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Problem 5 - Entrance Test

Two bodies of masses m1 and m2 are moving with velocities v1 and v2 respectively. If they collide and stick together, what is their common velocity after collision according to the Law of Conservation of Momentum?

A. (m1v1 + m2v2) / (m1 + m2)B. (m1v1 - m2v2) / (m1 + m2)C. (m1 + m2) / (m1v1 + m2v2)D. (m1v1 + m2v2)

Correct: A

The Law of Conservation of Momentum states that for a closed system, the total momentum before collision is equal to the total momentum after collision. Before collision, total momentum = m1v1 + m2v2. After collision, since they stick together, their combined mass is (m1 + m2) and they move with a common velocity, say V. So, total momentum after collision = (m1 + m2)V. Equating them: m1v1 + m2v2 = (m1 + m2)V. Therefore, V = (m1v1 + m2v2) / (m1 + m2).