, $R$, will act in the opposite direction to the weight of the ball. This time however the box is decelerating so $a=\\var{-decelerate} \\, \\mathrm{ms^{-2}}$.</p>\n<p>\\begin{align} <br/>F &amp; = ma \\\\<br/>R - mg &amp;= ma \\\\<br/>R &amp; = mg + ma \\\\<br/>&amp; = \\left(\\var{mass}\\times \\var{g}\\right) + \\left(\\var{mass} \\times \\var{-decelerate}\\right) \\\\<br/>&amp; = \\var{precround(mass*g - mass*decelerate,3)}. <br/>\\end{align}</p>\n<p>The normal reaction on the ball has magnitude $\\var{precround(mass*g - mass*decelerate,3)} \\, \\mathrm{N}$.</p>", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "<p>What is the magnitude,&nbsp;in Newtons to 3 decimal places,&nbsp;of the normal reaction of the floor of the box on the ball?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "mass*g + mass*a", "minValue": "mass*g + mass*a", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>The box then moves at a constant speed before&nbsp;decelerating to rest at $\\var{decelerate}\\ \\mathrm{ms^{-2}}$. What is the normal reaction, in Newtons to 3 decimal places, of the floor of the box to the ball during the time the box decelerates?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "mass*g-mass*decelerate", "minValue": "mass*g-mass*decelerate", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>A ball&nbsp;of mass $\\var{mass}kg$ is in a box which accelerates upwards at a rate of $\\var{a} \\, \\mathrm{ms}^{-2}$.&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(0.25..3#0.25)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "decelerate": {"definition": "random(0.3..5#0.35)", "templateType": "randrange", "group": "Ungrouped variables", "name": "decelerate", "description": ""}, "mass": {"definition": "random(1..100#1)", "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 inside a box which is suspended vertically by a cord. Question uses $F=ma$ for different accelerations.</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/"}]}