Discuss the below:
Kinetic energy, rest energy and inelastic collisions
Q1: Can you show that the momentum P and the kinetic energy T of a particle of rest mass M can be related by: P^2=2TM+T^2.
Q2: A particle of rest mass M moving with speed 'Beta-not' collides inelastically with (i.e. 'sticks to') a stationary particle of rest mass m. Find the speed of the composite particle. (Answer will contain Beta-not, gamma-not, M and m).
Q3: Find the rest energy of the composite particle of the previous particle in terms of the kinetic energy T of the initial particle and the masses M and m.