91Ó°ÊÓ

Kinetic Energy

$\mathit{K}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathit{m}{\mathit{v}}^{\mathbf{2}}$

Momentum

$\stackrel{\mathbf{→}}{\mathbf{P}}\mathbf{=}\mathit{m}\stackrel{\mathbf{→}}{\mathbf{v}}$

The moment is a vector quantity,Supposethe magnitude of the momentum of two objects is the same, but the direction is different then their moment can be given as p and -p and the total moment is zero or constant.

But kinetic energy is a scalar quantity and$K=p^2/2m$ is always positive. Therefore, it is positive for both the momentums p and -p. So kinetic energy is not zero in this event it is changing.

Hence, we can conclude that since kinetic energy is a scalar quantity and momentum is a vector quantity therefore it is possible to have an event during which the total momentum of the system is constant but the total kinetic energy changes.