General question about conservation of momentum

[vetgirl1990]

Referring to the Law of Conservation of Momentum: How is momentum always conserved? In a non-isolated system, an external force causes a change in momentum, so that initial momentum isn't the same as final momentum. Wouldn't this constitute a situation where momentum is not conserved?

Or, is the Law of Conservation of Momentum specifically talking about how momentum is conserved in all collisions, whether elastic or inelastic?

 

[PeroK]

Referring to the Law of Conservation of Momentum: How is momentum always conserved? In a non-isolated system, an external force causes a change in momentum, so that initial momentum isn't the same as final momentum. Wouldn't this constitute a situation where momentum is not conserved?

Or, is the Law of Conservation of Momentum specifically talking about how momentum is conserved in all collisions, whether elastic or inelastic?

1) Momentum is always conserved in both elastic and inelastic collisions. This is a consequence of Netwon's Third Law.

2) Kinetic Energy is also conserved in an elastic collision (but not in an inelastic collision).

3) Although momentum is always conserved, as you mention in your post, you need to consider all bodies involved. If an apple falls from a tree, then clearly the apple gains momentum. The momentum of the apple alone is not conserved. But, the Earth is subject to an equal an opposite gravitational force and is gaining equal and opposie momentum to the apple. The momentum of the apple-Earth system is, therefore, conserved.

 

[vetgirl1990]

3) Although momentum is always conserved, as you mention in your post, you need to consider all bodies involved. If an apple falls from a tree, then clearly the apple gains momentum. The momentum of the apple alone is not conserved. But, the Earth is subject to an equal an opposite gravitational force and is gaining equal and opposie momentum to the apple. The momentum of the apple-Earth system is, therefore, conserved.

Don't we normally exclude the force (and kinetic energy) of Earth (unless the problem involves say, a collision with Earth and an asteroid) from problems, as the force that the Earth exerts on an object is so much smaller compared to applied forces? While technically you need to consider all bodies involved, for the sake of specific questions,
say one that involves finding the change in momentum of the falling apple, wouldn't we look at this system as isolated and therefore momentum not being conserved?

 

[PeroK]

Don't we normally exclude the force (and kinetic energy) of Earth (unless the problem involves say, a collision with Earth and an asteroid) from problems, as the force that the Earth exerts on an object is so much smaller compared to applied forces? While technically you need to consider all bodies involved, for the sake of specific questions,
say one that involves finding the change in momentum of the falling apple, wouldn't we look at this system as isolated and therefore momentum not being conserved?

Yes. There are lots of problems where you don't make use of conservation of momentum. For example, in projectile motion problems. Often, however, you can solve problems by considering conservation of momentum in the horizontal direction, but not in the vertical direction (because you simply consider gravity as an external force). That's a neat trick that worth remembering.

The same is true for conservation of energy: it's always there. But if energy is dissipated to heat by an inelastic collision or by friction, then you lose Kinetic Energy from the system.

In short, total energy and total momentum are always conserved. But, sometimes they go outside the system you are considering. That's the key point always to consider: is my system losing or gaining energy or momentum to or from the outside world?

 

[CWatters]

In a non-isolated system, an external force causes a change in momentum, so that initial momentum isn't the same as final momentum. Wouldn't this constitute a situation where momentum is not conserved?

Conservation of momentum only apples to closed systems (eg systems with no external forces). See..

https://en.wikipedia.org/wiki/Momentum#Conservation

If you find a situation where conservation of momentum appears to be broken it can be a clue that you may have drawn your system boundary in the wrong place. For example if you draw you system boundary just around the apple (post #2) then CoM appears to be broken. If you draw it around the apple and the Earth CoM holds true.