# A spring with a constant of 8 (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 6 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

##### 1 Answer
Oct 21, 2017

$6 m$

#### Explanation:

Kinetic energy of object $= \frac{m {v}^{2}}{2}$
= (8 kg × (6 ms^-1)^2) / 2 = 144 J

Potential energy stored in spring $= \frac{k {x}^{2}}{2}$
= (8 kgs^-2 × x^2) / (2) = 4x^2kg.s^-2

According to law of Conservation of Energy
Total energy of object = Total energy absorbed by spring

$144 J = 4 {x}^{2} k g . {s}^{-} 2$

$x = \sqrt{\frac{144}{4}} m = \sqrt{36} m = 6 m$