// Numbas version: finer_feedback_settings {"name": "Find distance travelled and reaction force given mass and force", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["mass", "force1", "friction", "time", "a"], "name": "Find distance travelled and reaction force given mass and force", "tags": [], "advice": "

a)

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We resolve $F=ma$ in the horizontal direction of acceleration.

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\\begin{align}
F & = ma \\\\
\\var{force1} - \\var{friction} & = \\var{mass} \\times a \\\\
a & = \\frac{\\var{force1} - \\var{friction}}{\\var{mass}} \\\\
& = \\var{precround((force1 - friction)/mass,3)} \\, \\mathrm{ms^{-2}}
\\end{align}

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Therefore the acceleration of the particle is $\\var{a}\\, \\mathrm{ms^{-2}}$.

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b)

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To find the distance travelled we can use the equation $s = ut+\\frac{1}{2}at^2$. The particle begins at rest, so the initial velocity $u=0$, and we have the acceleration $a=\\var{a}$ from part a).

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\\begin{align}
s & = ut+ \\frac{1}{2}at^2 \\\\
& = \\left(0 \\times t \\right) + \\left( \\frac{1}{2} \\times \\var{a} \\times \\var{time}^2 \\right) \\\\
& = \\var{precround(0.5*a*time^2,3)} \\, \\mathrm{m}
\\end{align}

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Therefore the distance travelled is $\\var{precround(0.5*a*time^2,3)}\\ \\mathrm{m}$.

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c)

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We resolve $F=ma$ in the vertical direction, where acceleration is zero. The normal reaction, $R$, is the force which acts perpendicular to the surface, therefore $R$ is in the upwards direction. So $R$ is acting in the opposite direction to the weight of the particle which is $W=mg$.

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\\begin{align}
F & = ma \\\\
R - W &= m \\times 0 \\\\
R - mg & = 0 \\\\
R & = mg \\\\
& = \\var{mass} \\times 9.8 \\\\
& = \\var{precround(mass*9.8,3)} \\, \\mathrm{N}
\\end{align}

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So the normal reaction force has magnitude $\\var{precround(mass*9.8,3)}\\, \\mathrm{N}$.

", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "

What is the acceleration of the particle, in $\\mathrm{ms^{-2}}$?

", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "(force1-friction)/mass", "minValue": "(force1-friction)/mass", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "

In metres, how far does the particle travel in the first $\\var{time}$ seconds?

", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [{"variable": "a", "part": "p0", "must_go_first": false}], "precision": "3", "maxValue": "a*0.5*time^2", "minValue": "a*0.5*time^2", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "

Find the magnitude in $\\mathrm{N}$ of the normal reaction $R$ between the particle and the surface when $g= 9.8 \\, \\mathrm{ms^{-2}}$.

", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "mass*9.8", "minValue": "mass*9.8", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "

A particle of mass $\\var{mass}\\, \\mathrm{kg}$, which is initially at rest, is pushed across a rough surface by a horizontal force of $\\var{force1} \\, \\mathrm{N}$ against a frictional force of $\\var{friction}\\, \\mathrm{N}$.

\n

Give your answers to the following questions to 3 decimal places.

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "(force1-friction)/mass", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "force1": {"definition": "random(7..50#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "force1", "description": ""}, "mass": {"definition": "random(2..10#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "mass", "description": ""}, "friction": {"definition": "random(0.5..6#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "friction", "description": ""}, "time": {"definition": "random(2..8#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "time", "description": ""}}, "metadata": {"description": "

Find the acceleration, distance moved and magnitude of the normal reaction of a particle being pulled along a rough horizontal plane.

", "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/"}], "resources": []}]}], "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}]}