Question

A force of 4 lb is required to hold a spring stretched 1 ft. beyond its natural length. How much work is done in stretching the spring from 1 ft. beyond its natural length to 4 ft. beyond its natural length?

Answer 1

Answer:

Explanation:

Given

Force $F=4\ lb$

extension $x=1\ ft$

And Force $F=kx$

where k=spring constant

$k=\frac{F}{x}=\frac{4}{1}=4\ lb/ft$

Work done require to stretch the spring to 4 ft beyond its natural length

$W=\int_{0}^{4}Fdx$

$W=\int_{0}^{4}4xdx$

$W=\left [ 2x^2\right ]^{4}_{0}$

$W=2\times 6^2=32\ lb-ft$