Problem with kinetic energy and momentum

[stevetomgeorg]

Homework Statement

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.

Homework Equations

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?

 

[Dadface]

Homework Statement

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.

Homework Equations

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?

If the two have the same momentum then the person with the smaller mass will get a greater velocity and greater kinetic energy.
I'm guessing that you assumed both people traveled the same distance whist they were in contact this being equal to the distance they separated by.If so this assumption is wrong the separation distance being equal to the sum of the distances traveled by both persons.During the contact time the smaller mass person will accelerate more and travel a greater distance.

 

[kuruman]

You have already argued that the momenta of the two persons are equal in magnitude and I agree with that. Now answer this question: Can two different masses have the same momentum and the same kinetic energy at the same time?