// Numbas version: exam_results_page_options
{"name": "Three forces with angles & 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"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Three forces with angles & Solutions", "tags": [], "metadata": {"description": "<p>resultant force</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p><img src=\"resources/question-resources/fig2-35.png\" width=\"340\" height=\"248\"/></p>\n<p>Knowing that&nbsp;<i>$\\alpha=\\var{a}^\\circ$</i>, determine</p>", "advice": "<p>(a)</p>\n<table style=\"border-color: #000000; margin-left: auto; margin-right: auto;\" border=\"1\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Force</td>\n<td style=\"text-align: center;\">x-component, N</td>\n<td style=\"text-align: center;\">y-component, N</td>\n</tr>\n<tr>\n<td>100 N</td>\n<td>$100 \\cos \\var{a}^\\circ=\\var{x100}$</td>\n<td>$-100 \\sin \\var{a}^\\circ=\\var{y100}$</td>\n</tr>\n<tr>\n<td>150 N</td>\n<td>$150 \\cos (\\var{a}^\\circ+30^\\circ)=\\var{x150}$</td>\n<td>$-150 \\sin (\\var{a}^\\circ+30^\\circ)=\\var{y150}$</td>\n</tr>\n<tr>\n<td>200 N</td>\n<td>$-200 \\cos \\var{a}^\\circ=\\var{x200}$</td>\n<td>$-200 \\sin \\var{a}^\\circ=\\var{y200}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p style=\"text-align: center;\">$\\mathbf{R}=(\\sum F_x )\\mathbf{i}+(\\sum F_y )\\mathbf{j}=\\var{rx}\\mathbf{i}\\var{ry}\\mathbf{j},\\;\\text{N}$</p>\n<p style=\"text-align: center;\">$R=\\sqrt{(\\var{rx})^2+(\\var{ry})^2}=\\var{R}\\;\\text{N}\\quad\\blacktriangleleft$</p>\n<p>(b)</p>\n<p style=\"text-align: center;\">$\\theta=\\arctan \\dfrac{R_y}{R_x}=\\arctan \\dfrac{\\var{ry}}{\\var{rx}}=\\var{beta}^\\circ$&nbsp;<img src=\"resources/question-resources/angle2.png\" width=\"23\" height=\"15\"/>&nbsp;$\\quad\\blacktriangleleft$</p>", "rulesets": {}, "extensions": [], "variables": {"x200": {"name": "x200", "group": "Ungrouped variables", "definition": "precround(-200 cos(radians(a)),1)", "description": "", "templateType": "anything"}, "y200": {"name": "y200", "group": "Ungrouped variables", "definition": "precround(-200 sin(radians(a)),1)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(5 .. 60#5)", "description": "", "templateType": "randrange"}, "ry": {"name": "ry", "group": "Ungrouped variables", "definition": "precround(y100+y200+y150,1)", "description": "", "templateType": "anything"}, "x150": {"name": "x150", "group": "Ungrouped variables", "definition": "precround(150 cos(radians(a+30)),1)", "description": "", "templateType": "anything"}, "beta": {"name": "beta", 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"x100", "y100", "x150", "y150", "x200", "y200", "rx", "ry", "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>the magnitude of the resultant of the three forces shown, N:&nbsp;</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>its&nbsp;direction&nbsp;in $^\\circ$, with respect to the horizontal line&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": 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