# A spring with a constant of 1 kgs^-2 is lying on the ground with one end attached to a wall. An object with a mass of 8 kg and speed of 3 ms^-1 collides with and compresses the spring until it stops moving. How much will the spring compress?

Feb 4, 2016

In this instance kinetic energy is converted into spring potential energy. The spring compresses by $8.5$ $m$.

#### Explanation:

The initial kinetic energy of the moving mass is given by:

${E}_{k} = \frac{1}{2} m {v}^{2} = \frac{1}{2} \cdot 8 \cdot {3}^{2} = 36$ $J$

All of this energy (we are assuming no friction) will be converted to spring potential energy in the spring, according to the equation:

${E}_{p} = \frac{1}{2} k {x}^{2}$ where $k$ is the spring constant and $x$ is the distance compressed (or expanded).

We can rearrange this to make $x$ the subject:

$x = \sqrt{\frac{2 {E}_{p}}{k}} = \sqrt{\frac{2 \cdot 36}{1}} = \sqrt{72} = 8.5$ $m$