Is Newtonian Mechanics enough to explain KE transfer in collisions?

[scoutfai]

Without the use of 2nd law of thermodynamics, is it possible (if yes, please show me how), solely by using Newtonian Mechanics, to show that during a collision of two particles, the faster moving particle will lost KE after the collision and slow down, while the slower moving particle will gain KE after the collision and speed up?

Or, does Newtonian Mechanics does not prohibit the transfer of KE from a slower particle to a faster particle, i.e. when a slower moving particle collide with a faster moving particle, the slower particle loses KE to the faster particle and hence become even slower, while the faster particle gains KE and hence become even faster?

I just wondering without the 2nd law of thermodynamics, does Newton Laws alone sufficient to explain everything in the world of mechanics (excluding the relativistic speed situation and quantum scale situation).

 

[kowalskil]

Without the use of 2nd law of thermodynamics, is it possible (if yes, please show me how), solely by using Newtonian Mechanics, to show that during a collision of two particles, the faster moving particle will lost KE after the collision and slow down, while the slower moving particle will gain KE after the collision and speed up?

Or, does Newtonian Mechanics does not prohibit the transfer of KE from a slower particle to a faster particle, i.e. when a slower moving particle collide with a faster moving particle, the slower particle loses KE to the faster particle and hence become even slower, while the faster particle gains KE and hence become even faster?

I just wondering without the 2nd law of thermodynamics, does Newton Laws alone sufficient to explain everything in the world of mechanics (excluding the relativistic speed situation and quantum scale situation).

Masses of these particles must be specified.

 

[kowalskil]

Masses of these particles must be specified.

P.S. In other words, which particle is moving faster, more massive or less massive?

 

[scoutfai]

P.S. In other words, which particle is moving faster, more massive or less massive?

It matters? If it does, then why not we make the discussion a general one. i.e. we first consider the case where initially the massive particle is moving faster than the less massive particle.
Then we consider the case where initially the massive particle is moving slower than the less massive particle.

 

[AlephZero]

The question is fairly meaningless in Classical mechanics, because the velocity, and hence the kinetic energy, depends on the reference frame you use to measure it.

For the same perfectly elastic collision between two particles, you can have either particle slow down, stay at the same speed, or speed up, depending what you measure the velocities relative to.

For example in the reference frame fixed to the center of mass of the particles, the speeds of both particles before and after an elastic collision are the same (but the directions of motion are differenct, of course).

 

[sophiecentaur]

The question is fairly meaningless in Classical mechanics, because the velocity, and hence the kinetic energy, depends on the reference frame you use to measure it.

For the same perfectly elastic collision between two particles, you can have either particle slow down, stay at the same speed, or speed up, depending what you measure the velocities relative to.

For example in the reference frame fixed to the center of mass of the particles, the speeds of both particles before and after an elastic collision are the same (but the directions of motion are differenct, of course).

I'm pretty sure that, whichever frame of reference you choose, you will still get a consistent answer in terms of observable values for relative velocities and KEs.
Has anyone decided whether this collision is supposed to be elastic or inelastic - or with a known coefficient of restitution? I did these collision problems at School until they were coming out of my ears and I can't recall any serious problems.

 

[RedX]

Conservation laws don't say that the faster molecule has to slow down.

You can easily imagine a very fast moving marble moving in the x-direction getting hit by a slow moving marble from the y-direction. Conservation laws say that the marble moving in the y-direction would slow down, and that the x-moving particle would speed up in the y-direction while maintaining its speed in the x-direction.

 

[sophiecentaur]

This is another of those topics for which the actual sums tell you everything there is to say about what happens. Conservation laws are what you apply to get the right answer. It's not really a topic that lends itself to conversation - just do the sums and bob's your uncle.

 

[AlephZero]

I'm pretty sure that, whichever frame of reference you choose, you will still get a consistent answer in terms of observable values for relative velocities and KEs.

Yes, you get the same relative velocities. (In other words, Newtonian mechanics "works", at least for small enough velocities).

But if the OP says "one particle speeds up and the other slows down", that can't be talking about the velocities of the particles relative to each other, it must mean velocities relative to something else.

If the particle velocities were u1 and u2 before collision, and v1 and v2 after, you can choose a different inertial frame to make one of the four velocities (and the corresponding KE) zero, so you can get any "answer" you want for whether the particles "speed up" or "slow down", both for elastic and inelastic collisions.

This is the same basic problem with Newtonian mechanics as the fixed value of "c" in the solutions of Maxwell's equations in classical phyiscs, of course.

 

[scoutfai]

The question is fairly meaningless in Classical mechanics, because the velocity, and hence the kinetic energy, depends on the reference frame you use to measure it.

For the same perfectly elastic collision between two particles, you can have either particle slow down, stay at the same speed, or speed up, depending what you measure the velocities relative to.

For example in the reference frame fixed to the center of mass of the particles, the speeds of both particles before and after an elastic collision are the same (but the directions of motion are differenct, of course).

Pardon me, I should have be more clear on the frame of reference. I myself is thinking a frame of reference fix on ground, and then the two particles moving to hit each other, and I standing there to observe it.

So, is that means you are saying that Newtonian Mechanics alone, does not specify whether a faster moving particle will gain speed or lose speed after collide elastically with a slower moving particle, Newtonian Mechanics actually allows all possibilities to occur (gain speed, lose speed)?

 

[scoutfai]

I'm pretty sure that, whichever frame of reference you choose, you will still get a consistent answer in terms of observable values for relative velocities and KEs.
Has anyone decided whether this collision is supposed to be elastic or inelastic - or with a known coefficient of restitution? I did these collision problems at School until they were coming out of my ears and I can't recall any serious problems.

I was asking about the case of a perfectly elastic collision. Pardon for not being clear.

 

[scoutfai]

Conservation laws don't say that the faster molecule has to slow down.

You can easily imagine a very fast moving marble moving in the x-direction getting hit by a slow moving marble from the y-direction. Conservation laws say that the marble moving in the y-direction would slow down, and that the x-moving particle would speed up in the y-direction while maintaining its speed in the x-direction.

Are you saying that conservation law does not prohibit a particle to gain speed or lose speed after it collides with a either slower or faster particle? Meaning conservation law allows all possibilities to occur?

 

[sophiecentaur]

A ballbearing hitting the front of a locomotive will bounce off faster than it arrived. (as seen from the ground)

 

[AlephZero]

So, is that means you are saying that Newtonian Mechanics alone, does not specify whether a faster moving particle will gain speed or lose speed after collide elastically with a slower moving particle, Newtonian Mechanics actually allows all possibilities to occur (gain speed, lose speed)?

That's right. For example, think about what would happen in the same two particles were moving in the same direction, or opposite directions, before the collision. (I'm assuming you really do mean "speed", and not "velocity" in your question, because in your OP you mentioned KE, and only depends on the speed squared, not the direction of the velocity).

 

[kowalskil]

That's right. For example, think about what would happen in the same two particles were moving in the same direction, or opposite directions, before the collision. (I'm assuming you really do mean "speed", and not "velocity" in your question, because in your OP you mentioned KE, and only depends on the speed squared, not the direction of the velocity).

The term "collision" is often used for situations when no contact occurs, for example an alpha particle being scattered by a gold nucleus, or on a hydrogen nucleus. The impact parameter is most often different from zero.

 

[sophiecentaur]

The term "collision" is often used for situations when no contact occurs, for example an alpha particle being scattered by a gold nucleus, or on a hydrogen nucleus. The impact parameter is most often different from zero.

I think that is introducing a needless complication, at this stage. Can't we just stick to billiard balls for this one and sort that out before moving on to big boys' stuff?
In any case, you find that the conservation laws still apply (only there are a few more quantities that need to be conserved.).

 

[scoutfai]

That's right. For example, think about what would happen in the same two particles were moving in the same direction, or opposite directions, before the collision. (I'm assuming you really do mean "speed", and not "velocity" in your question, because in your OP you mentioned KE, and only depends on the speed squared, not the direction of the velocity).

Yes i do mean speed. You get me right.
Thank you, that explanation clear up my doubt.