Is momentum in Y direction conserved in this case ?

bksree

Hi
A person on a cart throws a ball with velocity V at angle θ to the ground. The cart is resting on a frictionless surface and therefore recoils. The velocity of recoil can be calculated using conservation of momentum in X direction.
But is the momentum in Y direction conserved ?

TIA

mikeph

Momentum in both directions is always conserved- whether your story obeys these conservation laws or not is another question. I would say "no" to this question, since the cart should recoil upwards.

szynkasz

Yes, it is. Earth gets some velocity in Y direction but because its huge mass this velocity is very small, practically zero.

ZapperZ

Yes, and no. It depends on what SYSTEM you are looking at.

The momentum of the cart+ball in the y-direction is not conserved. Why? Because there is a net force from the ground that pushes back on it! And when there is a net force acting on a system, the system does not have a conserved momentum, because by definition, the momentum has to change.

However, as has been mentioned, if you look at the cart+ball+earth system, then that system has a conserved momentum.

Zz.

sophiecentaur

In matters of Momentum, you need to follow conservation, even when you can't always spot where 'some of it goes'. Is there ANY situation where, looking deep enough, the rule is violated? It certainly wouldn't be in anything as humdrum as a ball-throwing example.