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resultant force
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "\n\nKnowing that $P_1=\\var{P1}$kN, $P_2=\\var{P2}$kN and $P_3=\\var{P3}$kN,
", "advice": "\n(a) You can define angles $\\alpha_1$, $\\alpha_2$ and $\\alpha_3$, as shown above.
\nThen you can either calculate the angles:
\n$\\alpha_1=\\arctan \\dfrac{900}{500}=58.11^\\circ$
\n$\\alpha_2=\\arctan \\dfrac{900}{480}=62.93^\\circ$
\n$\\alpha_3=\\arctan \\dfrac{600}{800}=36.87^\\circ$
\nor calculate the following cosines and sines using their definitions and Pythagoras' Theorem:
\nFor $\\alpha_1$:
\n$\\cos \\alpha_1=\\dfrac{560}{\\sqrt{560^2+900^2}}=\\dfrac{560}{1060}=0.5283$
\n$\\sin \\alpha_1=\\dfrac{900}{\\sqrt{560^2+900^2}}=\\dfrac{900}{1060}=0.8491$
\nFor $\\alpha_2$:
\n$\\cos \\alpha_2=\\dfrac{480}{\\sqrt{480^2+900^2}}=\\dfrac{480}{1020}=0.4706$
\n$\\sin \\alpha_2=\\dfrac{900}{\\sqrt{560^2+900^2}}=\\dfrac{900}{1060}=0.8824$
\nFor $\\alpha_2$:
\n$\\cos \\alpha_3=\\dfrac{800}{\\sqrt{800^2+600^2}}=\\dfrac{800}{1000}=0.8$
\n$\\sin \\alpha_3=\\dfrac{600}{\\sqrt{800^2+600^2}}=\\dfrac{600}{1000}=0.6$
\nSince you know these parameters, calculate the components, for example
\n$P_{2x}=P_2\\cos \\alpha_2=(\\var{P2}\\;\\text{kN}) 0.4706=\\var{comp[1][0]}\\;\\text{N}$
\n$P_{2y}=- P_2\\sin \\alpha_2=(\\var{P2}\\;\\text{kN})0.8824=\\var{comp[1][1]}\\;\\text{N}$
\nNow proceed the same way as in the previous question.
", "rulesets": {}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "precround(degrees(arctan(ry/rx)),2)", "description": "", "templateType": "anything"}, "L3": {"name": "L3", "group": "Ungrouped variables", "definition": "vector(800,600)/sqrt(800^2+600^2)", "description": "", "templateType": "anything"}, "comp": {"name": "comp", "group": "Ungrouped variables", "definition": "precround(\n matrix([{P1}*{L1},{P2}*{L2},{P3}*{L3}\n ]),2)", "description": "", "templateType": "anything"}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "precround(sqrt(rx^2+ry^2),2)", "description": "", "templateType": "anything"}, "P3": {"name": "P3", "group": "Ungrouped variables", "definition": "random(300 .. 700#25)", "description": "", "templateType": "randrange"}, "rx": {"name": "rx", "group": "Ungrouped variables", "definition": "comp[0][0]+comp[1][0]+comp[2][0]", "description": "", "templateType": "anything"}, "ry": {"name": "ry", "group": "Ungrouped variables", "definition": "comp[0][1]+comp[1][1]+comp[2][1]", "description": "", "templateType": "anything"}, "P1": {"name": "P1", "group": "Ungrouped variables", "definition": "random(300 .. 600#25)", "description": "", "templateType": "randrange"}, "L2": {"name": "L2", "group": "Ungrouped variables", "definition": "vector(480,-900)/sqrt(900^2+480^2)", "description": "", "templateType": "anything"}, "L1": {"name": "L1", "group": "Ungrouped variables", "definition": "vector(-560,-900)/sqrt(900^2+560^2)", "description": "", "templateType": "anything"}, "P2": {"name": "P2", "group": "Ungrouped variables", "definition": "random(300 .. 600#25)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["comp", "rx", "ry", "r", "a", "P1", "P2", "P3", "L1", "L2", "L3"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Determine the $x$ and $y$ components of each of the forces shown.
\n\nForce | \nx-component, kN | \ny-Component, kN | \n
$P_1=${P1} kN | \n[[0]] | \n[[1]] | \n
$P_2=${P2} kN | \n[[2]] | \n[[3]] | \n
$P_3=${P3} kN | \n[[4]] | \n[[5]] | \n
Determine the $x$ and $y$ components of the resultant force.
\n$R_x=$[[0]], kN
\n$R_y=$[[1]], kN
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\n$R=$[[0]]
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\n$\\alpha=$[[0]]
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