Assignment:
This question concerns a collision of two identical particles, A and B, each of mass m, which constitute an isolated system that is observed from an inertial frame. Assume that the particles, when sufficiently close, interact only through a potential energy function. At an instant long before the collision (when the distance between A and B is sufficiently large for the potential energy to be neglected) A has position (d, 0, -f) and velocity (0, 0, V) while B has position (-d, 0, f) and velocity (0, 0, -V), where you should assume f and V and d are positive constants.
i)
a) Describe the symmetry of this initial configuration. What happens to the coordinates of a general vector (x1, x2, x3) under this symmetry transformation?
For this inertial frame
b) What is the momentum vector of this system?
c) What is the total energy of the system?
d) What is the angular momentum vector of the system?
ii) Using the principle of relativity and the appropriate conservation laws, find which, if any, of the following are possible configurations of the system long after the collision when A and B are sufficiently far apart for the potential energy to be neglected. Explain you conclusions.
