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{"name": "Vectors: Resolving forces 1b", "extensions": [], "custom_part_types": [], "resources": [["question-resources/force_component_image_2.png", "/srv/numbas/media/question-resources/force_component_image_2.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Vectors: Resolving forces 1b", "tags": [], "metadata": {"description": "<p>Find the $x$ and $y$ components of a force which is&nbsp;applied at an angle to a particle. Resolve using $F \\cos \\theta$. The force is applied in the negative $x$ and negative $y$ direction.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><img style=\"display: block; margin-left: auto; margin-right: auto;\" src=\"resources/question-resources/force_component_image_2.png\"/></p>\n<p>$F = \\var{force} \\, \\mathrm{N}$ at an angle of $\\theta = \\var{theta}^{\\circ}$ from the downwards vertical line.&nbsp;</p>\n<p></p>\n<p>Give your answers to the following questions to 3 decimal places.</p>", "advice": "<h4>a)</h4>\n<p>We need to find the angle $\\theta_x$ of $F$ relative to the $x$-axis and then use $F \\times cos\\theta_x$.</p>\n<p>We consider the angle between the positive $x$-axis and $F$,&nbsp;i.e.&nbsp;$\\theta_x = 90 + \\var{theta}$.</p>\n<p>\\begin{align} <br/>\\text{component in the } x \\text{-direction} &amp; = F \\cos\\theta_x \\\\<br/>&amp; = \\var{force} \\times \\cos \\var{angle} \\\\<br/>&amp; = \\var{precround(force*cos(radians(angle)),3)} <br/>\\end{align}</p>\n<h4>b)</h4>\n<p>The positive $y$-direction is vertically upwards&nbsp;and&nbsp;we need the angle relative to the positive $y$-direction therefore $\\theta_y = 180 - \\var{theta}$.</p>\n<p>\\begin{align} <br/>\\text{component in the } y \\text{-direction} &amp; = F \\cos\\theta_y \\\\<br/>&amp; = \\var{force} \\times \\cos \\var{yangle} \\\\<br/>&amp; = \\var{precround(force*cos(radians(yangle)),3)} <br/>\\end{align}</p>\n<p>Notice that both these answers are negative as the force acts in the opposite direction to the positive. &nbsp;</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"yangle": {"name": "yangle", "group": "Ungrouped variables", "definition": "180-theta", "description": "", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Ungrouped variables", "definition": "random(2 .. 89#1)", "description": "", "templateType": "randrange", "can_override": false}, "force": {"name": "force", "group": "Ungrouped variables", "definition": "random(3 .. 20#0.5)", "description": "", "templateType": "randrange", "can_override": false}, "angle": {"name": "angle", "group": "Ungrouped variables", "definition": "90 + theta", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["force", "theta", "angle", "yangle"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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>Find the component of the force in the $x$-direction in Newtons.</p>", "minValue": "force*cos(radians(angle))", "maxValue": "force*cos(radians(angle))", "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"}, {"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>Find the component of the force in the $y$-direction in Newtons.</p>", "minValue": "force*cos(radians(yangle))", "maxValue": "force*cos(radians(yangle))", "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"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}