Question

A block of mass m moving at a speed $v$ compresses a spring through a distance $x$ before its speed becomes one fourth. Find the spring constant of the spring.

Answer 1

Given:

The speed of the block is halved after coving distance $x$.

The Initial Kinetic Energy of the block is = $\frac{1}{2}m{v}^2$

The Final Kinetic Energy of the block is= $\frac{1}{2}m(v/2{)}^2$

The Change in Kinetic Energy is given as

$\Delta KE=-\frac{1}{2}m\left(\frac{3v^2}{4}\right)$

So PE + Change in KE = 0

The PE stored in the spring is

$PE=\frac{1}{2}k{x}^2=\frac{3m{v}^2}{8}$

$k=\frac{6m{v}^2}{8x^2}=\frac{3m{v}^2}{4x^2}$