// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Resolve force into $x$ and $y$ components - negative $x$", "extensions": [], "custom_part_types": [], "resources": [["question-resources/force_component_image_3.png", "/srv/numbas/media/question-resources/force_component_image_3.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "parts": [{"showFeedbackIcon": true, "showPrecisionHint": false, "variableReplacements": [], "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "minValue": "-force*cos(radians(theta))", "mustBeReducedPC": 0, "allowFractions": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "customMarkingAlgorithm": "", "marks": 1, "notationStyles": ["plain", "en", "si-en"], "precision": "3", "showCorrectAnswer": true, "type": "numberentry", "prompt": "<p>Find the component of the force in the $x$-direction.</p>", "unitTests": [], "mustBeReduced": false, "maxValue": "-force*cos(radians(theta))"}, {"showFeedbackIcon": true, "showPrecisionHint": false, "variableReplacements": [], "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "minValue": "force*cos(radians(yangle))", "mustBeReducedPC": 0, "allowFractions": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "customMarkingAlgorithm": "", "marks": 1, "notationStyles": ["plain", "en", "si-en"], "precision": "3", "showCorrectAnswer": true, "type": "numberentry", "prompt": "<p>Find the component of the force in the $y$-direction.</p>", "unitTests": [], "mustBeReduced": false, "maxValue": "force*cos(radians(yangle))"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "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 is applied in the negative $x$ direction&nbsp;but the positive $y$.&nbsp;</p>"}, "name": "Simon's copy of Resolve force into $x$ and $y$ components - negative $x$", "advice": "<h4>a)</h4>\n<p>We resolve in the positive $x$-direction so the answer will be negative. We take $\\theta = \\var{theta}^{\\circ}$ as the angle is already between the force and the $x$-axis.</p>\n<p>\\begin{align} \\text{component in } x \\text{-direction} &amp; = -F \\cos \\theta \\\\<br/>&amp; = -\\var{force} \\times \\cos \\var{theta} \\\\<br/>&amp; = -\\var{precround(force*cos(radians(theta)),3)}<br/> \\end{align}</p>\n<h4>b)</h4>\n<p>We need the angle between the force and the direction we are resolving so take $\\alpha= 90 - \\var{theta}= \\var{90-theta}^{\\circ}$.</p>\n<p>\\begin{align} <br/>\\text{component in } y \\text{-direction} &amp; = F \\cos \\alpha\\\\<br/>&amp; = \\var{force} \\times \\cos \\var{yangle} \\\\<br/>&amp; = \\var{precround(force*cos(radians(yangle)),3)} <br/>\\end{align}</p>\n<p></p>\n<p>Alternatively we could just take $\\theta = \\var{theta}$ and use sin as follows:</p>\n<p>\\begin{align}&nbsp;<br/>\\text{component in } y \\text{-direction} &amp; = F \\sin \\theta \\\\<br/>&amp; = \\var{force} \\times \\sin \\var{theta} \\\\<br/>&amp; = \\var{precround(force*sin(radians(theta)),3)}&nbsp;<br/>\\end{align}</p>", "preamble": {"css": "", "js": ""}, "statement": "<p><img width=\"334\" height=\"304\" style=\"display: block; margin-left: auto; margin-right: auto;\" src=\"resources/question-resources/force_component_image_3.png\"/></p>\n<p>In the diagram above,&nbsp;$F = \\var{force} \\ \\mathrm{N}$ and $\\theta = \\var{theta}^{\\circ}$.</p>\n<p>Give your answers to the following questions in Newtons to 3 decimal places.</p>", "extensions": [], "ungrouped_variables": ["force", "theta", "angle", "yangle"], "variables": {"theta": {"group": "Ungrouped variables", "templateType": "randrange", "name": "theta", "definition": "random(5..85#1)", "description": ""}, "yangle": {"group": "Ungrouped variables", "templateType": "anything", "name": "yangle", "definition": "90-theta", "description": ""}, "force": {"group": "Ungrouped variables", "templateType": "randrange", "name": "force", "definition": "random(2..15#1)", "description": ""}, "angle": {"group": "Ungrouped variables", "templateType": "anything", "name": "angle", "definition": "180-theta", "description": ""}}, "functions": {}, "variable_groups": [], "rulesets": {}, "type": "question", "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}