// Numbas version: finer_feedback_settings
{"name": "MeQ2 - Friction on an Incline Plane - Randomised Variables Only", "extensions": [], "custom_part_types": [], "resources": [["question-resources/UWESbeMeCC1_-_Q2_Friction_on_a_Slope.jpg", "/srv/numbas/media/question-resources/UWESbeMeCC1_-_Q2_Friction_on_a_Slope.jpg"], ["question-resources/UWESbeMeCC1_-_Q2_Crate_A_FBD.png", "/srv/numbas/media/question-resources/UWESbeMeCC1_-_Q2_Crate_A_FBD.png"], ["question-resources/UWESbeMeCC1_-_Q2_Crate_A_B_FBD.png", "/srv/numbas/media/question-resources/UWESbeMeCC1_-_Q2_Crate_A_B_FBD.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "MeQ2 - Friction on an Incline Plane - Randomised Variables Only", "tags": [], "metadata": {"description": "<p>2 bodies on an incline plane</p>", "licence": "All rights reserved"}, "statement": "<h2 style=\"text-align: center;\">Friction on an Incline Plane</h2>\n<p>Two blocks, &nbsp;A &amp; B, &nbsp;rest on a slope at an angle of incline &theta;.&nbsp;</p>\n<p><img src=\"resources/question-resources/UWESbeMeCC1_-_Q2_Friction_on_a_Slope.jpg\" alt=\"2 Crates (A&amp;B) on a slope of given angle.  Crate B is higher up the slope and is connected to Crate A via a rope between them connected at point C and D\" width=\"521\" height=\"303\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>The mass and coefficents of friction between the crates and the plane are:</p>\n<table style=\"height: 102px; margin-left: auto; margin-right: auto; border-style: solid; border-color: #000000; width: 503px;\" border=\"3\" width=\"378\">\n<tbody>\n<tr style=\"height: 18px;\">\n<th style=\"height: 18px; width: 138.583px; text-align: center; vertical-align: middle;\"></th>\n<th style=\"height: 18px; width: 142.597px; text-align: center; vertical-align: middle;\">mass (kg)</th>\n<th style=\"height: 18px; width: 169.708px; text-align: center; vertical-align: middle;\">Coefficient of Friction (&mu;)</th>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 138.583px; vertical-align: middle; text-align: center;\">Crate A</td>\n<td style=\"height: 18px; width: 142.597px; text-align: right; vertical-align: middle;\">{mass_crate_A}</td>\n<td style=\"height: 18px; width: 169.708px; text-align: right; vertical-align: middle;\">{co_eff_A}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 138.583px; vertical-align: middle; text-align: center;\">Crate B</td>\n<td style=\"height: 18px; width: 142.597px; text-align: right; vertical-align: middle;\">{mass_crate_B}</td>\n<td style=\"height: 18px; width: 169.708px; text-align: right; vertical-align: middle;\">{co_eff_B}</td>\n</tr>\n</tbody>\n</table>", "advice": "<p>Worked answers to follow exam</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Acc_Grav": {"name": "Acc_Grav", "group": "Ungrouped variables", "definition": "9.81", "description": "<p>Gravitational Constant</p>", "templateType": "number", "can_override": false}, "mass_crate_A": {"name": "mass_crate_A", "group": "Ungrouped variables", "definition": "random(30 .. 40#1)", "description": "", "templateType": "randrange", "can_override": false}, "mass_crate_B": {"name": "mass_crate_B", "group": "Ungrouped variables", "definition": "random(19 .. 25#1)", "description": "<p>Mass of Crate B (kg)</p>", "templateType": "randrange", "can_override": false}, "co_eff_A": {"name": "co_eff_A", "group": "Ungrouped variables", "definition": "random(0.15 .. 0.2#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "Co_eff_B": {"name": "Co_eff_B", "group": "Ungrouped variables", "definition": "random(0.25 .. 0.32#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "Theta_A": {"name": "Theta_A", "group": "Ungrouped variables", "definition": "degrees(arctan(co_eff_a))", "description": "", "templateType": "anything", "can_override": false}, "Theta_B": {"name": "Theta_B", "group": "Ungrouped variables", "definition": "degrees(arctan(co_eff_b))", "description": "", "templateType": "anything", "can_override": false}, "Weight_Crate_A": {"name": "Weight_Crate_A", "group": "Ungrouped variables", "definition": "mass_crate_a*acc_grav", "description": "<p>N</p>", "templateType": "anything", "can_override": false}, "Weight_Crate_B": {"name": "Weight_Crate_B", "group": "Ungrouped variables", "definition": "mass_crate_b*acc_grav", "description": "<p>N</p>", "templateType": "anything", "can_override": false}, "fric_A": {"name": "fric_A", "group": "Ungrouped variables", "definition": "weight_crate_a*co_eff_a", "description": "", "templateType": "anything", "can_override": false}, "fric_b": {"name": "fric_b", "group": "Ungrouped variables", "definition": "co_eff_b*weight_crate_b", "description": "", "templateType": "anything", "can_override": false}, "Theta_AB": {"name": "Theta_AB", "group": "Ungrouped variables", "definition": "degrees(Arctan((fric_a+fric_b)/(weight_crate_a+weight_crate_b)))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Acc_Grav", "mass_crate_A", "mass_crate_B", "co_eff_A", "Co_eff_B", "Theta_A", "Theta_B", "Weight_Crate_A", "Weight_Crate_B", "fric_A", "fric_b", "Theta_AB"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "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><strong>Part a)</strong> Calculate (to within 1 decimal place) the angle &theta; when Crate A begins to slide.</p>\n<p><strong>[7 Marks]</strong></p>"}, {"type": "information", "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><strong>Part b)</strong> Calculate (to within 1 decimal place) the angle &theta; when Crate B begins to slide.</p>\n<p><strong>[2 Marks]</strong></p>"}, {"type": "information", "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><strong>Part c)</strong> If the 2 masses are connected at points C &amp; D by a cable.</p>\n<p>Calculate the angle (to within 1 decimal place) the two joined crates begin to slide.</p>\n<p><strong>[6 Marks]</strong></p>"}, {"type": "information", "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>Ensure you include a free body diagram in your workings.&nbsp;</p>\n<p><strong>[5 Marks]</strong></p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Robert Bauld", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19446/"}]}]}], "contributors": [{"name": "Robert Bauld", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19446/"}]}