// Numbas version: exam_results_page_options
{"name": "HW4 Prob2", "extensions": [], "custom_part_types": [], "resources": [["question-resources/hw4prob2.png", "/srv/numbas/media/question-resources/hw4prob2.png"], ["question-resources/hw4sol2.png", "/srv/numbas/media/question-resources/hw4sol2.png"], ["question-resources/plusrightarrow_04bHil4.png", "/srv/numbas/media/question-resources/plusrightarrow_04bHil4.png"], ["question-resources/plusuparrow_prc4U1T.png", "/srv/numbas/media/question-resources/plusuparrow_prc4U1T.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "HW4 Prob2", "tags": [], "metadata": {"description": "<p>Equilibrium</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p><img src=\"resources/question-resources/hw4prob2.png\" width=\"206\" height=\"287\"/></p>\n<p>The weight&nbsp;$W=\\var{W}$N is supported by the rope-and-pulley arrangement shown. Knowing that $\\beta=\\var{b}^\\circ$, determine the magnitude (in N) and direction (angle $\\alpha$ in degrees) of the force $\\mathbf{P}$ that must be exerted on the free end of the rope to maintain equilibrium.</p>", "advice": "<p>Free-Body Diagram: Pulley <em>A</em></p>\n<p><img src=\"resources/question-resources/hw4sol2.png\" width=\"181\" height=\"208\"/></p>\n<p>$\\overset{+}{\\rightarrow}\\sum F_x=0$: $\\quad$ &nbsp;$2P \\sin \\beta - P \\cos \\alpha=0$</p>\n<p style=\"text-align: center;\">$\\cos&nbsp;\\alpha=2\\sin\\beta=2\\sin \\var{b}^\\circ, \\quad\\Rightarrow\\quad \\alpha=\\var{a}^\\circ\\quad\\blacktriangleleft$</p>\n<p></p>\n<p>$+\\!\\!\\uparrow\\sum F_y=0$: $\\quad$ &nbsp;$2P\\cos \\beta+P\\sin\\alpha - W=0$</p>\n<p style=\"text-align: center;\">$2P\\cos \\var{b}^\\circ+P\\sin\\var{a}^\\circ=\\var{W}\\,\\text{N}$</p>\n<p style=\"text-align: center;\">$P=\\dfrac{\\var{W}\\,\\text{N}}{2\\cos \\var{b}^\\circ+\\sin\\var{a}^\\circ}=\\var{P}\\,\\text{N}\\quad\\blacktriangleleft$</p>", "rulesets": {}, "extensions": [], "variables": {"W": {"name": "W", "group": "Ungrouped variables", "definition": "random(100 .. 200#10)", "description": "", "templateType": "randrange"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "precround(degrees(arccos(2*sin(radians({b})))),1)", "description": "", "templateType": "anything"}, "P": {"name": "P", "group": "Ungrouped variables", "definition": "precround(W/(sin(radians(a))+2*cos(radians(b))),1)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(10 .. 28#2)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["W", "b", "a", "P"], "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>direction&nbsp;(angle $\\alpha$):</p>", "minValue": "{a}-0.5", "maxValue": "{a}+0.5", "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>magnitude:</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/"}]}