// Numbas version: finer_feedback_settings {"name": "Coefficient of restitution", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Coefficient of restitution", "tags": [], "metadata": {"description": "

Rearrange an equation for a variable e in k.1/(1-e) and then evaluate for e, given values for the variables.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

When a ball is dropped from rest onto a horizontal surface it will bounce before eventually coming to rest after a time \$T\$ where \\[T=\\frac{2v}{g}\\left(\\frac{1}{1-e}\\right)\\] where \$v\$ is the speed immediately after the first impact, and \$g\$ is the acceleration due to gravity.

", "advice": "

Part(a)

$\\begin{align}
T&=\\frac{2v}{g}\\left(\\frac{1}{1-e}\\right)\\\\
\\frac{Tg}{2v} &= \\left(\\frac{1}{1-e}\\right)\\\\
\\frac{2v}{Tg} &= \\left(\\frac{1-e}{1}\\right)\\\\
\\frac{2v}{Tg} &=1-e\\\\
e&=1-\\frac{2v}{Tg}
\\end{align}$

Part (b)

$\\begin{align}
e&=1-\\frac{2v}{Tg}\\\\
&=1-\\frac{2\\times\\var{velocity[velocity_s]}}{\\var{time}\\times 9.8}\\\\
&=1-\\var{(2*velocity[velocity_s])/(time*9.8)}\\\\
&\\approx\\var{precround(1-(2*velocity[velocity_s])/(time*9.8),2)}
\\end{align}$

", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"balls": {"name": "balls", "group": "Ungrouped variables", "definition": "[\"glass\",\"chrome steel\"]", "description": "", "templateType": "anything", "can_override": false}, "blocks": {"name": "blocks", "group": "Ungrouped variables", "definition": "[\"brass\",\"stainless steel\",\"granite\",\"rubber\"]", "description": "", "templateType": "anything", "can_override": false}, "ball_s": {"name": "ball_s", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "block_s": {"name": "block_s", "group": "Ungrouped variables", "definition": "random(0..3)", "description": "", "templateType": "anything", "can_override": false}, "velocity": {"name": "velocity", "group": "Ungrouped variables", "definition": "[1.74,1.93,2.17,2.43]", "description": "", "templateType": "anything", "can_override": false}, "velocity_s": {"name": "velocity_s", "group": "Ungrouped variables", "definition": "random(0..3)", "description": "", "templateType": "anything", "can_override": false}, "time": {"name": "time", "group": "Ungrouped variables", "definition": "switch(ball_s=0 & block_s=0,random(1.18..1.98 #0.01),\n ball_s=0 & block_s=1,random(1.87..3.54 #0.01),\n ball_s=0 & block_s=2,random(3.55..9.91 #0.01),\n ball_s=0 & block_s=3,random(0.54..0.82 #0.01),\n ball_s=1 & block_s=0,random(0.71..1.10 #0.01),\n ball_s=1 & block_s=1,random(0.96..1.55 #0.01),\n ball_s=1 & block_s=2,random(2.73..6.12 #0.01),\n random(0.61..0.93 #0.01))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["balls", "blocks", "ball_s", "block_s", "velocity", "velocity_s", "time"], "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": "

Transpose the formula to make \$e\$, the coefficient of restitution, the subject.

\$e=\$[[0]]

", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "1-(2*v)/(T*g)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "g", "value": ""}, {"name": "t", "value": ""}, {"name": "v", "value": ""}]}], "sortAnswers": false}, {"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": "

A {balls[ball_s]} ball is dropped vertically from rest onto a horizontal {blocks[block_s]} surface. The ball's speed immediately after its first impact is \$v = \\var{velocity[velocity_s]}\$ m/s and it comes to rest after \$T=\\var{time}\$ s. Assuming that \$g=9.8\$ m/s\$^2\$, estimate the coefficient of restitution for this ball/surface combination.

\$e=\$[[0]]

", "gaps": [{"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, "minValue": "1-(2*velocity[velocity_s])/(time*9.8)", "maxValue": "1-(2*velocity[velocity_s])/(time*9.8)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}