Solve the following :


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?


(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.

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