Is momentum in Y direction conserved in this case ?

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Discussion Overview

The discussion revolves around the conservation of momentum in the Y direction when a person on a cart throws a ball at an angle while the cart is on a frictionless surface. Participants explore whether momentum is conserved in this scenario, considering different systems and forces involved.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant asserts that momentum in both directions is always conserved, but concludes that it is not conserved in this case because the cart should recoil upwards.
  • Another participant claims that momentum in the Y direction is conserved, noting that the Earth experiences a negligible velocity change due to its large mass.
  • A different perspective emphasizes that the conservation of momentum depends on the system being analyzed, stating that the momentum of the cart and ball is not conserved due to a net force from the ground, but the combined system of cart, ball, and Earth does conserve momentum.
  • One participant raises a broader question about the potential for violations of momentum conservation, suggesting that such violations would not occur in straightforward scenarios like throwing a ball.

Areas of Agreement / Disagreement

Participants express differing views on whether momentum in the Y direction is conserved, with some arguing for conservation under specific conditions and others asserting that it is not conserved due to external forces. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants highlight the importance of defining the system under consideration, as well as the influence of external forces on momentum conservation. There are unresolved assumptions regarding the effects of the Earth’s mass and the nature of the forces acting on the cart.

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

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.
 
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.
 

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