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 3 kg and speed of 12 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

Jun 21, 2017

The compression is $= 9.3 m$

Explanation:

The spring constant is $k = 5 k g {s}^{-} 2$

The kinetic energy of the object is

$K E = \frac{1}{2} m {u}^{2}$

The mass is $m = 3 k g$

The speed is $u = 12 m {s}^{-} 1$

$K E = \frac{1}{2} \cdot 3 \cdot {\left(12\right)}^{2} = 216 J$

This kinetic energy will be stored in the spring as potential energy.

$P E = 216 J$

So,

$\frac{1}{2} k {x}^{2} = 216$

${x}^{2} = \frac{2 \cdot 216}{5} = 86.4 {m}^{2}$

$x = \sqrt{86.4} = 9.3 m$