   Chapter 6.3, Problem 6.6QQ

Chapter
Section
Textbook Problem

In a perfectly inelastic one-dimensional collision between two objects, what initial condition alone is necessary so that all of the original kinetic energy of the system is gone after the collision? (a) The objects must have momenta with the same magnitude but opposite directions, (b) The objects must have the same mass, (c) The objects must have the same velocity, (d) The objects must have the same speed, with velocity vectors in opposite directions.

To determine
The condition for the original kinetic energy to be zero.

Explanation

If all of the original kinetic energy is gone after collision, the objects will not be in motion. Therefore, the final momentum is zero.

Conclusion:

From the law of conservation of momentum, the initial momentum is also zero. This is possible only when the objects have equal and opposite momenta. Therefore, option (a) is correct...

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