Question

Determine the tension in the cable and the horizontal and vertical components of reaction of the pin

a. the pulley at d is frictionless and the cylinder weighs 80 lb . (

Answer 1

Since the pulley does not have friction, the two segments of the cable are subject to the same tension force T. Based on the free-body diagram shown above, we have


`EM _(A) = 0 {\to T x 5 + (2)/( √(5) ) T x 10 - W x 13 = 0`

Thus, we get


`T = (13W)/((5 + 20/ √(5)) ) = (13 x 80)/((5 + 20/ √(5))) = 74.583 (Ib)`

To find the horizontal support force, we have


`EF_(X) = 0 \to A_(X) - (1)/( √(5) ) T = 0`

Thus,


`A_(X) = (1)/( √(5) ) T = (1)/( √(5) ) x 74.583 = 33.354 (Ib)`