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{"name": "Mass held in tension by a string", "extensions": [], "custom_part_types": [], "resources": [["question-resources/statics4.png", "/srv/numbas/media/question-resources/statics4.png"], ["question-resources/statics5.png", "/srv/numbas/media/question-resources/statics5.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["F", "theta", "g", "T", "Tp", "M", "M2"], "name": "Mass held in tension by a string", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>Draw a diagram showing all the forces acting on the bag of mass.</p>\n<p><img src=\"resources/question-resources/statics5.png\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>The tension $T$ is the same in both sections of the string, and the weight of the mass acts downwards.&nbsp;</p>\n<h4>a)</h4>\n<p>We resolve the forces horizontally to get</p>\n<p>\\begin{align} <br/>T \\cos \\theta - F &amp; = 0, \\\\[0.5em]<br/>T &amp; = \\frac{F}{\\cos \\theta}, \\\\[0.5em]<br/>&amp; = \\frac{\\var{F}}{\\cos \\var{theta}^{\\circ}}, \\\\[0.5em]<br/>&amp; = \\var{precround(F/cos(radians(theta)),3)} \\mathrm{N}. <br/>\\end{align}</p>\n<p>The tension in the string is $\\var{precround(F/cos(radians(theta)),3)} \\mathrm{N}.$</p>\n<h4>b)</h4>\n<p>We resolve the forces vertically, and use our 3d.p. value of $T$ found in part <strong>a)</strong> to get</p>\n<p>\\begin{align} <br/>T + T \\sin \\theta - Mg &amp; = 0, \\\\<br/>Mg &amp; = T + T \\sin \\theta, \\\\[0.5em]<br/>M &amp; = \\frac{T + T \\sin \\theta}{g}, \\\\[0.5em]<br/>&amp; = \\frac{ \\var{Tp} + \\var{Tp} \\sin \\var{theta}^{\\circ}}{9.8}, \\\\[0.5em]<br/>&amp; = \\var{precround( (Tp +Tp*sin(radians(theta)))/9.8,3)} \\mathrm{kg}. <br/>\\end{align}</p>\n<p>The mass of the bag is $\\var{precround( (Tp +Tp*sin(radians(theta)))/9.8,3)} \\mathrm{kg}.$</p>", "rulesets": {}, "parts": [{"prompt": "<p>Find the tension, $T$, in the string in Newtons ($\\mathrm{N}$), to 3d.p.</p>\n<p>$T = $&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "T", "strictPrecision": false, "minValue": "T", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "3", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Using the value of $T$ found in part <strong>a)</strong> find $M$, the mass of the bag, in $\\mathrm{kg}$ to 3d.p.</p>\n<p>$M = $&nbsp;[[0]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "M", "strictPrecision": false, "minValue": "M", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "3", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>A small bag of mass&nbsp;$M \\, \\mathrm{kg}$&nbsp;is held by a light inextensible string. The ends of the string are attached to two fixed points $A$ and $B$ which are horizontally on the same level. The bag is held in equilibrium by a horizontal force of magnitude $F \\ \\mathrm{N} = \\var{F} \\ \\mathrm{N}$ acting parallel to $AB$. The bag is vertically below $A$ and the angle $A\\hat{B}M$ is $\\theta =\\var{theta}^{\\circ}$.</p>\n<p><img src=\"resources/question-resources/statics4.png\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>The acceleration due to gravity is $g = 9.8 \\mathrm{ms^{-2}}$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"g": {"definition": "9.8", "templateType": "number", "group": "Ungrouped variables", "name": "g", "description": ""}, "F": {"definition": "random(5..15#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "F", "description": ""}, "M": {"definition": "(Tp+Tp*sin(radians(theta)))/g", "templateType": "anything", "group": "Ungrouped variables", "name": "M", "description": "<p>mass using the tension to 3dp</p>"}, "Tp": {"definition": "precround(T,3)", "templateType": "anything", "group": "Ungrouped variables", "name": "Tp", "description": "<p>T to 3d.p. (answer to part a) students will use this in part b</p>"}, "T": {"definition": "F/cos(radians(theta))", "templateType": "anything", "group": "Ungrouped variables", "name": "T", "description": "<p>tension</p>"}, "M2": {"definition": "(T+T*sin(radians(theta)))/g", "templateType": "anything", "group": "Ungrouped variables", "name": "M2", "description": "<p>mass not using T to 3d.p. to check if part b answer is effected.</p>"}, "theta": {"definition": "random(10..40#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "theta", "description": ""}}, "metadata": {"description": "<p>A mass is&nbsp;hanging from&nbsp;a string,&nbsp;tethered to two points. A horizontal force applied to the mass holds it&nbsp;directly underneath one of the points. Given the magnitude of the force, find the tension in the string and the mass of the bag.</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/"}]}