**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