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

Feb 14, 2016

The kinetic energy, ${E}_{k} = \frac{1}{2} m {v}^{2}$, of the moving mass will be converted to spring potential energy in the spring, ${E}_{p} = \frac{1}{2} k {x}^{2}$. The compression in the spring will be $1.5$ $m$.

#### Explanation:

The kinetic energy of the moving mass is:

${E}_{k} = \frac{1}{2} m {v}^{2} = \frac{1}{2} \cdot 1 \cdot {3}^{2} = 4.5$ $J$

As it collides with the spring, this kinetic energy will be converted into spring potential energy:

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

Rearranging:

$x = \sqrt{\frac{2 {E}_{p}}{k}} = \sqrt{\frac{2 \cdot 4.5}{4}} = \sqrt{\frac{9}{4}} = \frac{3}{2} = 1.5$ $m$