Question

A spring has a natural length of 8 in. If it takes a force of 10 lb to compress the spring to a length of 6 in., how much work is required to compress the spring from its natural length to 7 in.

Answer 1

Answer: Required workdone is 5 lb.in

Explanation: Force acting on a spring is given by the relation,

F = -Kx

Here, K is the spring constant

x is the compression or expansion in spring

- Ve sign shows the direction of spring force is opposite to the externally applied force.

Natural length of spring = 8 inches

For final position of spring after compression = 6 inches

Force required to compress the spring by 2 inches (8 - 6 inches) is 10 lb

F = -Kx

10 = -K $\times$ 2

K = 5 lb/in  

If the final position is 7 in i.e. compression by 1 in (8 - 7 in)

F = -Kx = - 5 $\times$ 1 = - 5 lb  (-Ve sign shows the direction of spring force is outward)

Work done = Force $\times$ Displacement

WD = 5 $\times$ 1 = 5 lb.in