Question

A spring block system is compressed $x\text{m}$ from the mean position and released. Find out the total work done by the spring force when it reaches the other extreme point (fully stretched). Neglect friction.

• A. $\frac{1}{2}k{x}^2$
• B. $k{x}^2$
• C. $\frac{1}{2}k(2x{)}^2$
• D. $0$

Answer 1

The correct option is D $0$

When the block moves from compressed position to mean position, then spring force and displacement will be in the same direction.


Therefore, work done by spring force $W_1=\frac{1}{2}k{x}^2$
But when the spring moves from mean position to stretched position, then spring force is opposite to displacement.


Therefore work done by spring force $W_2=-\frac{1}{2}k{x}^2$
Hence, total work done $=W_1+W_2$
$=\frac{1}{2}k{x}^2-\frac{1}{2}k{x}^2$
$=0$

Aliter,
$W_{spring}=-\Delta U$
$W_{spring}=-(U_f-U_i)$
$=-\frac{1}{2}k{x}^2+\frac{1}{2}k{x}^2=0$