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

Mar 12, 2016

color(green)(therefore "the spring is compressed by " 3/2 sqrt 3 " m"

#### Explanation:

This is a routine case for using law of the conservation of energy

$\textcolor{red}{\text{The kinetic energy possessed by the body when it collides transfers to the springs potential energy}}$

$\textcolor{B l u e}{\text{KE of body = PE of spring}}$

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

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

m = 3, v = 3, k = 4 x = ?

$3 \cdot {3}^{2} = 4 {x}^{2}$

${3}^{3} / {2}^{2} = {x}^{2}$

$3 \cdot {3}^{2} / {2}^{2} = {x}^{2}$

$x = \sqrt{3 \cdot {3}^{2} / {2}^{2}} = \frac{3}{2} \sqrt{3}$

color(green)(therefore "the spring is compressed by " 3/2 sqrt 3 " m"