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 FAB and FBC
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