/sci/ - Science & Math

[Anonymous No.4348694]

Hello /sci/. I've always held the following as true, but now I'm quite confused.

Myquestion is: does conservation of momentum hold in situations in which energy is lost?

Take the case of a collision between two bodies. I wondered the following: could the magnitude of total momentum (i.e. the sum of the momenta of both bodies) after the collision be smaller than the magnitude of the total momentum before the collision if some energy is lost (dissipated as sound, heat, etc.) in the crash?

That is, does some momentum get lost (obviously, going somewhere else) in the collision, not appearing afterwards? And if so so, is there such thing as the "momentum equivalent" of lost energy?

One of lines of reasoning I came up with goes like the following:

1. Since energy is lost in the collision, some work is performed upon other elements of the system in order to generate the heat, sound, etc. corresponding to dissipated energy. Simply put, if energy is lost, work is done somewhere else.
2. Since work is done, forces act, even if for a vanishingly small time duration. (In the limit as this time interval goes to zero, the forces are impulsive and instantaneous, but still imply in transference of momentum, otherwise no energy would be lost.)
3. Since there are such forces acting over other elements, some momentum is transferred from the initial bodies and thus is lost.

Can anyone enlighten me?

[Anonymous No.4348695]

>"Does conservation of momentum hold"

Didn't read further. Yes. It always holds.

[Anonymous No.4348702]

dissipated as sound, heat, etc.

>converted kinetic energy (not momentum)

[Anonymous No.4348705]

Same poster from before, read the rest and it is actually a good conceptual question. Therefore I will answer.

2 types of collisions: elastic and inelastic.

Inelastic means kinetic energy is not conserved, elastic means it is.

Momentum, that is the sum of the mass and velocity of the system, does not change even though the kinetic energy may dissipate.

It is counter-intuitive but mathematically true. Reason a bit more with the concepts and you'll find it's consistent.

[Anonymous No.4348707]

>>4348695
Perhaps you could provide some better insight if you read it all the way through. I consider the system to be only two bodies, and all the momenta I care about is theirs. And all from a classic point of view.

[Anonymous No.4348712]

Sure is underageb& in here

[Anonymous No.4348713]

>>4348705
>momentum, that is the sum of the mass and velocity of the system

[Anonymous No.4348717]

conservation of momentum always holds

energy is not momentum

even when dissipated, energy is always conserved... heat and sound are forms of energy*
(well, mass-energy is conserved when you consider relativity, but yeah)

now repeat after me
momentum is not energy
momentum is not energy
momentum is not energy
momentum is not energy
momentum is not energy
momentum is not energy
momentum is not energy


If you really want to understand this at a deeper level, study Noether's theorem and symmetries in physics.

[Anonymous No.4348719]

>>4348713

Caught me, velocity. It's 2 o'clock here, fack off.

[Anonymous No.4348720]

>>4348705
What do you mean by "mathematically true"? The reasoning here is purely physical, and there is no point in saying that conservation of momentum is mathematically provable.

[Anonymous No.4348723]

>>4348719

LOL PRODUCT OMFG I HATE MYSELF.

[Anonymous No.4348730]

>>4348707
>I consider the system to be only two bodies, and all the momenta I care about is theirs. And all from a classic point of view.
>excludes dissipated energy and momentum as outside of system
>is asking if momentum is conserved in an open, dynamic system

it's like asking if liquid is conserved in a bottle when you pour it out of the bottle

fuck you, op, just fuck you

[Anonymous No.4348731]

Conservation of momentum holds in an isolated system, i.e. a system that doesn't lose or gain energy. Your two bodies aren't an isolated system though, they are radiating away energy, probably losing some through thermal conduction and convection, and most likely receiving some in the same way.
If however you make the approximation that no energy is received or lost during the collision then conservation of momentum will hold.

[Anonymous No.4348732]

>>4348720

What in the world are you talking about? Physical systems can be reduced to functions and equations. Otherwise physics would not work. Mathematics describes these "purely physical" things. The conservation of momentum is indeed mathematically provable. Have you taken a high school level physics course?

[Anonymous No.4348738]

One of the first things I learned in high school physics was that you can have a <span class="math">\Delta K[/spoiler] (and in real life almost always will) but <span class="math">\Delta p[/spoiler] always equals zero (for the whole system).

tl;dr op is underage or autistic

[Anonymous No.4348743]

>>4348730
>>4348731
At last, people with a decent explanation.
That is my very point.

>>4348732
IHABT.

[Anonymous No.4348762]

>>4348731
It's just that it seems that every textbook explanation about inelastic collisions I found makes conservation of momentum hold in its bare form (considering only the two colliding bodies) without acknowledging energy loss.
In fact, they mention energy loss, but never utter a word about loss of momentum by the bodies involved.

[Anonymous No.4348778]

>>4348762

Are you slow? It's because momentum is not lost and energy is, as has been explained previously.

[Anonymous No.4348786]

>>4348788

Converted, not lost. That's what I meant.

[Anonymous No.4348794]

>>4348778
Explained by whom?
Because in fact, what I have extracted from the previous posts is just the opposite (i.e. momentum does indeed get lost).

[Anonymous No.4348801]

>>4348786
Your misquoting gives you away as a newfag.

[Anonymous No.4348805]

>>4348762
When the bodies lose energy they do lose momentum, but in the same time this energy and momentum lost are gained by other particles. if you view heat as microscopic kinetic energy then it's easy to understand how the momentum of the universe is conserved.
However it would be false to say the bodies lose energy and yet conserve momentum.

[Anonymous No.4348817]

>>4348805
You pretty much hit the spot.
Indeed, I was considering my system to be only the two bodies involved in the collision, and nothing else.

[Anonymous No.4348826]

>>4348762
In isolated inelastic textbook collisions, momentum is conserved because the objects are considered to collide in a vacuum (no loss of energy or momentum via sound or convection) and not to radiate and heat. The macroscopic momentum is thus conserved in such examples.

[Anonymous No.4348835]

>>4348826
Yes indeed, and if you want to be perfectly rigorous this will always be an approximation, as all matter with a temperature above 0 Kelvin radiates away energy in the form of photons. (known as thermal radiation)

[Anonymous No.4348836]

>>4348826
And, in one such case, the same holds for energy, am I right?

[Anonymous No.4348854]

>>4348836
If you imagine aswell that the two bodies reflect all the energy reaching them as electromagnetic radiation (photons) from other objects around, and that your bodies aren't radioactive then yes.

[Anonymous No.4348905]

If your system is perfectly isolated, which will always be an approximation as no system inside the universe is perfectly isolated, then momentum is conserved, energy is conserved and angular momentum is conserved.
Now is it possible to imagine a non isolated system where one of these quantities is conserved, that I'm not quite sure about.