Question

A block of mass $m$ sliding on a smooth horizontal surface with a velocity $\overrightarrow{v}$ meets a long horizontal spring fixed at one end and having spring constant $k$ as shown in figure. Find the maximum compression of the spring . Will the velocity of the block be the same as $\overrightarrow{v}$ when it comes back to the original position shown?

Answer 1

The energy stored in the spring exists in the form of the potential energy and it is given as:

$PE=\frac{1}{2}k{x}^2$

When the block is left from maximum compression, the potential energy gets converted into kinetic energy of the block.

$KE=\frac{1}{2}m{v}^2$

At maximum compression
$KE=PE$
$\therefore \frac{1}{2}k{x}^2=\frac{1}{2}m{v}^2$
$\Rightarrow x=\sqrt{\frac{m}{k}}v$
The magnitude of velocity will be the same but the direction will be opposite.