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{"name": "Vectors: Resolving Forces 2", "extensions": [], "custom_part_types": [], "resources": [["question-resources/force_component_image_4.png", "/srv/numbas/media/question-resources/force_component_image_4.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Vectors: Resolving Forces 2", "tags": [], "metadata": {"description": "<p>Find the $x$ and $y$ components of the resultant force on an object, when multiple forces are&nbsp;applied at&nbsp;different angles.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><img width=\"430\" height=\"338\" style=\"display: block; margin-left: auto; margin-right: auto;\" src=\"resources/question-resources/force_component_image_4.png\"/></p>\n<p>$F = \\var{force1} \\, \\mathrm{N}$ at an angle of $\\theta = \\var{theta1}^{\\circ}$ clockwise from the left horizonatal.<br/>$P = \\var{force2} \\, \\mathrm{N}$ vertically upwards.<br/>$Q = \\var{force3} \\, \\mathrm{N}$ at an able of $\\theta^{\\ast} = \\var{theta2}^{\\circ}$ clockwise from the right horizontal.&nbsp;</p>\n<p><em>Give your answers to the following questions in Newtons to 3 decimal places.</em></p>", "advice": "<h4>a) - c)</h4>\n<p>Resolve each force in the&nbsp;HORIZONTAL:</p>\n<p>$P$ doesn't contribute.</p>\n<p>The force $F$ is at $\\var{theta1}^{\\circ}$ to the horizontal,&nbsp;therefore has a contribution of $F \\times \\cos \\var{theta1}^{\\circ} = \\var{force1} \\times \\cos \\var{theta1}^{\\circ} = \\var{precround(force1*cos(radians(theta1)),3)}$. &nbsp;This&nbsp;force is acting to the left.</p>\n<p>The force $Q$ is at $\\var{theta2}^{\\circ}$ to the horizontal,&nbsp;therefore has a contribution of $Q \\times cos&nbsp;\\var{theta2}^{\\circ} = \\var{force3} \\times \\cos\\var{theta2}^{\\circ} = \\var{precround(force3*cos(radians(theta2)),3)}$. This is acting to the right.</p>\n<p>Therefore the sum of components in the $x$-direction is</p>\n<p>forces acting to the right - forces acting to the left</p>\n<p>\\[\\var{precround(force3*cos(radians(theta2)),3)} - \\var{precround(-force1*cos(radians(180-theta1)),3)}\\]<br/>\\[= \\var{precround(force1*cos(radians(180-theta1)) + force3*cos(radians(theta2)),3)}\\]</p>\n<p>(if this value is positive then it is acting to the right, if it is negative it is acting to the left)</p>\n<h4>d) - g)</h4>\n<p>Resolve each force from the VERTICAL:</p>\n<p>For the force $P$ this is acting completely in the positive direction, at no angle. Therefore it's contribution is $\\var{force2}$. </p>\n<p>The force $F$ is at $\\var{theta1}^{\\circ}$ to the horizontal,&nbsp;therefore has a contribution of $F \\times \\sin \\var{theta1}^{\\circ} = \\var{force1} \\times \\sin \\var{theta1}^{\\circ} = \\var{precround(force1*sin(radians(theta1)),3)}$. &nbsp;This&nbsp;force is acting upwards.</p>\n<p>The force $Q$ is at $\\var{theta2}^{\\circ}$ to the horizontal,&nbsp;therefore has a contribution of $Q \\times cos&nbsp;\\var{theta2}^{\\circ} = \\var{force3} \\times \\cos\\var{theta2}^{\\circ} = \\var{precround(force3*cos(radians(theta2)),3)}$. This is acting to the right.</p>\n<p>Therefore the sum of components in the $y$-direction is</p>\n<p>forces acting up - forces acting down</p>\n<p>\\[\\var{precround(force3*sin(radians(theta2)),3)} - \\var{precround(-force1*sin(radians(180-theta1)),3)}\\]<br/>\\[= \\var{precround(force1*sin(radians(180-theta1)) + force3*sin(radians(theta2)),3)}\\]</p>\n<p>(if this value is positive then it is acting to the right, if it is negative it is acting to the left)</p>\n<p></p>\n<p>&nbsp;</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"f1y": {"name": "f1y", "group": "components", "definition": "force1*sin(radians(theta1))", "description": "", "templateType": "anything", "can_override": false}, "f1x": {"name": "f1x", "group": "components", "definition": "-force1*cos(radians(theta1))", "description": "", "templateType": "anything", "can_override": false}, "f3y": {"name": "f3y", "group": "components", 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