The rod OA is anchored at O and attached to the cable AB The

The rod OA is anchored at O and attached to the cable AB. The rod length is 2m The rod orientation is prescribed by two spherical angles: the rod forms a 60 degree angle with the z axis and the projection of the rod on the xy plane forms a 30 degree angle with the x-axis. The point B is prescribed by its coordinates (1, 2, 0) The magnitude of the tensile force in the cable is F = 1kN. Identify the force vector F. The projection of F along OA. The moment of F about O. The moment of F about the z axis.

Solution

coordinates of A:-

Z = 2*Cos(60)

= 1

x= 2*Sin(60)*Cos(30)

= 1.5

y = 2*Sin(60)*cos(60)

= 0.866

A= (1.5,0.866,1)

force vector is B-A = (1,2,0) - (1.5,0.866,1) = (-0.5,1.13,-1)KN

F.OA = (-0.5,1.13,-1)KN dot product(1.5,0.866,1)

= (-0.5*1.5 +1.13*0.866,+-1*1) KN

= -0.6KN in OA direction

Moment about 0 is cross product of (OA,F)

Moment about Z is the cross product of (F,OA)