# A spring with a constant of 4 (kg)/s^2 is lying on the ground with one end attached to a wall. An object with a mass of 6 kg and speed of 3 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

Apr 9, 2018

3.7m

#### Explanation:

Kinetic energy of the object just before hitting the spring:
${E}_{k} = \frac{1}{2} m {v}^{2}$
${E}_{k} = \frac{1}{2} \cdot 6 k g \cdot {\left(3 m \cdot {s}^{-} 1\right)}^{2}$
${E}_{k} = 27 J$

Spring potential energy:
${E}_{e} = \frac{1}{2} k {x}^{2}$
Where k is the spring constant and x is the spring change in length.

$27 J = \frac{1}{2} \cdot 4 N \cdot {m}^{-} 1 \cdot {x}^{2}$
$\frac{27}{2} {m}^{2} = {x}^{2}$
$\sqrt{\frac{27}{2}} m = x$
$3.67 \ldots = x$

So the spring will move 3.7m.