All Problems Laws of Conservation
Problem 1.174
A closed system consists of two particles of masses \(m_{1}\) and \(m_{2}\) which move at right angles to each other with velocities \(v_{1}\) and \(v_{2}\). Find: (a) the momentum of each particle and (b) the total kinetic energy of the two particles in the reference frame fixed to their centre of inertia.
1.174. (a) \(p=\mu \sqrt{v_{1}^{2}+v_{2}^{2}}\) (b) \(T=1 / 2 \mu\left(v_{1}^{2}+v_{2}^{2}\right)\). Here \(\mu=\) \(=m_{1} m_{2} /\left(m_{1}+m_{2}\right)\)