A 5.5 kg object moving in the +x direction at 5.5 m/s collides head-on with a 3.

Question

A 5.5 kg object moving in the +x direction at 5.5 m/s collides head-on with a 3.4 kg object moving in the -x direction at 4.0 m/s. Find the final velocity of each mass for each of the following situations. (Take the positive direction to be +x.) (a) The bodies stick together. m/s (5.5 kg mass) m/s (3.4 kg mass) (b) The collision is elastic. m/s (5.5 kg mass) m/s (3.4 kg mass) (c) The 5.5 kg body is at rest after the collision. m/s (5.5 kg mass) m/s (3.4 kg mass) (d) The 3.4 kg body is at rest after the collision. m/s (5.5 kg mass) m/s (3.4 kg mass) (e) The 5.5 kg body has a velocity of 4.0 m/s in the -x direction after the collision. m/s (5.5 kg mass) m/s(3.4 kg mass) Are the results in (c), (d), and (e) "reasonable"? Explain.

Explanation / Answer

Use conservation of momentum. Let the masses be m1, m2, their initial velocities be u1, u2, and their final velocities be v1, v2. Then in all cases: m1 u1 + m2 u2 = m1 v1 + m2 v2. m1 = 5.5 kg. m2 = 3.4 kg. u1 = 5.5 m/s. u2 = - 4.0 m/s (a) Put v2 = v1, and solve for v1. (b) Use also u1 + v1 = u2 + v2 derived from the momentum equation and the conservation of energy. Find u2, v2. (c) Put u1 = 0, and solve for u2. (d) Put u2 = 0, and solve for u1. (e) Put u1 = - 4.0 m/s and solve for u2.

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