# A spring with a constant of 9 (kg)/s^2 is lying on the ground with one end attached to a wall. An object with a mass of 2 kg and speed of 3 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

May 20, 2016

It compresses by $\sqrt{2}$ $m$

#### Explanation:

$\frac{1}{2} k {x}^{2} = \frac{1}{2} m {v}^{2}$

$k {x}^{2} = m {v}^{2}$

$9 \cdot {x}^{2} = 2 \cdot {3}^{2}$

${x}^{2} = 2 \implies x = \sqrt{2} m$