// Numbas version: exam_results_page_options
{"name": "Resolve a force into $x$ and $y$ components", "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": [{"tags": [], "parts": [{"variableReplacementStrategy": "originalfirst", "precisionMessage": "You have not given your answer to the correct precision.", "prompt": "<p>Find the component of the force in the $x$-direction, in Newtons to 3 decimal places.</p>", "showPrecisionHint": false, "correctAnswerFraction": false, "minValue": "force*cos(radians(angle))", "precisionPartialCredit": 0, "type": "numberentry", "precisionType": "dp", "variableReplacements": [], "scripts": {}, "marks": 1, "unitTests": [], "precision": "3", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "mustBeReducedPC": 0, "strictPrecision": false, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "maxValue": "force*cos(radians(angle))", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "mustBeReduced": false, "allowFractions": false}, {"variableReplacementStrategy": "originalfirst", "precisionMessage": "You have not given your answer to the correct precision.", "prompt": "<p>Find the component of the force in the $y$-direction,&nbsp;in Newtons to 3 decimal places.</p>", "showPrecisionHint": false, "correctAnswerFraction": false, "minValue": "force*cos(radians(yangle))", "precisionPartialCredit": 0, "type": "numberentry", "precisionType": "dp", "variableReplacements": [], "scripts": {}, "marks": 1, "unitTests": [], "precision": "3", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "mustBeReducedPC": 0, "strictPrecision": false, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "maxValue": "force*cos(radians(yangle))", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "mustBeReduced": false, "allowFractions": false}], "variable_groups": [], "ungrouped_variables": ["force", "angle", "yangle"], "statement": "<p style=\"text-align: center;\"><img width=\"552\" height=\"350\" src=\"resources/question-resources/force_component_image_PgpiR1U.png\"/></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>", "functions": {}, "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "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>"}, "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>", "type": "question", "variables": {"force": {"group": "Ungrouped variables", "description": "", "definition": "random(3..15#0.5)", "name": "force", "templateType": "randrange"}, "angle": {"group": "Ungrouped variables", "description": "", "definition": "random(1..89#1)", "name": "angle", "templateType": "randrange"}, "yangle": {"group": "Ungrouped variables", "description": "", "definition": "90-angle", "name": "yangle", "templateType": "anything"}}, "rulesets": {}, "extensions": [], "name": "Resolve a force into $x$ and $y$ components", "variablesTest": {"condition": "", "maxRuns": 100}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}]}]}], "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}]}