Question:
A block of mass $m$ sliding on a smooth horizontal surface with a velocity $v$ meets a long horizontal spring fixed at one end and having spring constant $k$ as shown in figure (8-E10). Find the maximum compression of the spring. Will the velocity of the block be the same as when it comes back to the original position shown?
Solution:
(a) By law of conservation of energy:
$\frac{\frac{1}{2}}{2} \mathrm{~m} \mathrm{v}^{2}=\frac{1}{2} \mathrm{kx} \mathrm{x}^{2}$
$\operatorname{Max} x=v \sqrt{m} / \mathrm{k}$
(b) Velocity of the block will not be the same when it comes back to the original position, it will be of smaller magnitude and opposite direction.