# 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 2 kg and speed of 5 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

Dec 18, 2016

Use conservation of energy to show that the compression of the spring will be 3.54 m.

#### Explanation:

Initially, the mass has kinetic energy equal to $\frac{1}{2} m {v}^{2}$ = $\frac{1}{2} \left(2\right) {\left(5\right)}^{2}$ = 25 J

During the collision, this kinetic energy is converted completely into potential energy in the compressed spring, given by $\frac{1}{2} k {x}^{2}$

So, Once the mass is stopped, all the initial KE is now PE:

25 J = $\frac{1}{2} k {x}^{2}$

Since k = $4 \frac{k g}{s} ^ 2$ we can solve for $x$

25 = 2 ${x}^{2}$

${x}^{2}$ = 12.5 ${m}^{2}$

$x$ = 3.54 $m$