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 7  kg and speed of 2 ms^-1 collides with and compresses the spring until it stops moving. How much will the spring compress?

Apr 28, 2016

When the initial kinetic energy, $14$ $J$ is converted to spring potential energy, the spring will be compressed by $2.16$ $m$.

Explanation:

The kinetic energy of the moving mass will be converted to spring potential energy.

Initial kinetic energy:

${E}_{k} = \frac{1}{2} m {v}^{2} = \frac{1}{2} \cdot 7 \cdot {2}^{2} = 14$ $J$.

Final spring potential energy:

${E}_{p} = \frac{1}{2} k {x}^{2}$.

Rearranging: $x = \sqrt{\frac{2 {E}_{p}}{k}} = \sqrt{\frac{2 \cdot 14}{6}} \approx 2.16$ $m$