Question

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

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

Answer 1

Answer: (C)

$30\, J$

Answer 2

Potential energy of the spring when stretched through a distance $x$, $U = \frac{1}{2}kx^{2} = 10\,J$ When $x$ becomes $2x$, the potential energy will be $U' = \frac{1}{2}k\left(2x\right)^{2}= 4 \times \frac{1}{2}kx^{2}$ $= 4 \times 10 = 40\,J$ $\therefore$ Work done $= U' - U = 4 0 - 10 = 30 \,J$