// Numbas version: exam_results_page_options
{"name": "Pushing a box up an inclined plane", "extensions": [], "custom_part_types": [], "resources": [["question-resources/force_acting_on_incline.png", "/srv/numbas/media/question-resources/force_acting_on_incline.png"], ["question-resources/force_acting_on_an_incline_solution.png", "/srv/numbas/media/question-resources/force_acting_on_an_incline_solution.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["mass", "P", "theta", "R"], "name": "Pushing a box up an inclined plane", "tags": [], "advice": "<h4>a)</h4>\n<p>We can draw a diagram to show the forces acting on the box. The plane is smooth so there is no friction.&nbsp;<img src=\"resources/question-resources/force_acting_on_an_incline_solution.png\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>To find the normal reaction between the box and the plane we solve $F=ma$ perpendicular to the plane.</p>\n<p>\\begin{align} <br/>F &amp; &nbsp;= ma, \\\\<br/>R - mg \\cos \\theta - P \\cos(90^{\\circ} - \\theta) &amp; = m \\times 0, \\\\<br/>R &amp; = mg \\cos \\theta - P \\cos(90^{\\circ} - \\theta), \\\\<br/>&amp; = (\\var{mass} \\times 9.8 \\cos(\\var{theta}^{\\circ})) - (\\var{P} \\cos(\\var{90-theta}^{\\circ})), \\\\<br/>&amp; = \\var{R}\\mathrm{N}. <br/>\\end{align}</p>\n<p>The normal reaction, $R$, is $\\var{R}\\mathrm{N}$ to 3d.p.</p>\n<h4>b)</h4>\n<p>To find the acceleration of the box up the plane we resolve parallel to the plane. The plane is smooth so there is no friction.&nbsp;</p>\n<p>\\begin{align} <br/>F&amp; = ma,\\\\<br/>P \\cos \\theta - mg \\cos (90^{\\circ} - \\theta) &amp; = ma, \\\\<br/>a &amp; = \\frac{&nbsp;P \\cos \\theta - mg \\cos (90^{\\circ} - \\theta)}{m}, \\\\<br/>&amp;= \\frac{ \\var{P} \\cos(\\var{theta}^{\\circ}) - (\\var{mass} \\times 9.8 \\cos(\\var{90-theta}^{\\circ}))}{\\var{mass}}, \\\\<br/>&amp;= \\var{precround((P*cos(radians(theta))-mass*9.8*cos(radians(90-theta)))/mass,3)}\\mathrm{ms^{-2}}. <br/>\\end{align}</p>\n<p>The acceleration of the box up the plane is $\\var{precround((P*cos(radians(theta))-mass*9.8*cos(radians(90-theta)))/mass,3)}\\mathrm{ms^{-2}}.$</p>", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "<p>Find the normal reaction between the box and the plane, in $\\mathrm{N}$ to 3 decimal places.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "mass*9.8*cos(radians(theta))+P*cos(radians(90-theta))", "minValue": "mass*9.8*cos(radians(theta))+P*cos(radians(90-theta))", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>Assuming&nbsp;the plane is smooth, find the acceleration of the box up the plane, in $\\mathrm{ms^{-2}}$ to 3 decimal places.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "(P*cos(radians(theta))-mass*9.8*cos(radians(90-theta)))/mass", "minValue": "(P*cos(radians(theta))-mass*9.8*cos(radians(90-theta)))/mass", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>A box of mass $\\var{mass}\\mathrm{kg}$ is being pushed up an inclined plane by a horizontal force $P =&nbsp;\\var{P}\\mathrm{N}$. The plane is inclined at an angle of $\\theta=\\var{theta}^{\\circ}$. above the horizontal.&nbsp;<img src=\"resources/question-resources/force_acting_on_incline.png\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>In the following the acceleration due to gravity is taken as $g=9.8\\mathrm{ms^{-2}}$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"P": {"definition": "random(15..50#2.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "P", "description": ""}, "R": {"definition": "precround(mass*9.8*cos(radians(theta))+P*cos(radians(90-theta)),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "R", "description": ""}, "mass": {"definition": "random(0.25..7#0.25)", "templateType": "randrange", "group": "Ungrouped variables", "name": "mass", "description": ""}, "theta": {"definition": "random(10..80#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "theta", "description": ""}}, "metadata": {"description": "<p>A box is being pushed up a slope&nbsp;by a horizontal force. Calculate the normal reaction force, and the acceleration of the box up the&nbsp;slope.</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/"}]}