Determine the moment of each of the forcesSolution call the

Determine the moment of each of the forces

Solution

call the forces

F1 = 52 lb

F2 = 70 lb

F3 = 75 lb

F4 = 95 lb

F1 , F2, F3 are in x-y plane and they can rotate the body only about z-axis, hence the moment of all these forces would be along z-axis and the moment about x and y would be zero.

F1 makes 45 deg with x and y axis and cuts at x and y at -12 and +12 in

perpendicular distance = 1/2 ft

Moment of F1= +52/2 k^

F2 is parallel to y-axis and perpendicular distance from z-axis = 12” = 1ft

F2 rotates the body CW and hence the moment is –ve as per convention

Moment of F2 = 70*1 = -70k”

F3 make -30 deg with the x-axis

perpendicular distance from origin(z-axis)

         12*Sin(60) = 63 in = 3/2 ft

it rotates the body CCW about z-axis

Moment of F3 = 753/2 k^

F4 makes 8 deg with the vertical face of the slab.

The slab is raised 5” with the x-y plane and makes

arcSin(5/12) = 26.5 deg with ethe x-y plane

Hence the force makes 8+26.5 = 34.5 deg with the –ve z-axis

component along z-axis = 95cos(34.5) = 77.5 lb

component along x-y plane = 95Sin(34.5) =53.8 lb

The component in x-y plane rotates the body about z-axis CW and is at 12/2 in from z-axis

moment of F4 along z-axis

                 = -53.8/2 k^

component along z-axis rotates the body about y-axis only as it cuts the x-axis at 12 in

Moment of F4 about y-axis = 77.5*1 j^

Total moment of F4

               = 77.5 j^ -53.8/2 k^