Question

The potential energy of a spring when stretched through a distance $x$ is $10J$. What is the amount of work done on the same spring to stretch it through an additional distance $x$?

• A. $10J$
• B. $20J$
• C. $30J$
• D. $40J$

Answer 1

Answer: (C)

$30J$

$F=\frac{1}{2}k{x}^2$

In the first case, $F=10J$ is required to stretch the spring by length x

$10=\frac{1}{2}k{x}^2$

$F$ is the force required to stretch the spring by an additional length x

$F=\frac{1}{2}k(2x{)}^2=4\times 10=40J$

Therefore additional force required is $40-10=30J$