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Knowing that $\\alpha=\\var{a}^\\circ$ and $\\beta=\\var{b}^\\circ$&nbsp;and that the combined weight of the boatswain's chair and the sailor is $\\var{W}\\,\\text{N}$, determine the tension (in N)&nbsp;</p>", "advice": "<p>Free-Body Diagram</p>\n<p><img src=\"resources/question-resources/hw4sol1.png\" width=\"260\" height=\"149\"/></p>\n<p><img src=\"resources/question-resources/plusrightarrow_KWX7OJ1.png\"/>$\\sum F_x=0$: $\\quad$ &nbsp; $T_{ACB}\\cos \\beta-T_{ACB}\\cos \\alpha-T_{CD} \\cos \\alpha=0$</p>\n<p style=\"text-align: center;\">$T_{ACB}\\cos \\var{b}^\\circ-T_{ACB}\\cos \\var{a}^\\circ-T_{CD} \\cos \\var{a}^\\circ=0$</p>\n<p style=\"text-align: center;\">$T_{CD}=T_{ACB}\\dfrac{\\cos \\var{b}^\\circ-\\cos \\var{a}^\\circ}{\\cos \\var{a}^\\circ}=\\var{kCD}\\,T_{ACB}$</p>\n<p><img src=\"resources/question-resources/plusuparrow.png\"/>$\\sum F_y=0$: $\\quad$ &nbsp; $T_{ACB}\\sin \\beta+T_{ACB}\\sin \\alpha+T_{CD} \\sin \\alpha-W=0$</p>\n<p style=\"text-align: center;\">$T_{ACB}\\sin \\var{b}^\\circ+T_{ACB}\\sin \\var{a}^\\circ+T_{CD} \\sin \\var{a}^\\circ-(\\var{W}\\,\\text{N})=0$</p>\n<p style=\"text-align: center;\">$T_{ACB}\\sin\\var{b}^\\circ+T_{ACB}\\sin\\var{a}^\\circ+\\var{kCD}\\,T_{ACB} \\sin\\var{a}^\\circ=(\\var{W}\\,\\text{N})$</p>\n<p style=\"text-align: center;\">$T_{ACB}=\\var{tACB}\\,\\text{N}\\quad\\blacktriangleleft$</p>\n<p style=\"text-align: center;\">$T_{CD}=\\var{kCD}\\,T_{ACB}=\\var{tCD}\\,\\text{N}\\quad\\blacktriangleleft$</p>", "rulesets": {}, "extensions": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "random(5 .. 20#5)", "description": "", "templateType": "randrange"}, "tCD": {"name": "tCD", "group": "Ungrouped variables", "definition": "precround({W}*(-cos(radians({a}))+cos(radians({b})))*cosec(radians({a}+{b})),1)", "description": "", "templateType": "anything"}, "W": {"name": "W", "group": "Ungrouped variables", "definition": "random(800 .. 1000#20)", "description": "", "templateType": "randrange"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(25 .. 45#5)", "description": "", "templateType": "randrange"}, "kCD": {"name": "kCD", "group": "Ungrouped variables", "definition": "precround((cos(radians({b}))-cos(radians({a})))/cos(radians({a})),4)", "description": "", "templateType": "anything"}, "tACB": {"name": "tACB", "group": "Ungrouped variables", "definition": "precround({W}*cos(radians({a}))*cosec(radians({a}+{b})),1)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "W", "tACB", "tCD", "kCD"], "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>in the support cable <em>ACB</em>,&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>in the traction cable <em>CD</em>.</p>", "minValue": "{tCD}-1", "maxValue": "{tCD}+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/"}]}