In the system shown in figure below the pulley at F is frict

In the system shown in figure below, the pulley at F is frict ionless and the cylinder weights 120 lb. Determine the tension in the cable and the horizontal and vertical suppor t reactions of the pin A.

Solution

Balancing moment (r x F) about hinge point,

[-10 x 3 ] + [ T x 10 ] + [Tsin@ x ((10 +12) ] - [ mg x (10 +12 +4)] = 0

sin@ = 2 / sqrt(2^2 + 1^2) = 0.894

mg = 120 lb (Given )

-30 + 10T + ( T x 0.894 x 22) - (120 x 26) = 0

29.68T = 3150

T = 106.13 lb ..............Ans

Balancing force in vertical direction,

Ax - 10 + 106.13 + 106.13sin@ - mg =0

Ax + 96.13 + 106.13x0.894 - 120 = 0

Ax + 71.01 = 0

Ax = - 71.01 lb

vertical support reaction is 71.01 lb in downwards direction.