// Numbas version: exam_results_page_options
{"name": "Three forces - a block on a slope & Solutions", "extensions": [], "custom_part_types": [], "resources": [["question-resources/fig2-35.png", "/srv/numbas/media/question-resources/fig2-35.png"], ["question-resources/angle2.png", "/srv/numbas/media/question-resources/angle2.png"], ["question-resources/fig2-37.png", "/srv/numbas/media/question-resources/fig2-37.png"], ["question-resources/angle1_Exe2Tlx.png", "/srv/numbas/media/question-resources/angle1_Exe2Tlx.png"], ["question-resources/hw2sol5.png", "/srv/numbas/media/question-resources/hw2sol5.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Three forces - a block on a slope & Solutions", "tags": [], "metadata": {"description": "<p>resultant force</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Knowing that&nbsp;<i>$\\alpha=\\var{a}^\\circ$</i>,&nbsp;</p>\n<p><img src=\"resources/question-resources/fig2-37.png\" width=\"305\" height=\"220\"/></p>", "advice": "<p>(a)</p>\n<p><img src=\"resources/question-resources/hw2sol5.png\" width=\"259\" height=\"148\"/></p>\n<table style=\"border-color: #000000;\" border=\"1\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Force, lb</td>\n<td style=\"text-align: center;\">x-component, lb</td>\n<td style=\"text-align: center;\">y-component, lb</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">60</td>\n<td style=\"text-align: left;\">$60\\cos 20^\\circ = \\var{f1[0]}$</td>\n<td style=\"text-align: left;\">$60\\sin 20^\\circ = \\var{f1[1]}$</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">80</td>\n<td style=\"text-align: left;\">$80\\cos (20^\\circ+\\alpha)=\\var{f2[0]}$</td>\n<td style=\"text-align: left;\">$80\\cos (20^\\circ+\\alpha)=\\var{f2[1]}$</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">120</td>\n<td style=\"text-align: left;\">$120\\sin(20^\\circ+\\alpha)=\\var{f3[0]}$</td>\n<td style=\"text-align: left;\">\n<p>$-120\\cos(20^\\circ+\\alpha)=\\var{f3[1]}$</p>\n</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">Resultant</td>\n<td style=\"text-align: left;\">$R_x=\\sum P_x=\\var{Rvec[0]}\\text{ lb}$</td>\n<td style=\"text-align: left;\">\n<p>$R_y=\\sum P_y=\\var{Rvec[1]}\\text{ lb}$</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>The magnitude of the resultant force is $R=\\sqrt{R_x^2+R_y^2}=\\var{R}\\;\\text{lb}\\quad\\blacktriangleleft$</p>\n<p></p>\n<p>(b) $\\theta=\\arctan\\dfrac{R_y}{R_x}=\\arctan\\dfrac{\\var{Rvec[1]}\\,\\text{lb}}{\\var{Rvec[0]}\\,\\text{lb}}=\\var{beta}^\\circ\\quad\\blacktriangleleft$&nbsp;</p>", "rulesets": {}, "extensions": [], "variables": {"Rvec": {"name": "Rvec", "group": "Ungrouped variables", "definition": "{f1}+{f2}+{f3}", "description": "", "templateType": "anything"}, "R": {"name": "R", "group": "Ungrouped variables", "definition": "precround(length(Rvec),2)", "description": "", "templateType": "anything"}, "f3": {"name": "f3", "group": "Ungrouped variables", "definition": "precround(120*vector(sin(radians(20+{a})),-cos(radians(20+{a}))),2)", "description": "", "templateType": "anything"}, "f2": {"name": "f2", "group": "Ungrouped variables", "definition": "precround(80*vector(cos(radians(20+{a})),sin(radians(20+{a}))),2)", "description": "", "templateType": "anything"}, "beta": {"name": "beta", "group": "Ungrouped variables", "definition": "precround(degrees(angle(vector(1,0),Rvec))*sign(Rvec[1]),1)", "description": "", "templateType": "anything"}, "f1": {"name": "f1", "group": "Ungrouped variables", "definition": "precround(60*vector(cos(radians(20)),sin(radians(20))),2)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(5 .. 50#5)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "f1", "f2", "f3", "Rvec", "R", "beta"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the magnitude of the resultant of the three forces shown, lb.</p>", "minValue": "{R}-0.5", "maxValue": "{R}+0.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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, "prompt": "<p>Determine its&nbsp;direction&nbsp;in $^\\circ$, with respect to the horizontal line (positive angle for&nbsp;<img src=\"resources/question-resources/angle1_Exe2Tlx.png\" width=\"24\" height=\"16\"/>&nbsp;and negative angle for&nbsp;<img src=\"resources/question-resources/angle2.png\" width=\"23\" height=\"15\"/>)&nbsp;</p>", "minValue": "{beta}-0.5", "maxValue": "{beta}+0.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Vladimir Vingoradov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1862/"}]}]}], "contributors": [{"name": "Vladimir Vingoradov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1862/"}]}