# A spring with a constant of 1 (kg)/s^2 is lying on the ground with one end attached to a wall. An object with a mass of 2 kg and speed of 4 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

Feb 28, 2016

Here mass$, m = 2$ $k g$
Velocity , $v = 4$ $m {s}^{-} 1$
spring constant, $k = 1$ $k g {s}^{-} 2$

By conservation of mechanical energy

PE of compressed spring= Initial kinetic energy of the moving object

$\therefore \frac{1}{2} \cdot k \cdot {x}^{2} = \frac{1}{2} \cdot m {v}^{2}$, where x = compression of spring
$\implies x = \sqrt{\frac{m {v}^{2}}{k}} = \sqrt{2 \cdot {4}^{2} / 1} = 4 \sqrt{2} m$