// Numbas version: exam_results_page_options
{"name": "UWEAppCeMf012 - Stress & Strain", "extensions": [], "custom_part_types": [], "resources": [["question-resources/UWESbeMeCC1_Q3_-_Tensile_Strength_SjvCCwh.png", "/srv/numbas/media/question-resources/UWESbeMeCC1_Q3_-_Tensile_Strength_SjvCCwh.png"], ["question-resources/Stress_Strain_Calculations_Advice_aOWOx3r.docx", "/srv/numbas/media/question-resources/Stress_Strain_Calculations_Advice_aOWOx3r.docx"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "UWEAppCeMf012 - Stress & Strain", "tags": [], "metadata": {"description": "<p>Stress &amp; Strain Question based on Tensile testing of materials lab session</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>v2.2</p>\n<p><img src=\"resources/question-resources/UWESbeMeCC1_Q3_-_Tensile_Strength_SjvCCwh.png\" width=\"415\" height=\"290\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p style=\"text-align: right;\"><em>Drawing is not to scale</em></p>\n<p style=\"text-align: right;\"><em>Forces are not shown</em></p>\n<p>A cylindrical, steel tensile test specimen with the original dimensions {Spec_len}mm and {Spec_dia}mm diameter performs as follows in a tensile test:&nbsp;</p>\n<ul>\n<li>At the limit of its elastic deformation the force exerted was {Elastic_Force} N.</li>\n<li>At its elastic limit the specimen was found to have a length of {Spec_fin} mm.</li>\n<li>The maximum force the material withstood was {Max_Force} N.</li>\n</ul>\n<p></p>", "advice": "<p><a href=\"https://numbas.mathcentre.ac.uk/question/141507/uweappcemf012-stress-strain/resources/question-resources/Stress_Strain_Calculations_Advice_CaziBkA.docx\" target=\"_blank\" rel=\"noopener\">Stress_Strain Advice</a></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>Acceleration due to Gravity ms^-2</p>", "templateType": "number", "can_override": false}, "Spec_len": {"name": "Spec_len", "group": "Ungrouped variables", "definition": "random(19 .. 21#0.5)", "description": "<p>Original Length of Sample (mm)</p>", "templateType": "randrange", "can_override": false}, "Delta_len": {"name": "Delta_len", "group": "Ungrouped variables", "definition": "random(0.6 .. 0.8#0.05)", "description": "<p>Change in length of the sample (mm)</p>", "templateType": "randrange", "can_override": false}, "Spec_dia": {"name": "Spec_dia", "group": "Ungrouped variables", "definition": "random(4.9 .. 5.1#0.02)", "description": "<p>Diameter of the sample in mm</p>", "templateType": "randrange", "can_override": false}, "Elastic_Force": {"name": "Elastic_Force", "group": "Ungrouped variables", "definition": "random(3450 .. 3550#15)", "description": "<p>Force at limit of elastic deformation.</p>", "templateType": "randrange", "can_override": false}, "Max_Force": {"name": "Max_Force", "group": "Ungrouped variables", "definition": "random(5100 .. 5150#25)", "description": "<p>The maximum force the material withstood (N).</p>", "templateType": "randrange", "can_override": false}, "Spec_xArea": {"name": "Spec_xArea", "group": "Ungrouped variables", "definition": "pi*((spec_dia/2)^2)", "description": "<p>Cross Sectional Area of the Sample (mm^2)</p>", "templateType": "anything", "can_override": false}, "Yield_Str": {"name": "Yield_Str", "group": "Ungrouped variables", "definition": "Elastic_Force/Spec_xArea", "description": "<p>Calculated Yield Strength(MPa)</p>", "templateType": "anything", "can_override": false}, "Ten_Str": {"name": "Ten_Str", "group": "Ungrouped variables", "definition": "{Max_Force}/{Spec_xArea}", "description": "<p>Calculated Maximum Tensile Strength(MPa)</p>", "templateType": "anything", "can_override": false}, "Max_Elas_Strain": {"name": "Max_Elas_Strain", "group": "Ungrouped variables", "definition": "{Delta_len}/{Spec_len}", "description": "<p>Calculated Strain</p>", "templateType": "anything", "can_override": false}, "Yon_Mod": {"name": "Yon_Mod", "group": "Ungrouped variables", "definition": "({Yield_Str}/{Max_Elas_Strain})/1000", "description": "<p>Youngs Modulus (GPa)</p>", "templateType": "anything", "can_override": false}, "spec_fin": {"name": "spec_fin", "group": "Ungrouped variables", "definition": "Spec_len+Delta_len", "description": "<p>The final length of the specimin in mm</p>", "templateType": "anything", "can_override": false}, "Hook_dia": {"name": "Hook_dia", "group": "Ungrouped variables", "definition": "random(3 .. 8#0.5)", "description": "<p>Diameter of the hook</p>", "templateType": "randrange", "can_override": true}, "Hook_safety": {"name": "Hook_safety", "group": "Ungrouped variables", "definition": "random(2 .. 5#1)", "description": "<p>Hook Safty factor&nbsp;</p>", "templateType": "randrange", "can_override": false}, "Hook_xArea": {"name": "Hook_xArea", "group": "Ungrouped variables", "definition": "pi*((hook_dia/2)^2)", "description": "<p>Cross sectional area of the hook</p>", "templateType": "anything", "can_override": false}, "Hook_Max_F": {"name": "Hook_Max_F", "group": "Ungrouped variables", "definition": "Yield_Str*Hook_xArea", "description": "<p>Maximum force that the hook can handle</p>", "templateType": "anything", "can_override": false}, "Hook_max_mass": {"name": "Hook_max_mass", "group": "Ungrouped variables", "definition": "hook_max_f/acc_grav", "description": "<p>The maximum mass on the hook</p>", "templateType": "anything", "can_override": false}, "Hook_safe_load": {"name": "Hook_safe_load", "group": "Ungrouped variables", "definition": "hook_max_mass/hook_safety", "description": "<p>The safe load that can be applied to the hook.&nbsp;</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Acc_Grav", "Spec_len", "Delta_len", "Spec_dia", "Elastic_Force", "Max_Force", "spec_fin", "Spec_xArea", "Yield_Str", "Ten_Str", "Max_Elas_Strain", "Yon_Mod", "Hook_dia", "Hook_safety", "Hook_xArea", "Hook_Max_F", "Hook_max_mass", "Hook_safe_load"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "Part a) Tensile Strength ", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the Tensile Strength (MPa) of the sample.</p>", "stepsPenalty": "1", "steps": [{"type": "numberentry", "useCustomName": true, "customName": "Step i) Cross Sectional Area", "marks": "0.3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the cross sectional area of the sample? (mm<sup>2</sup>)</p>", "minValue": "Spec_xArea-(Spec_xArea*0.05)", "maxValue": "Spec_xArea+(Spec_xArea*0.05)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": true, "customName": "Step ii) Tensile strength units", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Can either of the following units be given for Tensile Strength?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<ul>\n<li>N/mm<sup>2</sup></li>\n</ul>", "<ul>\n<li>mmHg</li>\n</ul>"], "matrix": ["0.2", 0], "distractors": ["", ""]}, {"type": "information", "useCustomName": true, "customName": "Step iii) Tensile Strength Advice", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Now use the cross sectional area and the correct expression to calculate the tensile strength (MPa)</p>"}], "minValue": "Ten_Str-(Ten_Str*0.05)", "maxValue": "Ten_Str+(Ten_Str*0.05)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "85", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Part b) Youngs Modulus", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the Youngs Modulus (GPa) of the sample.</p>", "stepsPenalty": "2.5", "steps": [{"type": "numberentry", "useCustomName": true, "customName": "Step i) Yield Strength", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the yield strength (MPa)</p>", "minValue": "Yield_Str-(Yield_Str*0.05)", "maxValue": "Yield_Str+(Yield_Str*0.05)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Step ii) Strain", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the Strain</p>", "minValue": "Max_Elas_Strain-(Max_Elas_Strain*0.05)", "maxValue": "Max_Elas_Strain+(Max_Elas_Strain*0.05)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "information", "useCustomName": true, "customName": "Step iii) Youngs Modulus Advice", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Use the results from step (i) and step (ii) to calculate Young&rsquo;s Modulus (GPa)</p>"}], "minValue": "Yon_Mod-(Yon_Mod*0.05)", "maxValue": "Yon_Mod+(Yon_Mod*0.05)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "85", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Part c) Safe working load", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The same steel is used to manufacture a hook with a minimum diameter d<sub>H</sub> of {Hook_dia} mm.&nbsp; The manufacturer has given a stated Factor of Safety (FoS) of {Hook_safety} based on its yeild strength.</p>\n<p>Calculate the maximum mass that can suspended from the lifting hook.</p>", "stepsPenalty": "1.5", "steps": [{"type": "numberentry", "useCustomName": true, "customName": "i) Cross Sectional Area", "marks": "0.25", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the cross sectional area (mm<sup>2</sup>) of the hook?</p>", "minValue": "Hook_xArea-(Hook_xArea*0.05)", "maxValue": "Hook_xArea+(Hook_xArea*0.05)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "85", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "ii) Maximum Weight", "marks": "0.25", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given the yield strength of {siground(Yield_Str,3)} MPa what is the maximum weight (N) that can be suspended before defomation?</p>", "minValue": "Hook_Max_F-(Hook_Max_F*0.05)", "maxValue": "Hook_Max_F+(Hook_Max_F*0.05)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "85", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "iii) Maximum mass ", "marks": "0.25", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the corresponding mass (kg) for this weight in normal gravity?</p>", "minValue": "Hook_max_mass-(Hook_max_mass*0.05)", "maxValue": "Hook_max_mass+(Hook_max_mass*0.05)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "85", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": true, "customName": "iv) Maximum Safe Load", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>choose one:</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["The maximum safe load(kg) will be less than the maximum possible load (kg)", "The maximum safe load(kg) will be the same as the maximum possible load (kg)", "The maximum safe load(kg) will be more than the maximum possible load (kg)"], "matrix": ["0.25", 0, 0], "distractors": ["", "", ""]}], "minValue": "Hook_safe_load-(Hook_safe_load*0.05)", "maxValue": "Hook_safe_load+(Hook_safe_load*0.05)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "85", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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/"}]}