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{"name": "HW4 Prob5", "extensions": [], "custom_part_types": [], "resources": [["question-resources/hw4prob4.png", "/srv/numbas/media/question-resources/hw4prob4.png"], ["question-resources/hw4sol4_MLsI1L9.png", "/srv/numbas/media/question-resources/hw4sol4_MLsI1L9.png"], ["question-resources/hw4sol5.png", "/srv/numbas/media/question-resources/hw4sol5.png"], ["question-resources/plusrightarrow_Ccbu4yZ.png", "/srv/numbas/media/question-resources/plusrightarrow_Ccbu4yZ.png"], ["question-resources/plusuparrow_DiMNvhX.png", "/srv/numbas/media/question-resources/plusuparrow_DiMNvhX.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "HW4 Prob5", "tags": [], "metadata": {"description": "<p>Equilibrium</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p><img src=\"resources/question-resources/hw4prob4.png\" width=\"327\" height=\"153\"/></p>\n<p>An $\\var{Q}\\,\\text{N}$&nbsp;load $\\mathbf{Q}$&nbsp;is applied to the pulley <em>C</em>, which can roll on the cable <em>ACB</em>. The pulley is held in the position shown by a second cable <em>CAD</em>, which passes over the pulley <em>A</em> and supports a load $\\mathbf{P}$.&nbsp;Determine</p>", "advice": "<p>Free-Body Diagram</p>\n<p><img src=\"resources/question-resources/hw4sol5.png\" width=\"234\" height=\"165\"/></p>\n<p></p>\n<p><img src=\"resources/question-resources/plusrightarrow_Ccbu4yZ.png\"/>$\\sum F_x=0$: &nbsp;$T_{ACB}\\cos 25^\\circ-T_{ACB}\\cos 55^\\circ-P\\cos 55^\\circ=0$</p>\n<p style=\"text-align: center;\">\\[P=T_{ACB}\\dfrac{\\cos 25^\\circ-\\cos 55^\\circ}{\\cos 55^\\circ}=\\var{kacb}\\,T_{ACB}\\]</p>\n<p style=\"text-align: left;\"><img src=\"resources/question-resources/plusuparrow_DiMNvhX.png\"/>$\\sum F_y=0$: &nbsp;$T_{ACB}\\sin 25^\\circ+T_{ACB}\\sin 55^\\circ+P\\sin 55^\\circ-Q=0$</p>\n<p style=\"text-align: center;\">$T_{ACB}=\\dfrac{Q}{\\sin 25^\\circ+\\sin 55^\\circ+\\var{kacb}\\sin 55^\\circ}=\\var{tACB}\\,\\text{N}\\quad\\blacktriangleleft$</p>\n<p style=\"text-align: center;\">$P=\\var{kacb}\\,T_{ACB}=\\var{P}\\,\\text{N}\\quad\\blacktriangleleft$</p>", "rulesets": {}, "extensions": [], "variables": {"P": {"name": "P", "group": "Ungrouped variables", "definition": "precround({Q}*sec(radians(10))*(cos(radians(25))-sin(radians(35))),1)", "description": "", "templateType": "anything"}, "tACB": {"name": "tACB", "group": "Ungrouped variables", "definition": "precround({Q}*sec(radians(10))*sin(radians(35)),1)", "description": "", "templateType": "anything"}, "kacb": {"name": "kacb", "group": "Ungrouped variables", "definition": "precround((cos(radians(25))-cos(radians(55)))/cos(radians(55)),4)", "description": "", "templateType": "anything"}, "Q": {"name": "Q", "group": "Ungrouped variables", "definition": "random(1000 .. 2000#50)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Q", "tACB", "P", "kacb"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>the tension in cable <em>ACB&nbsp;</em>(in N),&nbsp;</p>", "minValue": "{tACB}-1", "maxValue": "{tACB}+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>the magnitude of load $\\mathbf{P}$ (in N).</p>", "minValue": "{P}-1", "maxValue": "{P}+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Vladimir Vingoradov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1862/"}]}]}], "contributors": [{"name": "Vladimir Vingoradov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1862/"}]}