![](\"resources/question-resources/force_component_image_3.png\"/)
Find the component of the force in the $x$-direction.
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", "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "precision": "3", "precisionPartialCredit": 0, "showPrecisionHint": false, "variableReplacements": [], "type": "numberentry", "allowFractions": false, "scripts": {}, "minValue": "force*cos(radians(yangle))"}], "name": "Resolve force into $x$ and $y$ components - negative $x$", "question_groups": [{"pickQuestions": 0, "name": "", "pickingStrategy": "all-ordered", "questions": []}], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "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 $y$.
"}, "statement": "
In the diagram above, $F = \\var{force} \\ \\mathrm{N}$ and $\\theta = \\var{theta}^{\\circ}$.
\nGive your answers to the following questions in Newtons to 3 decimal places.
", "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["force", "theta", "angle", "yangle"], "rulesets": {}, "functions": {}, "variables": {"yangle": {"templateType": "anything", "name": "yangle", "description": "", "group": "Ungrouped variables", "definition": "90-theta"}, "angle": {"templateType": "anything", "name": "angle", "description": "", "group": "Ungrouped variables", "definition": "180-theta"}, "theta": {"templateType": "randrange", "name": "theta", "description": "", "group": "Ungrouped variables", "definition": "random(5..85#1)"}, "force": {"templateType": "randrange", "name": "force", "description": "", "group": "Ungrouped variables", "definition": "random(2..15#1)"}}, "preamble": {"js": "", "css": ""}, "tags": [], "variable_groups": [], "type": "question", "advice": "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.
\n\\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}
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}