# Conservation of momentum

1. May 26, 2015

### Nelson2436

1. The problem statement, all variables and given/known data
A 2 kg frictionless cart with a velocity of 6 m/s hits a wall and rebounds with a velocity of 4 m/s. What is the impulse on the cart by the wall? Is momentum conserved?

2. Relevant equations
J = Δp

3. The attempt at a solution
J = Δp = pf-pi = mvf-mvi = 2kg (-4m/s -6m/s) = -20 kgm/s

I think I solved the part for the impulse correctly but needed some help with the reasoning for the second part of the question. I think that the momentum would not be conserved in this case because there is an impulse so there's a net force on the system. On the other hand the system is not defined so the momentum can be conserved if the system is considered to be both the cart and the wall, since the wall would experience an impulse from the cart. Which line of reasoning is correct?

2. May 26, 2015

### PeroK

You are correct. The system is not defined so both arguments you make are valid. Who knows what the question setter intended.

3. May 26, 2015

### insightful

Okay, what is the velocity of the wall? What is the momentum of the wall?

4. May 27, 2015

### Nelson2436

The wall has no velocity and no momentum, unless the vibrations caused by the collision are considered. So does that mean that momentum is not conserved because there's an impulse?

5. May 27, 2015

### PeroK

To have conservation of momentum, you must take into acccount not just the wall but what it is attached to - probably the Earth.

These questions that ask whether momentum is conserved make no sense. Momentum is always conserved in a collision, as long as you consider all objects involved. It would be better to ask "discuss conservation of momentum in this case".

6. May 27, 2015

### insightful

I would suggest that one does not tell a teacher or professor that their question makes no sense. Many times it is the solver's job to make sense of the problem. Otherwise agree.

OP, you need to convince yourself that the momentum of the wall and therefore the Earth changes in this problem.