A point mass A with mass m moves at a constant speed v on a horizontal frictionless plane and collides with another point mass B with mass 2m that is at rest. The collision is elastic.
After the collision, point mass A is moving with a speed vA and point mass B with a speed vB.
What are vA and vB, in terms of v?
A) vA = v/2; vB = v/3
B) vA = v/3; vB = 2v/3
C) vA = 2v/3; vB = v/3
D) vA = v/3; vB = v/2
E) vA = v/2; vB = v/2
IMAT 2023 · Question 56
Q56 - Impulse and momentum
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The correct answer is B) vA = v/3; vB = 2v/3.
For an elastic collision with the second mass at rest:
v₁ = (m₁ − m₂)/(m₁ + m₂) · v
v₂ = 2m₁/(m₁ + m₂) · v
With m and 2m, A ends up at −v/3 (it bounces back) and B at 2v/3. So the speeds are v/3 and 2v/3.
You can check momentum: m(−v/3) + 2m(2v/3) = mv, the same as before.
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