A force of 6 lb is required to hold a spring stretched 4 in. beyond its natural length. How much work W is done in stretching it from its natural length to 8 in. beyond its natural length?

Explanation and answer:

Given:

6 lb is needed to stretch 4 inches beyond natural length.

Need work done to stretch same string from natural length to 8 inches.

Solution:

string stiffness, K

= Force / stretched distance

= 6 lb / 4 inches

= 1.5 lb/inch

Work done on a string of stiffness K

= (Kx^2) / 2 lb-in

= 1.5 lb/in * (8 in) ^2) / 2

= 48 lb-in.