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Forces => Vectors => 2D and 3D

y. x. z. Forces => Vectors => 2D and 3D Force System = 2 or more forces acting on a body (particle or mass) Resultant =  forces in the system R =  F = F 1 + F 2 + F 3 where R = R x î + R y ĵ + R z k

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Forces => Vectors => 2D and 3D

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  1. y x z Forces => Vectors => 2D and 3D Force System = 2 or more forces acting on a body (particle or mass) Resultant =  forces in the system R = F = F1 + F2 + F3 where R = Rxî + Ryĵ + Rzk Let’s look at three random forces and find the resultant analytically and graphically.

  2. F1 = 2N 30 1st quadrant F2 = 4N 150 2nd quadrant F3 = 6N -45 = 6N 315 4th quadrant F1 = 2N 30 = 2 cos 30î + 2 sin 30ĵ = 1.732 î + 1ĵ F2 = 4N 150 = 4 cos 150î + 4 sin 150ĵ = (-)3.464 î + 2 ĵ F3 = 6N 315 = 6 cos 315î + 6 sin 315ĵ = 4.243 î + (-)4.243 ĵ

  3. Add like terms of these forces to get the resultant, R = F = F1 + F2 + F3 F1 = 1.732 î + 1 ĵ + F2 = (-)3.464 î + 2 ĵ + F3= 4.243 î + (-)4.243 ĵ R = 2.511 î + (-)1.243 ĵ R = Rxî + Ry ĵ Convert resultant to polar coordinates. magnitude =  (2.511)² + (-1.243)² = 2.802  2.8 N orientation = tan-1 (rise / run) = tan-1 (-1.243/2.511) = -26.3  R = 2.8 N -26.3 2.8 N 334

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