# A spring with a constant of 12 (kg)/s^2 is lying on the ground with one end attached to a wall. An object with a mass of 8 kg and speed of 9 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

Dec 26, 2017

8 m

#### Explanation:

KE: Kinetic Energy = $\frac{1}{2} m {v}^{2}$

PE: Potential Energy = $\frac{1}{2} k {x}^{2}$

Energy Transformation:

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

$\frac{1}{2} \left(8 k g\right) {\left(9.81 \frac{m}{s} ^ 2\right)}^{2}$ = $\frac{1}{2} \left(12 \frac{k g}{s} ^ 2\right) {x}^{2}$

Solving for x: compression,

x = 8 m

Note: in absence of gravitational force.