# Frictionless shove - kinetic energy and momentum

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1. Nov 8, 2014

### PacFan01

1. The problem statement, all variables and given/known data
Edward and Jacob, standing face-to-face on a horizontal sheet of frictionless ice, push off each other, causing each to slide backward. Jacob is more massive than Edward. After the push, which of the two is moving faster?

2. Relevant equations
Conservation of momentum: Pi = Pf
Kinetic energy: K = 1/2mv2

3. The attempt at a solution
Intuitively, the answer to this problem is obvious (Edward is moving faster after the push). I also know that Edward's smaller mass means his acceleration must be greater so that F12 = -F21. However, this problem was assigned before our Force unit, so I would like an explanation of this phenomena in terms of momentum.

I don't know if this can be explained with conservation of momentum, because Vi = 0, so it is difficult compare their velocities in terms of momentum in a meaningful way. Also, we know that the momentum of the system is conserved, but that does not show, algebraically, that Edward is moving faster than Jacob after the push.

I am wondering if this problem can be solved using a kinetic energy equation, K = 1/2mv2. This expression can show that, if the kinetic energies are equal, SpeedEf > SpeedJi. However, I do not know how to show that KE = KJ.

Any help with an algebraic proof that Edward will be moving faster than Jacob after the push would be much appreciated.

2. Nov 8, 2014

### Simon Bridge

You are over-thinking things. This is a conservation of momentum problem.