# A spring with a constant of 3 (kg)/(s^2) is lying on the ground with one end attached to a wall. An object with a mass of 5 kg  and speed of  7 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

Feb 5, 2016

$\Delta x = 7 . \sqrt{\frac{5}{3}} m$

#### Explanation:

$\text{energy on object is :} {E}_{k} = \frac{1}{2.} m . {v}^{2}$
${E}_{k} = \frac{1}{2} . 5 {.7}^{2}$
${E}_{k} = \frac{1}{2} . 5. 49$
$\text{energy on spring :} {E}_{p} = \frac{1}{2} . k . \Delta {x}^{2}$
${E}_{k} = {E}_{P}$
$\cancel{\frac{1}{2}} .5 .49 = \cancel{\frac{1}{2}} .3 . \Delta {x}^{2}$
$\Delta {x}^{2} = \frac{5.49}{3}$
$\Delta x = 7 . \sqrt{\frac{5}{3}} m$