// Numbas version: finer_feedback_settings
{"name": "HW5 Prob1", "extensions": [], "custom_part_types": [], "resources": [["question-resources/hw5prob1and2.png", "hw5prob1and2.png"], ["question-resources/hw5sol1.png", "hw5sol1.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "HW5 Prob1", "tags": [], "metadata": {"description": "<p>Friction</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p><img src=\"resources/question-resources/hw5prob1and2.png\" width=\"244\" height=\"217\"/></p>\n<p>Determine whether the block shown is in equilibrium and find the magnitude and direction of the friction force when $\\theta=\\var{th}^\\circ$ and $P=\\var{P}\\,\\text{N}$</p>", "advice": "<p><strong><img src=\"resources/question-resources/hw5sol1.png\" width=\"202\" height=\"144\"/></strong></p>\n<p><strong>(a)</strong></p>\n<p>Assume equilibrium</p>\n<p>$+\\!\\!\\nearrow\\sum F_y=0,\\quad\\implies\\quad N-(800\\,\\text{N})\\cos 25^\\circ +(\\var{P}\\,\\text{N})\\sin(\\var{th}^\\circ-25^\\circ)=0$</p>\n<p style=\"padding-left: 30px;\">$N=\\var{normal_force}\\,\\text{N}$</p>\n<p>$+\\!\\!\\searrow\\sum F_x=0,\\quad\\implies\\quad -F_\\mu+(800\\,\\text{N})\\sin 25^\\circ-(\\var{P}\\,\\text{N})\\cos (\\var{th}^\\circ-25^\\circ)=0$</p>\n<p style=\"padding-left: 30px;\">$F_\\mu=\\var{friction_force_trial}\\,\\text{N}$ is required for equilibrium.</p>\n<p>Maximum friction force: $F_m=\\mu_s N=0.2\\times\\var{normal_force}=\\var{max_friction_force}\\,\\text{N}$</p>\n<div data-jme-visible=\"abs({friction_force_trial})&gt;{mu_s}*{normal_force}\">\n<p>Since $|F_\\mu| &gt; F_m$, the block is sliding,&nbsp;</p>\n<p><strong>(b)</strong></p>\n<p>and the magmitude of the friction force is</p>\n<p>\\[F_\\mu=\\mu_k N=\\var{abs(friction_force)}\\,\\text{N},\\quad\\var{direction_string}\\]&nbsp;</p>\n</div>\n<p></p>\n<div data-jme-visible=\"abs({friction_force_trial})&lt;={mu_s}*{normal_force}\">\n<p>Since $|F_\\mu| \\le F_m$, the block is in equilibrium, and</p>\n<p><strong>(b)</strong></p>\n<p>The magmitude of the friction force is</p>\n<p>\\[F_\\mu=\\var{abs(friction_force)}\\,\\text{N},\\quad\\var{direction_string}\\]&nbsp;</p>\n</div>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"mu_s": {"name": "mu_s", "group": "Ungrouped variables", "definition": "0.2", "description": "", "templateType": "number", "can_override": false}, "th": {"name": "th", "group": "Ungrouped variables", "definition": "random(25 .. 70#5)", "description": "", "templateType": "randrange", "can_override": false}, "mu_k": {"name": "mu_k", "group": "Ungrouped variables", "definition": "0.15", "description": "", "templateType": "anything", "can_override": false}, "friction_force_trial": {"name": "friction_force_trial", "group": "Ungrouped variables", "definition": "precround(800*sin(radians(25))-P*cos(radians(th-25)),1)", "description": "<p>Positive if up the slope</p>", "templateType": "anything", "can_override": false}, "equil": {"name": "equil", "group": "Ungrouped variables", "definition": "if(abs(friction_force_trial)<=(mu_s*normal_force),[1,0],[0,1])", "description": "", "templateType": "anything", "can_override": false}, "direction": {"name": "direction", "group": "Ungrouped variables", "definition": "if(friction_force<0,[0,1],[1,0])", "description": "", "templateType": "anything", "can_override": false}, "max_friction_force": {"name": "max_friction_force", "group": "Ungrouped variables", "definition": "precround(mu_s*normal_force,1)", "description": "", "templateType": "anything", "can_override": false}, "normal_force": {"name": "normal_force", "group": "Ungrouped variables", "definition": "precround(800*cos(radians(25))-P*sin(radians(th-25)),1)", "description": "", "templateType": "anything", "can_override": false}, "friction_force": {"name": "friction_force", "group": "Ungrouped variables", "definition": "if(abs(friction_force_trial)<=(mu_s*normal_force),friction_force_trial,sign(friction_force_trial)*precround(mu_k*normal_force,1))", "description": "", "templateType": "anything", "can_override": false}, "direction_string": {"name": "direction_string", "group": "Ungrouped variables", "definition": "if(friction_force<0,\"down the slope\",\"up the slope\")", "description": "", "templateType": "anything", "can_override": false}, "P": {"name": "P", "group": "Ungrouped variables", "definition": "random(100 .. 500#20)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["th", "P", "normal_force", "mu_s", "mu_k", "friction_force_trial", "max_friction_force", "equil", "friction_force", "direction", "direction_string"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>(a) Is the block in equilibrium? 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