Question

1) Determine the magnitude and coordinate direction angles of the force Frequired to keep the concurrent force system in equilibrium (25 pts) Box your answers F F = 450 N -0.40 m 303 0.75 m 2.5 m F = 450 N X Show all work below including EBD Cinsetet sheets paper i merespace de

Answer 1

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Solin:- > F WHO a F, = 450N 30° 0-75m - y 2.5m F = 450N x-component of force F = F cos 25° Cos 30° 450x COS 25°C05300 353.1985 N Y- component of force fi = -Fi Cos 25° sin 30° 450 COS 25° sin 300 203.92 N

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Z-component of force F Fi sin25° 450 x sin 250 190.1782 N u Now, co-ordinates of point a shown in the figure is, A(x,y,z) (2.5, 0.4, -0-75) Therefore, vector on is, 2.51 + 0.4j+ - 0.75 1 ОА Unit vector in the direction of ok is, n r = OA 2.5i +0.4j-0.75 K lo 2.52 + 0.4+ +0.75)2 A 2.51+0.4 ì -0.75 2.64055 0.946772ê + 0.151484 9 + - 0.284032 Â Therefore, force Fa in vector form is given by, F = Fat 450 (0.946772 î + 0.151 484 À -0-284032K) 426.0476 î + 68.16762 ſ 1 127.8143

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Therefore, 4260476 x-component of force F2 68. 16762 9- component of force F2 zo component of force F2 = -127.8143 Let Ex, Fy and fz be the x,y and z-components of force f respectively. Applying conditions of equilibrium , EFq =0 =) 353.1985 + 426.0476 + Fz = Fx = - 779.2461 N М. اع =O => 203.92 + 68.16 762 + Fy =) 135. 75238 N F2 = 0 190,1782 + -127.8143 + F2 = 0 => - 62:364N Therefore, resultant of force F is given by, F = √ Fx ²7 Fy't F 2 2 2 (-779.2461) + (135. 75238 +662-364)

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793.43712N ie, 793• 43712 N het d = Angle made by force F with ay plane. ß Angle made by the projection of F on xy plane with 3-axis : Then, 15) = F cosa cosB : 779.2461 = 793. 43712 cosa cos B =) Cosa cosa 0.9821145 (1) IFy F cosa sing 135. 75238 793.43712 cosa sing cosa sing 0.1711 - (2) (2) ; (1) =) 0:171) tans = 0.17.4 21 0.98 21145 tan' (0.17421) B = = > 9.88265 °

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substitute ß in (1), 0.98 21145 0.98 211 45 0.996907 cosa cosp cos(9.88265°) 4.50754° a = cos' Co.996907) =) Therefore, coordinate direction angles of force F is on B 4.50754° ( Angle made by F with X-y plane) 9.88265° C Angle made by the projection of F x-y plane with sc. axis)