Question

http://papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Physics%20(9702)/9702_s11_qp_11.pdf Question 9 - Momentum

Answer 1

A body of mass m, moving at velocity v, collides with a stationary body of the same mass and sticks to it.
There will be a final common velocity. The conservation of momentum principle applies:
\[m _{1}u _{1}+m _{2}u _{2}=(m _{1}+m _{2})v\]
\[If\ m _{1}=m _{2},\ also\ u _{2}=0\]
\[\mu _{1}=2mv\]
\[v=\frac{u _{1}}{2}\]
Therefore the final velocity will be half the initial velocity and the mass will be doubled.
The final momentum is
\[2m \times \frac{v}{2}=mv\]
The final kinetic energy is found by doubling the mass and halving the velocity:
\[Final\ kinetic\ energy=\frac{2m}{2}\times (\frac{v}{2})^{2}=\frac{1}{4}mv ^{2}\]