# A spring with a constant of 6 kgs^-2 is lying on the ground with one end attached to a wall. An object with a mass of 3 kg and speed of 4 ms^-1 collides with and compresses the spring until it stops moving. How much will the spring compress?

The kinetic energy of the moving object, ${E}_{k} = \frac{1}{2} m {v}^{2} = \frac{1}{2} \cdot 3 \cdot {4}^{2} = 24$ $J$, will be converted into spring potential energy, ${E}_{p} = \frac{1}{2} k {x}^{2}$. Rearranging, $x = \sqrt{\frac{2 {E}_{p}}{k}} = \frac{\sqrt{2 \cdot 24}}{6} = \sqrt{8}$ $m$.