Question

A horizontal spring is lying on a frictionless surface. Oneend

Answer 1

Answer:

$v_{f}=1.0644 m/s$

Explanation:

According to law of conservation of energy:

Total initial Energy= Total Final Energy

$E_{0} = E_{f}$

$\frac{1}{2}*mv_{0} ^{2}+\frac{1}{2}*kx_{0} ^{2}=\frac{1}{2}*mv_{f} ^{2}+\frac{1}{2}*kx_{f} ^{2}$

In above expression  

$v_{0}=0$ (System is initially at rest)

So above expression will become:

$\frac{1}{2}*kx_{0} ^{2}=\frac{1}{2}*mv_{f} ^{2}+\frac{1}{2}*kx_{f} ^{2}$

BY rearranging the above expression we will get final velocity/Speed:

$v_{f}=\sqrt{\frac{k}{m}}*\sqrt{x_{0} ^{2}-x_{f} ^{2}}$

$v_{f}=w*\sqrt{x_{0} ^{2}-x_{f} ^{2}}$

$v_{f}=15.3*\sqrt{(-0.077)^{2}-(0.033)^{2}}$

$v_{f}=1.0644 m/s$