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{"name": "HW3 Prob5", "extensions": [], "custom_part_types": [], "resources": [["question-resources/hw3prob5.png", "/srv/numbas/media/question-resources/hw3prob5.png"], ["question-resources/hw3sol5a.png", "/srv/numbas/media/question-resources/hw3sol5a.png"], ["question-resources/hw3sol5b.png", "/srv/numbas/media/question-resources/hw3sol5b.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "HW3 Prob5", "tags": [], "metadata": {"description": "<p>Equilibrium</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p><img src=\"resources/question-resources/hw3prob5.png\" width=\"389\" height=\"198\"/></p>\n<p>Knowing that&nbsp;$\\alpha=\\var{a}^\\circ$ and $W=\\var{W}\\,\\text{N}$, determine the tension&nbsp;</p>", "advice": "<p>Free-Body Diagram:</p>\n<p><img src=\"resources/question-resources/hw3sol5a.png\" width=\"205\" height=\"179\"/></p>\n<p>Force triangle:</p>\n<p><img src=\"resources/question-resources/hw3sol5b.png\" width=\"223\" height=\"215\"/></p>\n<p>Law of sines:</p>\n<p style=\"text-align: center;\">$\\dfrac{T_{AC}}{\\sin (90^\\circ+\\alpha)}=\\dfrac{T_{BC}}{\\sin 5^\\circ}=\\dfrac{W}{\\sin (85^\\circ-\\alpha)}$</p>\n<p style=\"text-align: center;\">$\\dfrac{T_{AC}}{\\sin \\var{a_90}^\\circ}=\\dfrac{T_{BC}}{\\sin 5^\\circ}=\\dfrac{\\var{W}\\,\\text{N}}{\\sin \\var{a_85}^\\circ}$</p>\n<p>(a)</p>\n<p style=\"text-align: center;\">$T_{AC}=\\dfrac{\\var{W}\\,\\text{N}}{\\sin \\var{a_85}^\\circ}\\sin \\var{a_90}^\\circ=\\var{tAC}\\,\\text{N}\\quad\\blacktriangleleft$</p>\n<p style=\"text-align: left;\">(b)</p>\n<p style=\"text-align: center;\">$T_{BC}=\\dfrac{\\var{W}\\,\\text{N}}{\\sin \\var{a_85}^\\circ}\\sin&nbsp;5^\\circ=\\var{tBC}\\,\\text{N}\\quad\\blacktriangleleft$</p>", "rulesets": {}, "extensions": [], "variables": {"tAC": {"name": "tAC", "group": "Ungrouped variables", "definition": "precround({W}*sin(radians(90+{a}))/sin(radians(85-{a})),1)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(15 .. 40#5)", "description": "", "templateType": "randrange"}, "a_90": {"name": "a_90", "group": "Ungrouped variables", "definition": "90+{a}", "description": "", "templateType": "anything"}, "W": {"name": "W", "group": "Ungrouped variables", "definition": "random(3000 .. 5000#100)", "description": "", "templateType": "randrange"}, "a_85": {"name": "a_85", "group": "Ungrouped variables", "definition": "85-{a}", "description": "", "templateType": "anything"}, "tBC": {"name": "tBC", "group": "Ungrouped variables", "definition": "precround({W}*sin(radians(5))/sin(radians(85-{a})),1)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "W", "tAC", "tBC", "a_90", "a_85"], "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 cable <em>AC </em>(in N),</p>", "minValue": "{tAC}-1", "maxValue": "{tAC}+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 rope <em>BC&nbsp;</em>(in N).</p>", "minValue": "{tBC}-1", "maxValue": "{tBC}+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/"}]}