// Numbas version: exam_results_page_options
{"name": "Vectors: Resolving forces 1a", "extensions": [], "custom_part_types": [], "resources": [["question-resources/force_component_image.png", "/srv/numbas/media/question-resources/force_component_image.png"], ["question-resources/force_component_image_PgpiR1U.png", "/srv/numbas/media/question-resources/force_component_image_PgpiR1U.png"], ["question-resources/Picture2_7CTf2tv.png", "/srv/numbas/media/question-resources/Picture2_7CTf2tv.png"], ["question-resources/Picture2_4njOTSR.png", "/srv/numbas/media/question-resources/Picture2_4njOTSR.png"], ["question-resources/Picture1_kv6rtT4.png", "/srv/numbas/media/question-resources/Picture1_kv6rtT4.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Vectors: Resolving forces 1a", "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 acts in the positive $x$ and positive $y$ direction.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p style=\"text-align: center;\"><img src=\"resources/question-resources/force_component_image_PgpiR1U.png\" width=\"552\" height=\"350\"/></p>\n<p style=\"text-align: left;\">In the above diagram the force $F=\\var{force} \\ \\mathrm{N}$ and the angle $\\theta = \\var{angle}^{\\circ}$.</p>", "advice": "<h4><img src=\"resources/question-resources/Picture2_7CTf2tv.png\" width=\"212\" height=\"96\"/><img src=\"resources/question-resources/Picture1_kv6rtT4.png\" width=\"257\" height=\"112\"/></h4>\n<h4></h4>\n<h4>a)</h4>\n<p>The component of force in the $x$-direction can be found using $\\cos\\theta \\times F$. Remember to set&nbsp;your calculator to use&nbsp;degrees and not radians.</p>\n<p>\\begin{align} \\text{component in the }x \\text{-direction } &amp; = F \\cos \\theta \\\\<br/>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &amp; = \\var{force} \\times \\cos \\var{angle} \\\\<br/>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&amp; = \\var{precround(force*cos(radians(angle)),3)}\\end{align}</p>\n<h4>b)</h4>\n<p>This time we are using sin</p>\n<p>\\begin{align} \\text{component in the y-direction } &amp; = F \\sin \\theta \\\\<br/>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &amp; = \\var{force} \\times \\sin \\var{angle} \\\\<br/>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&amp; = \\var{precround(force*sin(radians(angle)),3)}\\end{align}</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"yangle": {"name": "yangle", "group": "Ungrouped variables", "definition": "90-angle", "description": "", "templateType": "anything", "can_override": false}, "force": {"name": "force", "group": "Ungrouped variables", "definition": "random(3 .. 15#0.5)", "description": "", "templateType": "randrange", "can_override": false}, "angle": {"name": "angle", "group": "Ungrouped variables", "definition": "random(1 .. 89#1)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["force", "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 to 3 decimal places.</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,&nbsp;in Newtons to 3 decimal places.</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": "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": "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/"}]}