Compute the magnitude and direction of the force, Mechanical Engineering

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Compute the magnitude and direction of the force:

Problem:

Compute the magnitude and direction of the force

F¯ = (320 N) i¯ + (450 N) j¯ - (600 N) k¯

Solution

The magnitude of the force F is specified by

216_Compute the magnitude and direction of the force.png

          = 815.41N

cos θx = Fx / F =            320 /815.41 = 0.3924

∴ θ x = 66o  53′ 36′

cos θ y = Fy/  F

 = 450 / 815.41

 = 0.5519

∴ θ y = 56o  30′ 16′

cos θz = Fz /F =  - 600 / 815.41 = - 0.7358

∴ θz = 137o  22′ 29′′

Therefore, the force of 815.41 N is making an angle of 66o 53′ 36′′ along with x axis, 56o 30′ 16′′ along y axis and 137o 22′ with z axis.


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