# 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 8 kg and speed of 4 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

Mar 26, 2017

The spring will compress by $= 5.66 m$

#### Explanation:

Mass of the object is $m = 8 k g$

Speed of the object is $v = 4 m {s}^{-} 1$

The kinetic energy of the object is

$K E = \frac{1}{2} m {v}^{2} = \frac{1}{2} \cdot 8 \cdot {4}^{2} = 64 J$

This energy will be stored in the spring

$E = \frac{1}{2} k {x}^{2}$

Thre spring constant is $k = 4 k g {s}^{-} 2$

Therefore,

$64 = \frac{1}{2} \cdot 4 \cdot {x}^{2}$

${x}^{2} = \frac{64}{2} = 32 {m}^{2}$

$x = \sqrt{32} = 5.66 m$