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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": "(a) Build a table with the force components, for example $P_{2x}=P_2 \\cos 20^\\circ$, $P_{2y}=P_2 \\sin 20^\\circ$, paying attention to the direction of a component:
\n\n\n\n\nForce | \nx-component, kN | \ny-component, kN | \n
\n\n$P_1=\\var{P1}\\text{kN}$ | \n{comp[0][0]} | \n{comp[0][1]} | \n
\n\n$P_2=\\var{P2}\\text{kN}$ | \n{comp[1][0]} | \n{comp[1][1]} | \n
\n\n$P_3=\\var{P3}\\text{kN}$ | \n{comp[2][0]} | \n{comp[2][1]} | \n
\n\n
\n\n(b) Sum up the $x$-components $R_x=\\sum P_x$ and $y$-components $R_y=\\sum P_y$
\n$R_x=\\var{comp[0][0]}+\\var{comp[1][0]}+\\var{comp[2][0]}=\\var{rx}\\text{kN}$
\n$R_y=\\var{comp[0][1]}+\\var{comp[1][1]}\\simplify{+{comp[2][1]}}=\\var{ry}\\text{kN}$
\n\n\n(c) The resultant is $R=\\sqrt{R_x^2+R_y^2}=\\sqrt{(\\var{rx})^2+(\\var{ry})^2}=\\var{r}\\text{kN}$
\n\n(d) The angle with the horizontal is $\\alpha=\\arctan \\dfrac{R_y}{R_x}=\\arctan \\dfrac{\\var{ry}}{\\var{rx}}=\\var{a}^\\circ$
\n$\\alpha=\\var{a}^\\circ$ $\\quad \\blacktriangleleft$
", "rulesets": {}, "extensions": [], "variables": {"r": {"name": "r", "group": "Ungrouped variables", "definition": "precround(sqrt(rx^2+ry^2),2)", "description": "", "templateType": "anything"}, "P2": {"name": "P2", "group": "Ungrouped variables", "definition": "random(1 .. 10#0.5)", "description": "", "templateType": "randrange"}, "P1": {"name": "P1", "group": "Ungrouped variables", "definition": "random(1 .. 10#0.5)", "description": "", "templateType": "randrange"}, "ry": {"name": "ry", "group": "Ungrouped variables", "definition": "comp[0][1]+comp[1][1]+comp[2][1]", "description": "", "templateType": "anything"}, "P3": {"name": "P3", "group": "Ungrouped variables", "definition": "random(5 .. 20#0.5)", "description": "", "templateType": "randrange"}, "comp": {"name": "comp", "group": "Ungrouped variables", "definition": "precround(\n matrix([\n [{P1}*cos(radians(50)), {P1}*sin(radians(50))],\n [{P2}*cos(radians(20)), {P2}*sin(radians(20))],\n [{P3}*cos(radians(35)), -{P3}*sin(radians(35))]\n ]),2)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "precround(degrees(arctan(ry/rx)),2)", "description": "", "templateType": "anything"}, "rx": {"name": "rx", "group": "Ungrouped variables", "definition": "comp[0][0]+comp[1][0]+comp[2][0]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["comp", "rx", "ry", "r", "a", "P1", "P2", "P3"], "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\n\n\nForce | \n x-component, kN | \n y-Component, kN | \n
\n\n{P1} kN | \n[[0]] | \n[[1]] | \n
\n\n{P2} kN | \n[[2]] | \n[[3]] | \n
\n\n{P3} kN | \n[[4]] | \n[[5]] | \n
\n\n
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\n\n\n\nx-Component, kN | \ny-Component, kN | \n
\n\n[[0]] | \n[[1]] | \n
\n\n
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