Momentum Conservation

[ydoaPs]

Is momentum conserved in every interaction, or only in closed systems? If momentum pops into existence at one end of the universe and cancelling momentum pops into existence at the other end, is that conservation or is it breaking conservation twice?

[ajb]

You need a closed system. You would not get momentum conservation if matter was entering or leaving your system or it was being acted on by some external force.

[ydoaPs]

But does it apply to interactions within the system or to the system itself? If momentum pops into existence at one end of the universe and cancelling momentum pops into existence at the other end, is that conservation or is it breaking conservation twice?

[studiot]

 

Is momentum conserved in every interaction, or only in closed systems?

 

Momentum is conserved whether the system is open or closed. Open systems allow a mass flux, which carries additional momentum into or out of the system. This must be accounted for in the balance.

 

Total momentum, with due allowance for these fluxes, is a system property. You don't need to go to the ends of the universe to find momentum popping into or out of existence though, just to your local fire station or car wash.

 

Consider a water jet impinging on the side of a wall or car.

The jet has considerable momentum normal to the wall. All of this disappears in applying a force to the wall, which appears as the stagnation pressure on the wall.

Parallel to the wall momentum suddenly appears and is carried away with the draining fluid.

 

Or consider two identical blocks of identical mass sliding towards each other at identical speeds along a common line on a frictionless surface.

 

What happens when they meet?

 

Well each block had momentum, but the total momentum of the system is zero, although each individual block has momentum before the collision.

 

Remembering that momentum is a vector quantity

 

mv + m(-v) = 0 before collision.

 

At and after collision total system momentum remains at zero so the blocks collide and become still.

[swansont]

Momentum is conserved whether the system is open or closed. Open systems allow a mass flux, which carries additional momentum into or out of the system. This must be accounted for in the balance.

A nit: There's a difference between conservation and a balance. I can apply a force to a system and balance it to account for the momentum change, but momentum is not conserved in that situation.

 

Total momentum, with due allowance for these fluxes, is a system property. You don't need to go to the ends of the universe to find momentum popping into or out of existence though, just to your local fire station or car wash.

 

Consider a water jet impinging on the side of a wall or car.

The jet has considerable momentum normal to the wall. All of this disappears in applying a force to the wall, which appears as the stagnation pressure on the wall.

Parallel to the wall momentum suddenly appears and is carried away with the draining fluid.

In the example here you can do a momentum balance at any arbitrarily small volume along the way. In the example given by ydoaPs that's not the case.

[studiot]

 

A nit: There's a difference between conservation and a balance. I can apply a force to a system and balance it to account for the momentum change, but momentum is not conserved in that situation.

 

 

 

Go on.

 

If you apply a force to a moving object to change its momentum by say gravity or electromagnetic means there is a reaction on the mass of the generator which alters its momentum by a corresponding amount is there not? Normally we discount this since the generator is highly massive or attached to something that is.

 

Alternatively if I hit a cricket ball with a cricket bat both suffer a change of momentum and there is an impact force to take into account.

 

I am using the word 'balance' in the engineering sense, ask captain panic, he is a chemical engineer and they do lots of momentum balances, includng the forces acting on control volumes.

Edited October 2, 2013 by studiot

[Sensei]

You need a closed system. You would not get momentum conservation if matter was entering or leaving your system or it was being acted on by some external force.

 

"Closed system" is purely theoretical physics term.

In true Universe none system is perfectly close, neutrinos are flying through, photons are absorbed and emitted all the time, constantly changing state of system. Not to mention charged particles, and molecules.

[ajb]

"Closed system" is purely theoretical physics term.

So what?

 

The term momentum is a purely theoretical physics term.

 

Anyway, we are quite happy to make idealisations when discussing real systems as long as that does not push things too far away from what is observed.

 

In true Universe none system is perfectly close, neutrinos are flying through, photons are absorbed and emitted all the time, constantly changing state of system. Not to mention charged particles, and molecules.

Sure, but if these effects are small then we should be happy approximating real systems with idealised ones, closed or not.

If momentum pops into existence at one end of the universe and cancelling momentum pops into existence at the other end, is that conservation or is it breaking conservation twice?

That depends on of momentum conservation is expressed in differential or integral form!

 

Well, they are the same for flat space-times, but one ends up with difficulties on curved space-times with the integral form.

 

The differential expression tells us that momentum is not created or destroyed in an infinitesimal region of space-time, the same can be said for energy. The interesting thing here is that we know gravitational waves can carry energy and momentum and these have to be taken into account when dealing with conservation laws.

[decraig]

Is momentum conserved in every interaction, or only in closed systems? If momentum pops into existence at one end of the universe and cancelling momentum pops into existence at the other end, is that conservation or is it breaking conservation twice?

 

Unfortunately, it's broken twice, but it does depend upon who is doing the accounting. Say you are in some inertial frame of reference. Simultaneously, the momentum disappears from system A, and appears in system B. But, I have some non-zero velocity with respect to your inertial frame, such that the events are no longer simultaneous. For me, the momentum either disappears for a while, or doubles-up.

 

But, this is the Classical section of this forum, so maybe this answer is out of bounds.

That depends on of momentum conservation is expressed in differential or integral form!

 

Well, they are the same for flat space-times, but one ends up with difficulties on curved space-times with the integral form.

 

The differential expression tells us that momentum is not created or destroyed in an infinitesimal region of space-time, the same can be said for energy. The interesting thing here is that we know gravitational waves can carry energy and momentum and these have to be taken into account when dealing with conservation laws.

 

Hello again, ajb.

 

Could you share these expressions.

 

I'm hard pressed to find an expression for the momentum of a system of ponderable matter fields.

Edited November 20, 2013 by decraig

[ajb]

You can read more about energy conservation in GR at

 

www.math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html‎

[decraig]

You can read more about energy conservation in GR at

 

www.math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html‎

Thanks.

 

On the surface, the integral appears too ugly be true. It's hardly surprising that is fails general covariance.

 

According to Wikipeda, the stress energy tensor with upper indices is integrated. Take for instance, a space-space component. It's really an element of per-distance squared. Now integrate over the cube of distance. We are off by 5 dimensions!

Edited November 20, 2013 by decraig