Example 9: A vertical force of 25 lb is applied to the ends of cable AB and spring BC. For the condition of equilibrium, determine
a. the forces F_AB and F_BC
b. the stretch in spring BC if it has a stiffness of k = 100 lb/ft.

Solution:

The force in cable AB is along its length so is the force in spring BC. The free-body diagram shows a system of three concurrent forces.

Part a:

It is convenient to choose the x in horizontal and y in vertical directions. The force system consists of one known and two unknown forces. We apply the equilibrium equations to solve for the two unknown foces as

Part b:

Knowing the force in the spring and its stiffness, we find the stretch as