Question

A block of mass $m$ is moving with an initial velocity $v_0$ towards a stationary spring of stiffness $k$ attached to the wall as shown. Find the maximum compression in the spring.

• A. $v_0\sqrt{\frac{m}{k}}$
• B. $v_0\sqrt{\frac{k}{m}}$
• C. $2v_0\sqrt{\frac{m}{k}}$
• D. $2v_0\sqrt{\frac{k}{m}}$

Answer 1

The correct option is A $v_0\sqrt{\frac{m}{k}}$

The force exerted by the spring is opposite to the displacement of block. Therefore, the work done by spring force is negative.
Let $x_0$ be the maximum compression in the spring (Final velocity of block =0).
Work done by spring $=-\frac{1}{2}k{x}_0^2$
Work done $=\Delta KE$
$-\frac{1}{2}k{x}_0^2=0-\frac{1}{2}m{v}_0^2$
$\Rightarrow x_0=v_0\sqrt{\frac{m}{k}}$