Express the force in vector form, Mechanical Engineering

Express the force in vector form:

A force of 400 N forms angles of 45o, 65o and 120o, respectively, along with the x, y and z axes. Express the force in vector form.

Solution

486_Express the force in vector form.gif

Substituting     F = 400 N, θx = 45o, θy = 60o and θz = 120o, we obtain

Fx  = F cos θx = 400 cos 45o  = 282.84 N

Fy  = F cos θ y  = 400 cos 60o  = 200.00 N

Fz  = F cos θz  = 400 cos 120o  = - 200.00 N

F¯ = F¯x i¯ + F¯y  j¯ + F¯z

= (282.84 N) i¯ + (200.00 N) j¯ + (- 200.00 N) k¯

= 282.84i¯ + 200.00 j¯ - 200.00 k¯

where i¯ , j¯ and k¯ are the unit vectors along with x, y and z axes, respectively.

Posted Date: 1/28/2013 4:45:26 AM | Location : United States







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