How are momentum and kinetic energy related?

[Strange]

How is the Wiki integral the same as mine?

 

Have you heard of "scrolling"? Or are you to busy cherry-picking evidence to hide your mistakes...

[studiot]

Since when was scrolling a valid integration technique?

 

There it is, writ large at the head of their page, like a banner for all to see.

 

An indefinite integral that needs an arbitrary constant to complete the integration.

 

But that is irrelevant to the point I made that the impulsive force has a beginning and an end.

That is what makes it different from say, gravity.

Edited May 21, 2015 by studiot

[Strange]

But that is irrelevant to the point I made that the impulsive force has a beginning and an end.

 

As the Wikipedia page says: http://en.wikipedia.org/wiki/Impulse_%28physics%29#Mathematical_derivation_in_the_case_of_an_object_of_constant_mass

[tar]

SwansonT,

 

I thought the solenoid setup asked my question. How does the energy get from one end of the shaft, to the other, in relation to the momentum getting from one end to the other?

 

Regards, TAR

[Sensei]

However there are systems in which momentum is conserved and kinetic energy is not. KE is but one form of energy, while momentum is momentum, and is only changed by an external force. Momentum is conserved, for example, in an inelastic collision, but KE is not.

But in such case kinetic energy is converted to heat, or photons. So total energy remain the same before collision and after collision.

 

Take for example vacuum tube, with two electrodes, and piece of metal between them.

Plug high voltage to electrodes. Electrons are emitted, and accelerated.

They have significant kinetic energy, and upon collision with metal on their path, x-ray photons are created. And their energy will depends on applied voltage.

 

There was such nice experiment: scientists were accelerating metal balls (dozen/hundreds), and shooting to water, and measuring increase of temperature of water.

Edited May 22, 2015 by Sensei

[MigL]

I think swansont's point was that Kinetic energy can be converted away to other forms. Momentum cannot. It is always conserved as momentum.

 

@studio and strange...

I don't recall impulse even being mentioned in the OP.

Or are you guys just itching for a dust-up ?

[Strange]

I don't recall impulse even being mentioned in the OP.

Or are you guys just itching for a dust-up ?

 

It was brought up by the OP:

 

But as an "impulse" that comes from one direction, and is heading in one direction, can be conceptually considered as a thing...

 

I think he was using it in an informal sense, so thought it would be useful for him to understand what it really means. (And not what studiot thinks it means. )

[studiot]

 

I think he was using it in an informal sense, so thought it would be useful for him to understand what it really means. (And not what studiot thinks it means. )

 

It is a pity some fool chose to formalise the definition of the word action in physics, he was a jerk.

 

I can't now say that there are several mechanisms that action (in the general english sense) can be transferred from one place to another and impulse would certainly be one of them.

 

But impulse is tricky and not the main subject of this thread.

 

That is why I have discontinued our cordial discussion on that subject here.

 

However I would be happy to continue in a brand spanking new thread, designed expressly for that purpose, if you so wish.

We could discuss examples of fire hoses, jack-in-the-boxes and sledge hammers and the impulse-momentum theorem there.

 

Perhaps tar might also read it and derive something of value.

Edited May 22, 2015 by studiot

[swansont]

But in such case kinetic energy is converted to heat, or photons. So total energy remain the same before collision and after collision.

 

 

Yes, exactly. Kinetic energy is a subset of total energy. Thus, KE is not generally a conserved quantity, though it is conserved in special cases, e.g. perfectly elastic collisions.

SwansonT,

 

I thought the solenoid setup asked my question. How does the energy get from one end of the shaft, to the other, in relation to the momentum getting from one end to the other?

 

Regards, TAR

 

 

"Are they related" is not the same question as "how does X happen"

[tar]

SwansonT,

 

This morning, I was rocking back and forth in my recliner, thinking about how best to post my findings that my college physics book described centrifugal forces (the lack thereof) in exactly the way you have been telling us.

 

I was rocking about 40 cycles a minute, exerting an upward force with my right toe, and letting the chair/me combo come back down for another tangential thrust. The motion back and forth was interesting to think about and witness. In particular, among the many observations I made about direction and extent of motion in this back and forth, along the arc of circle, I noticed that holding my two hands up radially, one infront of up and one behind up, was difficult, as the momentum of the one hand, in respect to gravity, was different than the momentum of the other. In one case, inertia was working with gravity and then against, while the other hand was undergoing the opposite inertia and working against gravity, and then with. Consistent with this finding was the fact that when I pushed up with my toe, my left hand went down, and my right hand went up, even though they at all times were traveling in tandem relative to the arc of the circle (either clockwise or counterclockwise looking at the chair from the side.) I found the right hand and left hand did not keep the same distance from each other, as the motor signals and feelings in the two hands were conflicting, until I imagined holding a saw, at which point, my predictive motor simulator could send the right signals to keep my two hands at the same distance from each other, along their respective radials.

 

Point here, is that momentum and inertia is a two way street. There is as much a consideration for the body wanting to stay motionless, as there is for the body to want to continue moving in a straight line. And the kenetic energy present in the straight line motion, or the potential energy building up trades places, and hence direction, simultaneously with the momentum and inertia. The KE seems married to the momentum, in this regard.

 

Regards, TAR

[swansont]

The KE seems married to the momentum, in this regard.

 

The overarching principle behind physics (and science as a whole) is to find behaviors that are generally true, not specific instances where these things are true. As such, the approach of finding times when an idea holds is backwards from how one must approach science. You need to do things in a way that can falsify an idea, not incorrectly confirm it. You have already been given examples where momentum and kinetic energy do not share behaviors. That should be enough to put this notion to rest.

[studiot]

tar, I just read and commented in the centrifugal thread and I thought you had cracked it.

 

You seem to have forgotten that

 

1) It is possible for a body to loose all its momentum, whilst its KE remains unchanged.

 

2) It is possible for a body to gain double its momentum, whilst its KE is unchanged.

 

Does that sound like they are directly related?

 

Yes they are related, they both belong to or are attributable to the same body.

But that is not quite the answer you are seeking.

[tar]

Studiot,

 

No, I have not cracked it. I have the general understanding that I am barking up the wrong tree. But I am not convinced yet that the tree has no occupant.

 

My wondering is based on a video in the centrifugal thread where the host "gets the ball going" inside a ring, and then lifts the ring and the ball goes off tangentially.

 

Watching the thing over and over, I kept seeing the host apply a tangential force on the ball and then coax that motion into a circular path with the ring. I am "stuck" on this "getting the ball going" and I am seeing this force "carried" by the ball, constrained by the ring, and then released by the ring, back into the straight line motion, that was intially imparted onto or into the ball.

 

This inertia was given to the ball and nothing is said about it. Its important to me that the ball is carrying that force, and just because it is redirected, and other forces are applied to it, does not erase the initial force. The ball still has it, when the ring is lifted.

 

I do not know which part of the force the ball is carrying is momentum and which part is KE.

 

 

Regards, TAR

Edited May 23, 2015 by tar

[swansont]

The ball doesn't "carry" force.

 

If you exert a force on an object, you will impart kinetic energy and momentum to it. Those are two properties it has. They have different characteristics.

 

The momentum depends on how long you exerted the force. The KE depends on the distance through which it was imparted, and at what angle the force was relative to the displacement.

[studiot]

 

No, I have not cracked it. I have the general understanding that I am barking up the wrong tree. But I am not convinced yet that the tree has no occupant.

 

Sorry to hear that.

 

 

My wondering is based on a video in the centrifugal thread where the host "gets the ball going" inside a ring, and then lifts the ring and the ball goes off tangentially.

 

Don't think I saw that video but it sound as though the author was trying to be 'clever' and complicated.

I recommend sticking to the ball and string.

 

To get the ball going as you say you start off by dragging it in a line with the string.

You then give it a second yank sideways to the motion to divert it from that line into a curved path.

You repeat this as many times as necessary to get it swinging round.

 

The first initial pull is linear and the tension in the string has no special name.

The sideways pull is still tension but is now called centripetal force.

 

But this is where the problems start.

 

 

This inertia was given to the ball and nothing is said about it.

 

 

No inertia was not 'given to the ball', it is an inherent property of the ball (or any other piece of matter).

It cannot be given to anything, and equally it cannot be taken away.

Inertia is measured by mass. It is not momentum, but as swansont said backalong, it is one part of momentum, the other being velocity.

 

You haven't made any comment or asked any questions about momentum in my post 37 ?

 

This was meant to be encouraging BTW.

[tar]

Studiot,

 

I appreciated the encouragement in #37 but did not understand your point 1 and 2, nor could I generate the examples, in my mind where those things would be true.

 

I am stuck on a few things, and do not "get" why a mass can not "carry" a force. And I think I start to crack it, and put things in their proper place, definitionally, and then some inconsistency comes up that I don't know how to resolve. For instance I am told KE is a scalar, with no directional component, that it is a speed, not a velocity, and then SwansonT says: "The KE depends on the distance through which it was imparted, and at what angle the force was relative to the displacement."

 

My current misconception, the one that I got RobbityBob1 all engaged in, is that a mass can "carry a force". Definitionally there is this thing about inertia, that a mass has it, and can not lose it. The relationship of force to acceration depends on the mass staying exactly the same, throughout the exercise. But since the mass might be moving in relation to another mass, and the two masses might contact each other, and exchange, something, and both retain exactly their mass, then the thing that they exchange, must be something they are carrying, and can off load, or gain more of. It is this "force" I am struggling with, this impetus, or action, relative to other stuff around, that is being "carried" by a moving thing, from point A to point B, that the mass is merely a carrier of, and does not stay with the mass. This energy seems different to me than the inertia of the body, but related. I am asking in this thread, to understand why a mass cannot carry a force, when there seems so many examples in life, like thrown balls, and shot bullets, where the energy takes a ride on the mass, in a particular direction.

 

Regards, TAR

[studiot]

 

I appreciated the encouragement in #37 but did not understand your point 1 and 2, nor could I generate the examples, in my mind where those things would be true.

 

So ask, that's how we find things out.

 

 

If a (perfectly elastic) ball travelling from left to right hits a wall and bounces horizontally back,

 

It starts with a momentum m in the left to right direction.

 

After bouncing it now has a momentum of (-m) ie in the right to left direction.

 

This is a change of 2m.

 

But its speed has not altered so its KE has not altered.

 

 

Thinking about the same wall I have already directed a fire hose at it.

 

All the momentum from left to right is destroyed, the water has zero left to right momentum, upon impact.

 

But since it must move away (it does not stick on the side of the wall), it still has some or all of its KE.

 

Please don't get into objects carrying a force.

That is the realm of sub atomic physics and so called exchange particles that does not belong in ordinary common or garden classical physics.

[swansont]

Studiot,

 

I appreciated the encouragement in #37 but did not understand your point 1 and 2, nor could I generate the examples, in my mind where those things would be true.

 

I am stuck on a few things, and do not "get" why a mass can not "carry" a force. And I think I start to crack it, and put things in their proper place, definitionally, and then some inconsistency comes up that I don't know how to resolve. For instance I am told KE is a scalar, with no directional component, that it is a speed, not a velocity, and then SwansonT says: "The KE depends on the distance through which it was imparted, and at what angle the force was relative to the displacement."

 

My current misconception, the one that I got RobbityBob1 all engaged in, is that a mass can "carry a force". Definitionally there is this thing about inertia, that a mass has it, and can not lose it. The relationship of force to acceration depends on the mass staying exactly the same, throughout the exercise. But since the mass might be moving in relation to another mass, and the two masses might contact each other, and exchange, something, and both retain exactly their mass, then the thing that they exchange, must be something they are carrying, and can off load, or gain more of. It is this "force" I am struggling with, this impetus, or action, relative to other stuff around, that is being "carried" by a moving thing, from point A to point B, that the mass is merely a carrier of, and does not stay with the mass. This energy seems different to me than the inertia of the body, but related. I am asking in this thread, to understand why a mass cannot carry a force, when there seems so many examples in life, like thrown balls, and shot bullets, where the energy takes a ride on the mass, in a particular direction.

 

Regards, TAR

 

 

Force is not a conserved quantity, so there is no way to account for how much force an object could "carry". It's not a property of a particle. KE and momentum are. To the extent the analogy works, that is what they "carry". (but that's bad terminology, since these are not substances, they are properties)

 

Please don't get into objects carrying a force.

That is the realm of sub atomic physics and so called exchange particles that does not belong in ordinary common or garden classical physics.

 

And in that realm it's an interaction.

[tar]

SwansonT and Studiot,

 

OK, I will try and drop the "carry the force" idea, because it is so opposite the definition of force to begin with, as a force is an outside thing that acts upon a mass, to accelerate (decelerate, change direction of) it.

 

And I will try and keep KE as a scalar consideration, just a speed, just a quantity, with no direction.

 

But in the garden hose stream, hitting the wall, some force is absorbed by the wall, there is a push on the wall, not enough to move it, so maybe its not a force, but there is an energy that it absorbs, and some of the momentum of the water molecules is imparted onto the wall. 2m worth. If the wall was made of styrofoam peanuts (loose and unattached to each other), the 2m transfer would not be so clean and obvious. The peanuts would take on a momentum, they would be accelerated in the direction the water molecules were traveling, they (the peanuts) would have an outside force applied to them, by the moving water molecules. A power washer might even take the mortar out from between the bricks of our solid wall and send the peices flying.

 

In my rocking recliner experiment, with my two arms above my head, one behind and one infront of up, I had elements of gravity, and circular motion combined, along with change in direction. 80 changes a minute. Considering just a hand as a mass, there were forces that needed to be applied by my muscles, to keep the hand locked in its radial position, with respect to the chair. The inertia of my hand could be felt, and observed, wanting to continue to move in the former direction, when the chair's direction changed, and then again, when the direction changed again. The mass itself had the inertia, that was resisting the change in direction.

 

This might not be garden variety physics, but it is at least "armchair" physics.

 

Regards, TAR

[studiot]

 

But in the garden hose stream, hitting the wall, some force is absorbed by the wall, there is a push on the wall, not enough to move it, so maybe its not a force, but there is an energy that it absorbs, and some of the momentum of the water molecules is imparted onto the wall. 2m worth. If the wall was made of styrofoam peanuts (loose and unattached to each other), the 2m transfer would not be so clean and obvious. The peanuts would take on a momentum, they would be accelerated in the direction the water molecules were traveling, they (the peanuts) would have an outside force applied to them, by the moving water molecules. A power washer might even take the mortar out from between the bricks of our solid wall and send the peices flying.

 

That is what I have been trying to tell you.

 

Yes if there is change of momentum a force is involved/generated.

 

Yes in reality some of the KE is lost to the wall, especially if the water damages it, but once again you are trying to mix up KE and momentum.

 

Don't, it doesn't work like that.

 

And there is a difference between the momentum change for the water which is 1m_water and the momentum change for a ball bouncing off, which is 2m_ball.

 

There is no reason for m_water to be the same as m_ball.

[tar]

Studiot,

 

The speed of the ball was not altered?

 

Perhaps, but was there no time period where it decellerated from it's incoming speed, to zero, and another period of time where it accelerated from 0 to it's outgoing speed in the other direction?

 

 

Regards. TAR

Studiot,

 

"There is no reason for m_water to be the same as m_ball."

 

 

Can't you think of a stream of water being a bunch of tiny BBs? A bunch of balls. Wouldn't the physics of each of the bunch be the physics assigned to one ball?

 

 

Regards, TAR

[studiot]

 

The speed of the ball was not altered?

 

That is what perfectly elastic means.

 

 

Perhaps, but was there no time period where it decellerated from it's incoming speed, to zero, and another period of time where it accelerated from 0 to it's outgoing speed in the other direction?

 

Of course, that is what happens.

What difference do you think that makes?

 

 

Can't you think of a stream of water being a bunch of tiny BBs? A bunch of balls. Wouldn't the physics of each of the bunch be the physics assigned to one ball?

 

No the physics of the water impact is nothing at all like that of little balls, and much more complicated.

 

The ball, mass M, has velocity +V momentum +MV as it approches the wall.

 

It hits the wall and bounces back along the same trajectory, but in the opposite direction with velocity -V

 

So it now has momentum M(-V) = -MV.

 

So (Momentum before - momentum after) = (MV) - (-MV) = 2MV.

 

KE before = 1/2 MV²

 

KE after = 1/2 M(-V)²

 

So KE before = KE after.

 

If you are happy with this then we can proceed to the more complicated situation of the water.

Edited May 24, 2015 by studiot

[swansont]

 

But in the garden hose stream, hitting the wall, some force is absorbed by the wall, there is a push on the wall, not enough to move it, so maybe its not a force, but there is an energy that it absorbs, and some of the momentum of the water molecules is imparted onto the wall. 2m worth. If the wall was made of styrofoam peanuts (loose and unattached to each other), the 2m transfer would not be so clean and obvious. The peanuts would take on a momentum, they would be accelerated in the direction the water molecules were traveling, they (the peanuts) would have an outside force applied to them, by the moving water molecules. A power washer might even take the mortar out from between the bricks of our solid wall and send the peices flying.

 

You're missing the forest for the trees here. In the non-ideal case a small amount of KE may be converted to other forms and the wall may even move a tiny amount. But momentum changes by ~100%. Contrast this with a perfectly elastic collision of two equal-mass objects, where 100% of the KE and 100% of the momentum is transferred. But only in that one case; if the collision is not elastic, or the masses differ, the KE transfer is different. KE is not generally a conserved quantity.

 

You can't just cherry pick where a pattern works. You have to look at where it fails, and KE and momentum do not act identically in most situations. They are two distinct parameters of motion.

[tar]

Studiot,

 

A little confused about the physical meaning of a squared velocity and a little confused about why there is a v in the KE equation, but I guess I am happy with that.

 

SwansonT,

 

In the inelastic collision of the equal masses, the momentum is conserved, and the first mass gives up its momentum, and now the same momentum is a property of the second body.

 

Can the situation be considered as one where the first body applies a force upon the second body?

 

Regards, TAR

[swansont]

SwansonT,

 

In the inelastic collision of the equal masses, the momentum is conserved, and the first mass gives up its momentum, and now the same momentum is a property of the second body.

 

Can the situation be considered as one where the first body applies a force upon the second body?

 

Yes. And by Newton's third law, the second imparts an equal and opposite force on the first. Since they necessarily exert these forces for the same duration, the impulse is equal and opposite, i.e. momentum is conserved. But if it's inelastic, KE is NOT conserved. (Which also means the scenario of transferring all of the momentum can't work. The incident particle will recoil)