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{"name": "HW5 Prob5", "extensions": [], "custom_part_types": [], "resources": [["question-resources/hw5prob4.png", "/srv/numbas/media/question-resources/hw5prob4.png"], ["question-resources/hw5prob5.png", "/srv/numbas/media/question-resources/hw5prob5.png"], ["question-resources/hw5sol4a_FAl4pmC.png", "/srv/numbas/media/question-resources/hw5sol4a_FAl4pmC.png"], ["question-resources/hw5sol5b.png", "/srv/numbas/media/question-resources/hw5sol5b.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "HW5 Prob5", "tags": [], "metadata": {"description": "<p>Friction</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p><img src=\"resources/question-resources/hw5prob5.png\" width=\"326\" height=\"113\"/></p>\n<p>The coefficient of friction is $\\mu_s=\\var{mu_s}$ between all surfaces of contact. Knowing that $M_1=\\var{M1}$kg and $M_2=\\var{M2}$kg, determine the smallest force $\\mathbf{P}$ required to start the block $M_2$ moving if:</p>", "advice": "<p><strong>(a)</strong></p>\n<p>Free body: $\\var{M1}$-kg block</p>\n<p><img src=\"resources/question-resources/hw5sol4a_FAl4pmC.png\" width=\"134\" height=\"80\"/></p>\n<p style=\"padding-left: 30px;\">$W_1=M_1 g=\\var{m1}\\times 9.81=\\var{m1*9.81}\\,\\text{N}$</p>\n<p>$+\\!\\!\\uparrow\\sum F_y=0:\\quad N_1=W_1$</p>\n<p style=\"padding-left: 30px;\">$F_1=\\mu_s N_1=\\var{mu_s}\\times\\var{m1*9.81}=\\var{mu_s*m1*9.81}\\,\\text{N}$</p>\n<p>$\\overset{+}{\\rightarrow}\\sum F_x=0:\\quad T-F_1=0,\\quad T=F_1=\\var{mu_s*m1*9.81}\\,\\text{N}$</p>\n<p style=\"padding-left: 30px;\"></p>\n<p style=\"padding-left: 30px;\"></p>\n<p>Free body: $\\var{M2}$-kg block</p>\n<p><img src=\"resources/question-resources/hw5sol5b.png\" width=\"133\" height=\"81\"/></p>\n<p style=\"padding-left: 30px;\">$W_2=M_2g=\\var{M2}\\times 9.81=\\var{m2*9.81}\\,\\text{N}$</p>\n<p>$+\\!\\!\\uparrow\\sum F_y=0: \\quad N_2-N_1-W_2=0,\\quad N_2=W_1+W_2=\\var{(m1+m2)*9.81}\\,\\text{N}$</p>\n<p style=\"padding-left: 30px;\">$F_2=\\mu_s N_2=\\var{mu_s}\\times\\var{(m1+m2)*9.81}=\\var{mu_s*(m1+m2)*9.81}\\,\\text{N}$</p>\n<p>$\\overset{+}{\\rightarrow}\\sum F_x=0: -P+F_1+F_2=0$</p>\n<p style=\"padding-left: 30px;\">\\[P=F_1+F_2=\\var{P1}\\,\\text{N}\\quad\\blacktriangleleft\\]</p>\n<p style=\"padding-left: 30px;\"></p>\n<p><strong>(b)</strong></p>\n<p>Blocks move together (same as in Question 4)</p>\n<p>\\[P=\\var{P2}\\,\\text{N}\\quad\\blacktriangleleft\\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"P1": {"name": "P1", "group": "Ungrouped variables", "definition": "precround(mu_s*(2*M1+M2)*9.81,1)", "description": "", "templateType": "anything", "can_override": false}, "M2": {"name": "M2", "group": "Ungrouped variables", "definition": "random(5 .. 40#5)", "description": "", "templateType": "randrange", "can_override": false}, "P2": {"name": "P2", "group": "Ungrouped variables", "definition": "precround(mu_s*(M1+M2)*9.81,1)", "description": "", "templateType": "anything", "can_override": false}, "mu_s": {"name": "mu_s", "group": "Ungrouped variables", "definition": "random(0.15 .. 0.5#0.05)", "description": "", "templateType": "randrange", "can_override": false}, "M1": {"name": "M1", "group": "Ungrouped variables", "definition": "random(5 .. 40#5)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["mu_s", "M1", "M2", "P1", "P2"], "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>cable&nbsp;<em>AB</em>&nbsp;is attached as shown,&nbsp;</p>", "minValue": "P1-1", "maxValue": "P1+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "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>cable&nbsp;<em>AB</em> is removed.</p>", "minValue": "P2-1", "maxValue": "P2+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "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/"}, {"name": "Haoyu Huang", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/17657/"}]}]}], "contributors": [{"name": "Vladimir Vingoradov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1862/"}, {"name": "Haoyu Huang", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/17657/"}]}