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height: 101px; text-align: left; vertical-align: top;\">\n<p>The hook supports two cables&nbsp; $F_1$&nbsp; and&nbsp; $F_2$&nbsp; at angles&nbsp; $\\theta$&nbsp; and $\\phi$&nbsp; as shown in the figure.</p>\n<p>The resultant of these forces is vertically downwards and has a magnitude of&nbsp; $3000\\ N.$</p>\n</td>\n<td style=\"width: 137.406px; height: 101px; text-align: left; vertical-align: top;\"><img src=\"resources/question-resources/Q5_P5LHyyP.JPG\" width=\"131\" height=\"188\"/></td>\n</tr>\n</tbody>\n</table>", "advice": "<p>5.1&nbsp; &nbsp;&nbsp;</p>\n<p>&nbsp; &nbsp; &nbsp;<img src=\"resources/question-resources/Q5_FB1_a9tZE1a.jpg\"/></p>\n<p>5.2&nbsp; &nbsp;&nbsp;</p>\n<p><img src=\"resources/question-resources/Q5_FB2_NZsWSVT.jpg\"/><img src=\"resources/question-resources/Q5_FB3_DQ2rJy2.jpg\" width=\"127\" height=\"245\"/></p>\n<p><img src=\"resources/question-resources/Q5_FB_rAQfLqN.jpg\"/></p>\n<p></p>\n<p></p>\n<p></p>", "rulesets": {}, "extensions": ["quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Answer": {"name": "Answer", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "Unit": {"name": "Unit", "group": "Ungrouped variables", "definition": "if(2.6<answer<=2.7,kN,N)", "description": "", "templateType": "anything", "can_override": false}, "N": {"name": "N", "group": "Ungrouped variables", "definition": "Parse(\"N\")", "description": "", "templateType": "anything", "can_override": false}, "kN": {"name": "kN", "group": "Ungrouped variables", "definition": "parse(\"kN\")", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Answer", "Unit", "N", "kN"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "alwaysreplace", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>5.1&nbsp; &nbsp; Write down the resultant of the forces in vector form&nbsp;$\\left\\langle {x,y} \\right\\rangle $.</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;$\\left\\langle{}\\right.$&nbsp;[[0]],[[1]] $\\left.{}\\right\\rangle$</p>\n<p>&nbsp;5.2&nbsp; &nbsp;Determine the magnitude of the force in $F_2$, given that</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;$\\theta=\\frac{\\pi}{3}$ and $\\phi=\\frac{\\pi}{4}$, using either vectors, or trigonometry.</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [[2]] [[3]](units)</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0", "maxValue": "0", "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": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-3000", "maxValue": "-3000", "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": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "minValue": "2.68", "maxValue": "2.69", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "2689.7", "maxValue": "2689.74", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "Answer", "part": "p0g2", "must_go_first": false}], "variableReplacementStrategy": "alwaysreplace", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{unit}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": true, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "JPO AddMath", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2346/"}]}]}], "contributors": [{"name": "JPO AddMath", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2346/"}]}