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From an AP physics exam.

Two people of different mass are standing still wearing roller skates on a waxed, level surface made of wood. They then simultaneously push each other horizontally. Which of the following would be true after the push?

a. The person with less mass has a smaller initial acceleration than the person with more mass.

b. The center of mass between the two people moves in the direction with the less massive person.

c. The momenta magnitudes of the two people are equal.

d. The speeds of the two people are equal.

e. The kinetic energies of the two people are equal.

2. Relevant equations

3. The attempt at a solution

a, b, and d are obviously wrong. The answer is c since momentum is conserved.

The problem is that I don't understand why e is wrong. The same amount of work was done to each person and their potential energies do not change so by the conservation of mechanical energy, their kinetic energies should increase by the same amount. Since both intital kinetic energies were zero, shouldn't they be equal after they push each other?

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# Homework Help: Problem with kinetic energy and momentum

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