# A spring with a constant of 2/5 (kg)/s^2 is lying on the ground with one end attached to a wall. An object with a mass of 7/5 kg and speed of 2 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

Mar 31, 2017

I got $3.7 m$

#### Explanation:

At the start there will be the Kinetic Energy $K$ of the object that will be converted into Elastic Potential Energy ${U}_{e l}$ by compressing the spring.
So we have:
$K = {U}_{e l}$
or:
$\cancel{\frac{1}{2}} m {v}^{2} = \cancel{\frac{1}{2}} k {x}^{2}$
the compression $x$ will then be given by:
$x = v \sqrt{\frac{m}{k}} = 2 \sqrt{\frac{\frac{7}{5}}{\frac{2}{5}}} = 2 \sqrt{\frac{7}{2}} = 3.7 m$