// Numbas version: finer_feedback_settings
{"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"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["force", "angle", "yangle"], "name": "Resolve a force into $x$ and $y$ components", "tags": [], "advice": "<h4>a)</h4>\n<p>The component of force in the $x$-direction can be found using $F \\times \\cos\\theta$. 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>Now we need to make sure we find the angle between the force and the direction we are resolving in. Therefore $\\theta = 90 - \\var{angle} = \\var{yangle}$.</p>\n<p>\\begin{align} \\text{component in the y-direction } &amp; = F \\cos \\theta \\\\<br/>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &amp; = \\var{force} \\times \\cos \\var{yangle} \\\\<br/>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&amp; = \\var{precround(force*cos(radians(yangle)),3)}\\end{align}</p>\n<p>Since $\\sin \\theta = \\cos(90-\\theta)$, we could also use $\\sin \\var{angle}$ in our calculations instead of $\\cos(90 - \\var{angle})$.</p>", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "<p>Find the component of the force in the $x$-direction, in Newtons to 3 decimal places.</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,&nbsp;in Newtons to 3 decimal places.</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 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>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"yangle": {"definition": "90-angle", "templateType": "anything", "group": "Ungrouped variables", "name": "yangle", "description": ""}, "force": {"definition": "random(3..15#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "force", "description": ""}, "angle": {"definition": "random(1..89#1)", "templateType": "randrange", "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 acts in the positive $x$ and positive $y$ direction.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}]}]}], "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}]}