// Numbas version: exam_results_page_options
{"name": "Resolve force into $x$ and $y$ components", "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": [{"functions": {}, "ungrouped_variables": ["force", "theta", "angle", "yangle"], "name": "Resolve force into $x$ and $y$ components", "tags": [], "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. You could also answer these by resolving in the negative $x$ or $y$ direction and changing the sign of your solution. For example in part <strong>b)</strong> you could use $\\theta_y = \\var{theta}$ which gives $F \\cos \\theta_y =&nbsp;\\var{precround(-force*cos(radians(yangle)),3)}$ and then change the sign.</p>", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "<p>Find the component of the force in the $x$-direction in Newtons.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "force*cos(radians(angle))", "minValue": "force*cos(radians(angle))", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>Find the component of the force in the $y$-direction in Newtons.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "force*cos(radians(yangle))", "minValue": "force*cos(radians(yangle))", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p><img style=\"display: block; margin-left: auto; margin-right: auto;\" src=\"resources/question-resources/force_component_image_2.png\"/></p>\n<p>In the above diagram, $F = \\var{force} \\, \\mathrm{N}$ and $\\theta = \\var{theta}^{\\circ}$.&nbsp;</p>\n<p>Give your answers to the following questions to 3 decimal places.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"yangle": {"definition": "180-theta", "templateType": "anything", "group": "Ungrouped variables", "name": "yangle", "description": ""}, "theta": {"definition": "random(2..89#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "theta", "description": ""}, "force": {"definition": "random(3..20#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "force", "description": ""}, "angle": {"definition": "90 + theta", "templateType": "anything", "group": "Ungrouped variables", "name": "angle", "description": ""}}, "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"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "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/"}]}]}], "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/"}]}