# A spring with constant 2 kgs^-2 is lying on the ground with one end attached to a wall. An object with a mass of 1/2 kg and speed of 3/5 ms^-1 collides with and compresses the spring until it stops moving. How much will the spring compress?

The kinetic energy of the moving mass, ${E}_{k} = \frac{1}{2} m {v}^{2} = \frac{1}{2} \times \frac{1}{2} \times {\left(\frac{3}{5}\right)}^{2} = 0.09$ $J$, will be converted into spring potential energy in the spring, ${E}_{p} = \frac{1}{2} k {x}^{2}$. Rearranging, $x = \sqrt{\frac{2 {E}_{p}}{k}} = \sqrt{\frac{2 \times 0.09}{2}} = 0.30$ $m$ = $30$ $c m$.