Question

Consider a system consisting of two masses in which the mass1 moving towards right with a velocity U1 collides with another mass2 moving towards left with a velocity U2 and they stick together after the collision. Then the combined mass comes to rest. How do you express their total initial momentum? And total final momentum?

Answer 1

Explanation:

Loss in K.E during inelastic collision

If a body of mass $m_{1}$ moving with velocity $u_{1}$ collides in elastically with a stationary mass $m_{2} \text{ then the loss in kinetic energy is given by } K E=\frac{1}{2} \frac{m_{1} m_{2}}{m_{1}+m_{2}}\left(u_{1}-u_{2}\right)^{2}\left(1-e^{2}\right)$In case of perfectly inelastic collision $e=0$

then $K E=\frac{1}{2} \frac{m_{1} m_{2}}{m_{1}+m_{2}}\left(u_{1}-u_{2}\right)^{2}$

For same mass replace $m_{1}$ and $m_{2}[tex] with [tex]m$ that gives us loss of energy $=\frac{1}{4} m\left(u_{1}-u_{2}\right)^{2}$