# A spring with a constant of 8 kgs^-2 is lying on the ground with one end attached to a wall. An object with a mass of 7 kg and speed of 6 ms^-1 collides with and compresses the spring until it stops moving. How much will the spring compress?

The initial kinetic energy is ${E}_{k} = \frac{1}{2} m {v}^{2} = \frac{1}{2} \cdot 7 \cdot {6}^{2} = 126$ $J$.
This will be converted to spring potential energy, which will have the same value, $126$ $J$. The equation is ${E}_{s p} = \frac{1}{2} k {x}^{2}$.
Rearranging to make the compression distance, $x$, the subject: $x = \sqrt{\frac{2 {E}_{s p}}{k}} = \sqrt{\frac{2 \cdot 126}{8}} = 5.6$ $m$.