// Numbas version: exam_results_page_options {"name": "HW3 Prob4", "extensions": [], "custom_part_types": [], "resources": [["question-resources/hw3prob4.png", "/srv/numbas/media/question-resources/hw3prob4.png"], ["question-resources/hw3sol4a.png", "/srv/numbas/media/question-resources/hw3sol4a.png"], ["question-resources/hw3sol4b.png", "/srv/numbas/media/question-resources/hw3sol4b.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "HW3 Prob4", "tags": [], "metadata": {"description": "

Equilibrium

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

\n

Two cables are tied together at C and are loaded as shown. Knowing that the mass $M=\\var{M}\\,\\text{kg}$, determine the tension (in N)

", "advice": "

Weight: $W=M g=(\\var{M}\\,\\text{kg})(9.81 \\text{m/s}^2)=\\var{W}\\,\\text{N}$.

\n

Free-Body Diagram:

\n

\n

Force triangle:

\n

\n

Law of sines:

\n

$\\dfrac{T_{AC}}{\\sin 15^\\circ}=\\dfrac{T_{BC}}{\\sin 105^\\circ}=\\dfrac{W}{\\sin 60^\\circ}$

\n

$\\dfrac{T_{AC}}{\\sin 15^\\circ}=\\dfrac{T_{BC}}{\\sin 105^\\circ}=\\dfrac{\\var{W}\\,\\text{N}}{\\sin 60^\\circ}$

\n

(a)

\n

$T_{AC}=\\dfrac{\\var{W}\\,\\text{N}}{\\sin 60^\\circ}\\sin 15^\\circ=\\var{tAC}\\,\\text{N}\\quad\\blacktriangleleft$

\n

(b)

\n

$T_{BC}=\\dfrac{\\var{W}\\,\\text{N}}{\\sin 60^\\circ}\\sin 105^\\circ=\\var{tBC}\\,\\text{N}\\quad\\blacktriangleleft$

", "rulesets": {}, "extensions": [], "variables": {"W": {"name": "W", "group": "Ungrouped variables", "definition": "{M}*9.81", "description": "", "templateType": "anything"}, "M": {"name": "M", "group": "Ungrouped variables", "definition": "random(10 .. 30#1)", "description": "", "templateType": "randrange"}, "tAC": {"name": "tAC", "group": "Ungrouped variables", "definition": "precround({W}*sin(radians(15))/sin(radians(60)),1)", "description": "", "templateType": "anything"}, "tBC": {"name": "tBC", "group": "Ungrouped variables", "definition": "precround({W}*sin(radians(105))/sin(radians(60)),1)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["M", "W", "tAC", "tBC"], "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": "

in cable AC

", "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": "

in cable BC.

", "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/"}]}