// Numbas version: finer_feedback_settings
{"name": "Reaction forces", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Reaction forces", "tags": [], "metadata": {"description": "<p>Students need to find solution to simultaneous linear equations with randomised coefficients.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>We need to solve \\begin{align} R_1+R_2 - \\var{W} &amp;=0\\\\\\var{a}R_1 -\\var{b}R_2 &amp;=0\\end{align} which can be written as \\begin{align} R_1+R_2 &amp;= \\var{W}\\quad (1)\\\\ \\var{a}R_1 -\\var{b}R_2 &amp;=0\\quad (2)\\end{align}</p>\n<p>Using the method of elimination to eliminate \\(R_2\\) we multiply equation \\((1)\\) by \\(\\var{b}\\) to get \\begin{align}\\var{b}R_1+\\var{b}R_2 &amp;= \\var{b*W}\\quad (3)\\\\ \\var{a}R_1 -\\var{b}R_2 &amp;=0\\quad (4)\\end{align}</p>\n<p>Taking \\((3)+(4)\\) we obtain \\[\\var{a+b}R_1=\\var{B*W}\\]</p>\n<p>and hence \\[R_1=\\simplify{{b*W/(a+b)}}\\]</p>\n<p>Substituting this into \\((1)\\) gives us \\[\\simplify[unitFactor]{{b*W/(a+b)}}+R_2 = \\var{W}\\] and hence \\[R_2=\\simplify{{W-b*W/(a+b)}}\\]</p>\n<p>Thus the reaction forces are \\(R_1=\\simplify{{b*W/(a+b)}}\\) N and \\(R_2=\\simplify{{W-b*W/(a+b)}}\\) N.</p>\n<p>(Note that this problem could also be solved by eliminating \\(R_1\\) instead of \\(R_2\\) or by the method of substitution, however the final answers will be the same.)</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"W": {"name": "W", "group": "Ungrouped variables", "definition": "random(1500..6000 #500)", "description": "<p>Weight of vehicle in kg, random between 1500 and 6000 in steps of 500.</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(3..9)", "description": "<p>Coefficient of reation force 1, random integer between 3 and 9</p>", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(3..9 except a)", "description": "<p>Coefficient of reaction force 2, random integer between 3 and 9 except for value of a/</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["W", "a", "b"], "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 weight of a vehicle is supported by reaction forces \\(R_1\\) and \\(R_2\\) at its front and rear wheels. If the weight of the vehicle is \\(W=\\var{W}\\) N, the reaction forces satisfy the following system of equations: \\begin{align} R_1+R_2 - \\var{W} &amp;=0\\\\\\var{a}R_1 -\\var{b}R_2 &amp;=0 \\end{align} Find the values of \\(R_1\\) and \\(R_2\\). Write your final answer in the box below and show full working on your handwritten notes. (Note: Leave answers in fraction form wher appropriate. For example to enter the fraction \\(\\frac32\\) type <code>3/2</code>.)</p>\n<p>\\(R_1=\\)[[0]] N</p>\n<p>\\(R_2=\\)[[1]] N</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "\\(R_1\\)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "b*W/(a+b)", "maxValue": "b*W/(a+b)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "\\(R_2\\)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "W-b*W/(a+b)", "maxValue": "W-b*W/(a+b)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": 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/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}