HSC Physics Two Dimensional Collisions

A tutorial sheet of two dimensional collision problems is given below.

1. A particle A of mass m is at rest on a smooth horizontal surface. It is struck off centre by a moving particle B of mass M. The magnitude of the change in momentum of B due to the collision is ∆p. What is the magnitude of the change in momentum of A?
2. A particle of mass m has a momentum vector p to the north. An identical particle has a momentum vector of 2p to the east. (a) What is the magnitude of the total momentum of this system? (b) The particles collide and join together. What is the kinetic energy of the combined mass after collision?
3. A ball of mass m moving at a velocity u to the east strikes an identical ball that is at rest. After collision one ball moves to the north-east at a speed u/2. What is the speed of the second ball after collision? [0.737u]
4. Two objects of the same mass having the same initial speed collide and join together. If the comined mass moves away at one-half their initial speed, what is the angle between the initial velocity vectors of each object? [120°]
5. Two particles of equal mass undergo a glancing perfectly elastic collision. If one of the particles was initially at rest, determine the angle between the velocity vectors after collision. [90°]
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