Two particles move perpendicular to each other unM they collide Particle 1 has m

Question

Two particles move perpendicular to each other unM they collide Particle 1 has mass m and momentum of magnitude 2p, and particle 2 has mass 2m and momentum of magnitude p Suppose that after the collision, the particles trade' thee momenta, as shown in the figure That is. partido 1 now has magnitude of momentum p. and particle 2 has magnitude of momontum 2p. furthermore, each particle is now moving m the direction m which the other had been moving How much kinetic energy. hM. is lost in the collision? Express your answer In terms of m and p. Consider an alternative situation: This time the particles collide completely inelastically. How much kinetic energy K_lost is lost in this case? Express your answer in terms of m and p.

Explanation / Answer

Energy of particle:
E = (1/2)mv2  = 1/2 p²/m

E1 = 1/2 [(2p)²/m + p²/(2m)] = 1/2 x 9/2 x p²/m
E2 = 1/2 [p²/m + (2p)²/(2m)] = 1/2 x 3 x p²/m

Answer(a)
Energy loss E1 - E2 = 3/4 p²/m


B)

Net momentum (Pithagorean):
Po² = (2p)² + (p)² = 5p²
Net mass
M = m + 2m = 3m
Energy of the center of mass:
Ecm = 1/2 Po²/M = 1/2 x 5/3 x p²/m

Answer(b)
Maximum energy loss possible is
E1 - Ecm = 1/2 [9/2 - 5/3] p²/m = 17/12 p²/m

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