# A spring with a constant of 12 kgs^-2 is lying on the ground with one end attached to a wall. An object with a mass of 5 kg and speed of 3 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, ${E}_{k} = \frac{1}{2} m {v}^{2} = \frac{1}{2} \cdot 5 \cdot {3}^{2} = 22.5$ $J$, will be converted to spring potential energy, ${E}_{p} = \frac{1}{2} k {x}^{2}$. Rearranging this yields a compression of $x = \sqrt{\frac{2 {E}_{p}}{k}} = 1.94$ $m$.