Suppose that a particle of mass m1 approaches a stationary mass m2 and that m2 >

Question

Suppose that a particle of mass m1 approaches a stationary mass m2 and that m2 >> m1.
(1) Describe the velocity of m2 after an elastic collision - that is, one in which both momentum and kinetic energe are conserved, Justify your answer mathematically.

(2) What is the approximate momentum of m1 after collision?

Explanation / Answer

1) before the collision P1 = m1v1 + m2(0) = m1v1 after the collision P2 = m1v1f + m2v2f and P1 = P2 m1v1 = m1v1f + m2v2f KE before KEa = (1/2) m1v1^2 KE after KE2 = (1/2) m1v1f^2 + (1/2) m2v2f^2 and KE1 = KE2 (1/2) m1v1^2 = (1/2) m1v1f^2 + (1/2) m2v2f^2 m1v1^2 = m1v1f^2 + m2v2f^2 m1(v1^2 - v1f^2) = m2v2f^2 the velocity of m1 after the collision is most likely in the negative direction,ie back where it came from since m2 >>> m1 m2 may gain some velocity in the direction m1 was going in before the collision 2) after the collision m1 has a momentum that is a little less than its beginning momentum but in the opposite direction that is m1 bounces off m2 and returns to where it came from if m2 doesn't move then m1v1f = - m1v1

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