// Numbas version: finer_feedback_settings {"name": "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": [{"functions": {}, "ungrouped_variables": ["force", "theta", "angle", "yangle"], "name": "Resolve force into $x$ and $y$ components - negative $x$", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "

a)

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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.

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\\begin{align} \\text{component in } x \\text{-direction} & = F \\cos \\theta \\\\
& = \\var{force} \\times \\cos \\var{theta} \\\\
& = \\var{precround(force*cos(radians(theta)),3)}
\\end{align}

\n

b)

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We need the angle between the force and the direction we are resolving so take $\\theta = 90 - \\var{theta}= \\var{90-theta}^{\\circ}$.

\n

\\begin{align}
\\text{component in } y \\text{-direction} & = F \\cos \\theta \\\\
& = \\var{force} \\times \\cos \\var{yangle} \\\\
& = \\var{precround(force*cos(radians(yangle)),3)}
\\end{align}

", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "

Find the component of the force in the $x$-direction.

", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "force*cos(radians(theta))", "strictPrecision": false, "minValue": "force*cos(radians(theta))", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "3", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "

Find the component of the force in the $y$-direction.

", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "force*cos(radians(yangle))", "strictPrecision": false, "minValue": "force*cos(radians(yangle))", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "3", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "

\n

In the diagram above, $F = \\var{force} \\ \\mathrm{N}$ and $\\theta = \\var{theta}^{\\circ}$.

\n

Give your answers to the following questions in Newtons to 3 decimal places.

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"yangle": {"definition": "90-theta", "templateType": "anything", "group": "Ungrouped variables", "name": "yangle", "description": ""}, "theta": {"definition": "random(5..85#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "theta", "description": ""}, "force": {"definition": "random(2..15#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "force", "description": ""}, "angle": {"definition": "180-theta", "templateType": "anything", "group": "Ungrouped variables", "name": "angle", "description": ""}}, "metadata": {"description": "

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \\cos \\theta$. The force is applied in the negative $x$ direction but the positive $y$. 

", "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/"}]}