// Numbas version: finer_feedback_settings
{"name": "FS0041 Unit 5 CLE1", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", ""], "questions": [{"name": "CLE W1 Q1 Inelastic collision", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "John Bridges", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/913/"}, {"name": "Stuart Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/997/"}, {"name": "Doug Satterford", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3185/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>A $\\var{m1}$ kg&nbsp;mass&nbsp;travelling at $\\var{u1}$ ms<sup>-1</sup> collides into&nbsp;a mass $\\var{m2}$ kg&nbsp;moving in the same direction $\\var{u2}$ ms<sup>-1</sup>.</p>\n<p><em>Give your answers to the appropriate number of significant figures.</em></p>", "advice": "<p>B) Use conservation of linear momentum to determine the final velocity.</p>\n<p>C) $KE=\\frac{1}{2}mv^2$</p>\n<p>See section 3.24 (pg 92) in Advanced Physics by Adams and Allday.</p>", "rulesets": {}, "variables": {"u2": {"name": "u2", "group": "Ungrouped variables", "definition": "random(10..13)", "description": "", "templateType": "anything"}, "delta_ke": {"name": "delta_ke", "group": "Ungrouped variables", "definition": "siground((keb-kea)/1000,2)", "description": "", "templateType": "anything"}, "m2": {"name": "m2", "group": "Ungrouped variables", "definition": "random(65..74)*10", "description": "", "templateType": "anything"}, "kea": {"name": "kea", "group": "Ungrouped variables", "definition": "0.5*(m1+m2)*(v^2)", "description": "", "templateType": "anything"}, "u1": {"name": "u1", "group": "Ungrouped variables", "definition": "random(23..26)", "description": "", "templateType": "anything"}, "keb": {"name": "keb", "group": "Ungrouped variables", "definition": "(0.5*m1*(u1^2))+(0.5*m2*(u2^2))", "description": "", "templateType": "anything"}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "siground((m1*u1+m2*u2)/(m1+m2),2)", "description": "", "templateType": "anything"}, "m1": {"name": "m1", "group": "Ungrouped variables", "definition": "random(15..18)*100", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "delta_ke>0", "maxRuns": "10000"}, "ungrouped_variables": ["u1", "m2", "m1", "u2", "v", "keb", "kea", "delta_ke"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "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>Which statement defines an inelastic collision?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>Kinetic energy is not conserved, but momentum is conserved.</p>", "<p>Gravitational potential energy is converted into kinetic energy.</p>", "<p>Both momentum and kinetic energy are conserved.</p>", "<p>Momentum is not conserved, but kinetic energy is conserved.</p>", "<p>Both momentum and kinetic energy are not conserved.</p>"], "matrix": ["0.33", 0, 0, 0, 0], "distractors": ["", "", "", "", ""]}, {"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>What is the velocity of the two masses immediately after the collision if they lock together?</p>\n<p>[[0]] ms<sup>-1</sup>&nbsp;&nbsp;</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.33", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "v-1", "maxValue": "v+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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": "<p>How much kinetic energy is transferred to other forms in the collision?</p>\n<p>[[0]] kJ&nbsp; &nbsp;&nbsp;</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.34", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "v", "part": "p0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "delta_ke-1", "maxValue": "delta_ke+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Conservation of Energy", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "John Bridges", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/913/"}, {"name": "Stuart Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/997/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>You throw a $\\var{m}$ kg ball straight up in the air, giving it an initial velocity of $\\var{u}$&nbsp;ms<sup>-1</sup>.</p>\n<p><em>Take $g$ = 9.81 ms<sup>-2</sup> and give your answers to three signficant figures.</em></p>", "advice": "<p>Part a) At the point of maximum height the ball will have transferred all its' kinetic energy to gravitational potential energy, hence:</p>\n<p>$\\frac{1}{2}mv^2=mgh$</p>\n<p>Part b)&nbsp;i) Sum the change in graviational potential and kinetic energies, then divide by the change in height.</p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ii) Sum the initial and final gravitational potential and kinetic energies, rearrange for the unknown $v$ and solve.</p>\n<p>See section&nbsp;3.13 (pg 70) in Advanced Physics by Adams and Allday.</p>", "rulesets": {}, "variables": {"point_h": {"name": "point_h", "group": "Ungrouped variables", "definition": "random(10..20)", "description": "", "templateType": "anything"}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "9.81", "description": "", "templateType": "anything"}, "v_3": {"name": "v_3", "group": "Ungrouped variables", "definition": "sqrt(u^2-(2*g*point_h))", "description": "", "templateType": "anything"}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "(u^2)/(2*g)", "description": "", "templateType": "anything"}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(20..40)/100", "description": "", "templateType": "anything"}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "((m*g*hand_h)+(0.5*m*u^2))/hand_h", "description": "", "templateType": "anything"}, "u": {"name": "u", "group": "Ungrouped variables", "definition": "random(30..40)", "description": "", "templateType": "anything"}, "hand_h": {"name": "hand_h", "group": "Ungrouped variables", "definition": "random(4..8)/10", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "v_3<100", "maxRuns": "10000"}, "ungrouped_variables": ["m", "u", "g", "h", "hand_h", "p", "point_h", "v_3"], "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>Use conservation of energy to calculate how high it goes.</p>\n<p>[[0]]m</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "h-0.1", "maxValue": "h+0.1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "90", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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": "<p>Suppose that your hand moves up $\\var{hand_h}$ m while giving the ball its upward velocity of $\\var{u}$ ms<sup>-1</sup>.</p>\n<p>Assuming that your hand exerts a constant upward force on the ball,&nbsp;what is&nbsp;the magnitude of that force?</p>\n<p>[[0]]N</p>\n<p>What is&nbsp;the speed of the ball at a point $\\var{point_h}$ m above the point where it leaves your hand?</p>\n<p>[[1]]ms<sup>-1</sup></p>\n<p><sup></sup></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "p-1", "maxValue": "p+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "90", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "v_3-0.1", "maxValue": "v_3+0.1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "90", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "CLE W1 Q3 Impulse and spring", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [["question-resources/Week_3_Q1.png", "/srv/numbas/media/question-resources/Week_3_Q1.png"], ["question-resources/Week_3_Q1_v2.png", "/srv/numbas/media/question-resources/Week_3_Q1_v2.png"], ["question-resources/Week_3_Q1_v3.png", "/srv/numbas/media/question-resources/Week_3_Q1_v3.png"], ["question-resources/Week_3_Q2.png", "/srv/numbas/media/question-resources/Week_3_Q2.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "John Bridges", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/913/"}, {"name": "Stuart Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/997/"}, {"name": "Doug Satterford", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3185/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Two carts <strong>A</strong> and <strong>B</strong>, with a compressed spring between them, are pushed together and held at rest, as shown in the figure. The spring is not attached to either cart. The carts are then released.</p>\n<p><em>Give your answers to two decimal places.</em></p>\n<p><img src=\"resources/question-resources/Week_3_Q1_v3.png\"/></p>\n<p></p>\n<p></p>", "advice": "<p>See section 3.22 (pg 88) in Advanced Physics by Adams and Allday.</p>", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "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>The graph below shows how the force, <em>F</em>, exerted by the spring on the carts varies with time, <em>t</em>, after release.</p>\n<p><img src=\"resources/question-resources/Week_3_Q2.png\"/></p>\n<p>When the spring returns to its unstretched length, and the unattached spring drops down, cart <strong>A</strong> is moving at 0.60 ms<sup>-1</sup>.</p>\n<p>Calculate the impulse given to each cart by the spring as it expands:[[0]] Ns.</p>\n<p>Calculate the mass of cart <strong>A</strong>:[[1]]&nbsp;kg.</p>\n<p>State the final momentum of the system at the instant the spring drops away:[[2]]&nbsp;kgms<sup>-1</sup></p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.33", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.13", "maxValue": "0.14", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "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": false, "customName": "", "marks": "0.33", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.22", "maxValue": "0.23", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "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": false, "customName": "", "marks": "0.34", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "CLE W1 Q4 Collision in Two Dimensions", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Collision_in_2d_CLE3.png", "/srv/numbas/media/question-resources/Collision_in_2d_CLE3.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "John Bridges", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/913/"}, {"name": "Doug Satterford", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3185/"}], "tags": [], "metadata": {"description": "<p>Is a little restrictive on the formatting - requires minuses in set places that the question allows to cancel&hellip; recommend use as practice not assessed</p>", "licence": "None specified"}, "statement": "<p>A snooker ball moving with speed&nbsp; v<sub>A</sub> = {v} ms<sup>-1</sup> in the +x direction strikes an equal mass ball B which is initially at rest. The two balls are observed to move off at 45<sup>o</sup> above and below the x axis.</p>\n<p>We want to find the speeds of the two balls after the collision.</p>\n<p></p>\n<p><img src=\"resources/question-resources/Collision_in_2d_CLE3.png\" width=\"227\" height=\"202\"/>&nbsp;</p>\n<p>Fig. A collision in two dimensions between snooker balls A and B, of equal mass.</p>\n<p>Note that we use the prime symbol (') here and in the answers to denote v and $\\theta$ after the collision.</p>", "advice": "", "rulesets": {}, "variables": {"v": {"name": "v", "group": "Ungrouped variables", "definition": "random(2 .. 5#0.1)", "description": "<p>Speed of the snooker ball A before the collision.</p>", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["v"], "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>Firstly, complete the follow equations for momentum in the x and y directions.&nbsp;</p>\n<p></p>\n<p>For the x direction: mv<sub>A</sub> = m[[0]]<sub>A&nbsp;&nbsp;</sub>[[1]](45<sup>o</sup>) + m[[0]]<sub>B&nbsp;&nbsp;</sub>[[1]](-45<sup>o</sup>)</p>\n<p></p>\n<p>and for the y direction: 0&nbsp;= [[3]]<sub>A&nbsp;&nbsp;</sub>[[2]](45<sup>o</sup>) + [[3]]<sub>B&nbsp;&nbsp;</sub>[[2]](-45<sup>o</sup>)</p>", "gaps": [{"type": "patternmatch", "useCustomName": true, "customName": "Gap 1", "marks": "0.0625", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "v'", "displayAnswer": "", "caseSensitive": true, "partialCredit": "50", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "Gap 2.", "marks": "0.0625", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "cos", "displayAnswer": "", "caseSensitive": true, "partialCredit": "50", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "Gap 3.", "marks": "0.0625", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "sin", "displayAnswer": "", "caseSensitive": true, "partialCredit": "50", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "Gap 4.", "marks": "0.0625", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "mv'", "displayAnswer": "", "caseSensitive": true, "partialCredit": "50", "matchMode": "exact"}], "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": "<p>Bearing in mind that the two balls have equal masses and also noting that sin(-$\\theta$) = -sin($\\theta$), cos(-$\\theta$) = cos($\\theta$), complete the following expressions:</p>\n<p>v'<sub>B</sub> = [[2]]<sub>A&nbsp;&nbsp;</sub>[[0]](45<sup>o</sup>)/[[1]](45<sup>o</sup>) = v'<sub>A</sub></p>\n<p>v<sub>A</sub> = v'<sub>A</sub>[[3]](45<sup>o</sup>) + [[4]]<sub>B&nbsp;&nbsp;</sub>[[3]](45<sup>o</sup>) = 2[[4]]<sub>A&nbsp;&nbsp;</sub>cos(45<sup>o</sup>)</p>\n<p></p>\n<p></p>\n<p></p>", "gaps": [{"type": "patternmatch", "useCustomName": true, "customName": "Gap 1", "marks": "0.05", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "sin", "displayAnswer": "", "caseSensitive": true, "partialCredit": "50", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "Gap 2", "marks": "0.05", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "-sin", "displayAnswer": "", "caseSensitive": true, "partialCredit": "50", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "Gap 3", "marks": "0.05", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "-v'", "displayAnswer": "", "caseSensitive": true, "partialCredit": "50", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "Gap 4.", "marks": "0.05", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "cos", "displayAnswer": "", "caseSensitive": true, "partialCredit": "50", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "Gap 5.", "marks": "0.05", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "v'", "displayAnswer": "", "caseSensitive": true, "partialCredit": "50", "matchMode": "exact"}], "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": "<p>Calculate v'<sub>A</sub> = v'<sub>B</sub> =&nbsp;[[0]] ms<sup>-1</sup>&nbsp;</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Gap 1", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "v/(2*0.707)-0.1", "maxValue": "v/(2*0.707)+0.1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "2", "precisionPartialCredit": "50", "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"}, {"name": "CLE W1 Q5 Collisions Conservation of Momentum - Linear Air track", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "John Bridges", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/913/"}, {"name": "Stuart Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/997/"}, {"name": "Doug Satterford", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3185/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>In an experiment using a linear air track a $\\var{m1}$ kg rider travelling to the right at $\\var{u1}$ ms<sup>-1</sup> collides with a second, stationary rider of mass $\\var{m2}$ kg. Find the velocities v<sub>1</sub> and v<sub>2</sub> of the two riders if: a) the collision is perfectly elastic; and b) the velocity v if the collision is totally inelastic.</p>\n<p><em>From the question, we know: &nbsp;$m_1=\\var{m1}$&nbsp;</em>kg<em>, &nbsp;$m_2=\\var{m2}$ </em>kg<em>, &nbsp;$u_1=\\var{u1}$ </em>ms<sup>-1</sup><em>, &nbsp;and &nbsp;$u_2=\\var{u2}$ </em>ms<sup>-1</sup><em>.</em></p>\n<p><em>Give your answers to two significant figures.</em></p>", "advice": "<p>See section 3.24 (pg 92) in Advanced Physics by Adams and Allday.</p>", "rulesets": {}, "variables": {"v1": {"name": "v1", "group": "Ungrouped variables", "definition": "siground(((m1-m2)/(m1+m2))*u1,2)", "description": "", "templateType": "anything"}, "m1": {"name": "m1", "group": "Ungrouped variables", "definition": "random(45..55)/100", "description": "", "templateType": "anything"}, "m2": {"name": "m2", "group": "Ungrouped variables", "definition": "random(8..12)/10", "description": "", "templateType": "anything"}, "u2": {"name": "u2", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything"}, "b_v1": {"name": "b_v1", "group": "Ungrouped variables", "definition": "siground((m1*u1)/(m1+m2),2)", "description": "", "templateType": "anything"}, "u1": {"name": "u1", "group": "Ungrouped variables", "definition": "random(17..23)/10", "description": "", "templateType": "anything"}, "v2": {"name": "v2", "group": "Ungrouped variables", "definition": "siground(sqrt((m1*((u1^2)-(v1^2)))/m2),2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["m1", "m2", "u1", "u2", "v1", "v2", "b_v1"], "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>Hint: If the collision is perfectly elastic, both momentum and kinetic energy are conserved.</p>\n<p><em></em></p>\n<p>first rider: $v_1 =$ [[0]] ms<sup>-1</sup></p>\n<p>second stationary rider: $v_2 =$ [[1]] ms<sup>-1</sup></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "v1", "maxValue": "v1", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "v2", "maxValue": "v2", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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": "<p>Hint: If the collision is totally&nbsp;inelastic, only&nbsp;linear momentum is conserved.</p>\n<p><em></em></p>\n<p>$v =$ [[0]] ms<sup>-1</sup></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "b_v1-0.02", "maxValue": "b_v1+0.02", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], 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