# A spring with a constant of 7 (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 4 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

Jun 13, 2017

I got $214 c m$

#### Explanation:

During this process the initial kinetic energy $K$ of the object will be converted into elastic potential energy ${U}_{e l}$; so we have:

$K = {U}_{e l}$

Or:

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

Where $x$ represents the compression of the spring. Rearranging:

$x = v \sqrt{\frac{m}{k}} = 4 \sqrt{\frac{2}{7}} = 2.14 m = 214 c m$