// Numbas version: exam_results_page_options
{"name": "UWESbeMeCC2 Q5 - Centre of Gravity - Randomised Variables Only", "extensions": [], "custom_part_types": [], "resources": [["question-resources/UWESbeMeCC1_Q5_-_Centre_of_Gravity.png", "/srv/numbas/media/question-resources/UWESbeMeCC1_Q5_-_Centre_of_Gravity.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "UWESbeMeCC2 Q5 - Centre of Gravity - Randomised Variables Only", "tags": [], "metadata": {"description": "<p>Determinig the CoG of a composite part</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p style=\"text-align: left;\">A component consists of 3 horizontal concentric solid cylinders, A, B &amp; C fixed together as shown in the diagram.</p>\n<p><img src=\"resources/question-resources/UWESbeMeCC1_Q5_-_Centre_of_Gravity.png\" alt=\"Component with multiple sections\" width=\"550\" height=\"416\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>The dimensions and material properties are:</p>\n<table style=\"width: 568px; margin-left: auto; margin-right: auto; border-style: solid; border-color: #000000;\" height=\"282\">\n<tbody>\n<tr style=\"background-color: #b8b6b6; text-align: center;\">\n<td style=\"width: 68.125px; border-style: solid; border-color: #000000;\">\n<p>Cylinder</p>\n</td>\n<td style=\"width: 74.9219px; border-style: solid; border-color: #000000;\">\n<p>Material</p>\n</td>\n<td colspan=\"2\" style=\"width: 132.324px; border-style: solid; border-color: #000000;\">\n<p>Density &rho; (kgm<sup>-3</sup>)</p>\n</td>\n<td colspan=\"2\" style=\"width: 106.055px; border-style: solid; border-color: #000000;\">\n<p>Diameter (mm)</p>\n</td>\n<td colspan=\"2\" style=\"width: 104.062px; border-style: solid; border-color: #000000;\">\n<p>Length (mm)</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 68.125px; border-style: solid; border-color: #000000;\">\n<p>A</p>\n</td>\n<td style=\"width: 74.9219px; border-style: solid; border-color: #000000;\">\n<p>Aluminium Alloy</p>\n</td>\n<td style=\"width: 41.0352px; border-style: solid; border-color: #000000;\">\n<p>&rho;<sub>A</sub></p>\n</td>\n<td style=\"width: 75.0391px; border-style: solid; border-color: #000000;\">\n<p>{Den_a}</p>\n</td>\n<td style=\"width: 20.6836px; border-style: solid; border-color: #000000;\">\n<p>d<sub>A</sub></p>\n</td>\n<td style=\"width: 69.1211px; border-style: solid; border-color: #000000;\">\n<p>{Dia_a}</p>\n</td>\n<td style=\"width: 15.6836px; border-style: solid; border-color: #000000;\">\n<p>l<sub>A</sub></p>\n</td>\n<td style=\"width: 72.1289px; border-style: solid; border-color: #000000;\">\n<p>{Len_a}</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 68.125px; border-style: solid; border-color: #000000;\">\n<p>B</p>\n</td>\n<td style=\"width: 74.9219px; border-style: solid; border-color: #000000;\">\n<p>Copper Alloy</p>\n</td>\n<td style=\"width: 41.0352px; border-style: solid; border-color: #000000;\">\n<p>&rho;<sub>B</sub></p>\n</td>\n<td style=\"width: 75.0391px; border-style: solid; border-color: #000000;\">\n<p>{Den_b}</p>\n</td>\n<td style=\"width: 20.6836px; border-style: solid; border-color: #000000;\">\n<p>d<sub>B</sub></p>\n</td>\n<td style=\"width: 69.1211px; border-style: solid; border-color: #000000;\">\n<p>{Dia_b}</p>\n</td>\n<td style=\"width: 15.6836px; border-style: solid; border-color: #000000;\">\n<p>l<sub>B</sub></p>\n</td>\n<td style=\"width: 72.1289px; border-style: solid; border-color: #000000;\">\n<p>{Len_b}</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 68.125px; border-style: solid; border-color: #000000;\">\n<p>C</p>\n</td>\n<td style=\"width: 74.9219px; border-style: solid; border-color: #000000;\">\n<p>Steel</p>\n</td>\n<td style=\"width: 41.0352px; border-style: solid; border-color: #000000;\">\n<p>&rho;<sub>C</sub></p>\n</td>\n<td style=\"width: 75.0391px; border-style: solid; border-color: #000000;\">\n<p>{Den_c}</p>\n</td>\n<td style=\"width: 20.6836px; border-style: solid; border-color: #000000;\">\n<p>d<sub>C</sub></p>\n</td>\n<td style=\"width: 69.1211px; border-style: solid; border-color: #000000;\">\n<p>{Dia_c}</p>\n</td>\n<td style=\"width: 15.6836px; border-style: solid; border-color: #000000;\">\n<p>l<sub>C</sub></p>\n</td>\n<td style=\"width: 72.1289px; border-style: solid; border-color: #000000;\">\n<p>{Len_c}</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "advice": "<p>.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Den_a": {"name": "Den_a", "group": "Ungrouped variables", "definition": "random(2650 .. 2750#20)", "description": "", "templateType": "randrange", "can_override": false}, "Den_b": {"name": "Den_b", "group": "Ungrouped variables", "definition": "random(8900 .. 8990#10)", "description": "", "templateType": "randrange", "can_override": false}, "Den_c": {"name": "Den_c", "group": "Ungrouped variables", "definition": "random(7830 .. 7890#5)", "description": "", "templateType": "randrange", "can_override": false}, "Dia_a": {"name": "Dia_a", "group": "Ungrouped variables", "definition": "random(25 .. 35#5)", "description": "", "templateType": "randrange", "can_override": false}, "Dia_b": {"name": "Dia_b", "group": "Ungrouped variables", "definition": "random(50 .. 70#5)", "description": "", "templateType": "randrange", "can_override": false}, "Dia_c": {"name": "Dia_c", "group": "Ungrouped variables", "definition": "random(30 .. 45#1)", "description": "", "templateType": "randrange", "can_override": false}, "Len_a": {"name": "Len_a", "group": "Ungrouped variables", "definition": "random(180 .. 220#10)", "description": "", "templateType": "randrange", "can_override": false}, "Len_b": {"name": "Len_b", "group": "Ungrouped variables", "definition": "random(120 .. 160#5)", "description": "", "templateType": "randrange", "can_override": false}, "Len_c": {"name": "Len_c", "group": "Ungrouped variables", "definition": "random(25 .. 50#5)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Den_a", "Den_b", "Den_c", "Dia_a", "Dia_b", "Dia_c", "Len_a", "Len_b", "Len_c"], "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 the total volume of the component.</p>\n<p><strong>[4 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 the total mass of the component.</p>\n<p><strong>[4 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>Calculate the total weight of the component.</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 d) </strong>Calculate the coordinate of the Centre of Gravity along its length.</p>\n<p><strong>[5 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 show the position of the CoG on a diagram in your workings.</p>\n<p><strong>[5 Marks]</strong></p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "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/"}]}