# A spring with a constant of 5 (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 12 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

Apr 22, 2016

12m

#### Explanation:

We can use conservation of energy.

Initially;

Kinetic energy of the mass : $\frac{1}{2} m {v}^{2} = \frac{1}{2} \cdot 6 \cdot {12}^{2} J$

Finally:

Kinetic energy of the mass : 0

Potential energy : $\frac{1}{2} k {x}^{2} = \frac{1}{2} \cdot \left(5 \frac{k g}{s} ^ 2\right) {x}^{2}$

equating, we get :

$\frac{1}{2} \cdot 6 \cdot {12}^{2} J = \frac{1}{2} \cdot \left(5 \frac{k g}{s} ^ 2\right) {x}^{2} \implies x \approx 12 m$

*I would be so happy if $k$ and $m$ were the same.