# KE of system / different reference frames question

1. Jan 1, 2012

### jduffy77

I am re-posting this question here in a new thread as Humber mistakenly posted it in a two year old thread.

2. Jan 1, 2012

### Ken G

I'm not sure what your issue is with "literal thinking", to me the quote is a clear example of not thinking literally. Literal thinkers imagine that energy is innate, so a car that is moving along the road has it, in any frame of reference. But energy is frame dependent-- conservation of energy means the energy stays the same in a given frame, it doesn't mean it is the same in all frames. So choosing different frames always repartitions the energy, and therefore it also changes the language about what the energy is doing or where it is coming from. This is all perfectly normal, it is what you find when you relax the need to think literally.

So there is no problem at all with saying that a car can extract energy from the road when it uses KERS, but the language sounds awkward unless one is being extremely clear about the choice of reference frame. For example, one can have a car that accelerates from rest to 10 m/s, and if we start in a frame already moving at 10 m/s, this will look like a car that uses its fuel energy yet loses all its kinetic energy-- the missing energy shows up in the Earth's kinetic energy in that frame. That's just how it is, in that frame. We can argue that isn't the best frame to think about, or we can argue it is, but it certainly isn't wrong.

3. Jan 1, 2012

### 256bits

I had to look up KERS and that is Kinetic Energy Recovery System.

It is so far so good up to the 5th paragraph.
The 10kg object can be considered to be at rest in a frame, call it frame A, moving at 10 m/s relative to the earth. But once the braking occurs, the object will have a force applied to it and begin to move relative to that frame. ( Otherwise you are dealing with a moving frame of reference. ) At the end of it all, the object will have a velocity of -10 m/s in frame A.

Suppose there are 2 cars moving side by side. You have a tiny window to look out from car 1 out but all you can see is the car 2 beside you, which would appear to be not moving relative to your reference frame A. Person X on the earth can see both Car1 and 2 and conclude that both cars are mving at 10 m/2 relative to the earth.
Car2 signals you that he is going to apply KERS. As he does so, to you in Car 1, it would look as if Car2 is accelerating in the backward direction up to a maximun of -10 m/s. You in Car1 would begin to wonder how in the world did Car2 accelerate if Car2 was using KERS.

4. Jan 1, 2012

### 256bits

A really bad statement all in all. It is not put together in any coherent fashion. You usually find something like this on a site promoting the newest crackpot idea which is meant to confuse, and not for an explanation of KERS. I cannot tell if the writer is saying that the energy of the fuel is being recovered or the kinetic energy of the vehicle. If he is saying it is the energy of the fuel, then why not go farther back and say it is the energy of the sun trapped in the plant material, from 600 million years ago, that became hydrocarbons through transformation under the earth's surface.

The fuel provides energy to the car to move. The chemical energy is transformed into kinetic energy. KERS would recover some of the kinetic energy.

5. Jan 1, 2012

### rcgldr

I think the point missed in the old DDWFTTW thread is the source of the force at the tires. For a KERS vehicle, the force at the tires equals the mass of the vehicle times it's rate of acceleration (or deceleration) (ignoring rolling resistance and aerodynamic drag). For a DDWFTTW vehicle, the force at the tires equals the torque used to drive the propeller divided by the radius of the tires, which is independent of the mass of the vehicle.

Last edited: Jan 1, 2012
6. Jan 1, 2012

### mender

Not a problem since for any given situation, there is only one non-moving frame of reference and an infinite number of moving ones.

I think what you're meaning is an accelerating frame of reference.

7. Jan 1, 2012

### Humber

That is indeed the thinking I was taking about. That "all things are relative".

Acceleration is not one of those things, and the fuel in that tank, is another.
Can you justify that the fuel consumed, is capable of accelerating the Earth by same amount it accelerates the car?

8. Jan 1, 2012

### Humber

The first few statements are not mine. The claim there, is that the Earth can transfer 100W to the KERS.
But, regardless of its origins, the fuel is the store of some energy form somewhere. It could equally be a battery. When the car accelerates, some of that energy becomes KE in the car's mass, and that is the energy that is recovered, and not something that comes from the ground.

9. Jan 1, 2012

### Humber

Yes. F=ma.
When the car brakes, momentum is transferred from the car, to the ground, dp/dt = F.
For a KERS to work, that same force is present, but the KE of the car is not dissipated as heat in the brake pads and disks, but becomes stored in a mass as angular KE, or by direct conversion to electrical energy and so stored in a battery.
Apart form some work at the tyres and surface deformation, which is a result of F, and energy that can't be recovered, there is no energy from the ground.

10. Jan 1, 2012

### jduffy77

No, those are correct. The incorrect one he mentioned was not put forth in a coherent fashion was yours though.

As was already pointed out; whether or not the energy comes from the ground depends on the reference frame chosen to analyze.

11. Jan 1, 2012

### Subductionzon

No one has made that claim Humber. You are trying to use a straw man argument.

Why don't you lay out your claim here that all energy must be calculated relative to the Earth and see how that flies here. Or as you claimed elsewhere, that no energy can come from the ground.

12. Jan 1, 2012

### RCP

Mender old bean!! You've been missed at TR. Did you ever get around to do that test pulling your cart to wind speed and then releasing it along with some packing popcorn? I would still love to see a video of that.

Also looking forward to 256bits response. And what about a decelerating FoR?

13. Jan 1, 2012

### Humber

Which is a contradiction of both my statement, and that of 256bits, which is paraphrasing of mine.
When the car accelerates, momentum is transferred from the ground to the car, and when it brakes, the other way. That is conservation of momentum at work, which leaves you to explain if the ground powers the KERS, why fuel is needed to transfer momentum one way, but not the other. And, if you can possibly manage it, please keep your personal remarks and references to the cart to yourself.

14. Jan 1, 2012

### jduffy77

Please check your quotes. The two sentences you have quoted were mine but the body of your post is responding to someone else.

15. Jan 1, 2012

### mender

Happy New Year, RP!
Nothing yet and not likely in the foreseeable future, too much real work to do! I haven't stopped in because I didn't think there was anything left but some stirring of the ashes!

ETA: wow - part 30??!!

Last edited: Jan 1, 2012
16. Jan 1, 2012

### Staff: Mentor

In some valid frames, when the car accelerates it loses KE, and can even come to rest. When it is at rest there is 0 KE. Furthermore, KE can never be negative. So, how do you propose to recover energy from something with 0 energy and whose energy cannot go negative?

Have you even attempted to calculate the energy in a moving reference frame and see how it works out?

17. Jan 1, 2012

### RCP

Best wishes for the new year back atcha mender. Yep, Cartville is still accelerating, and FYI humber has now posted pictures of 3 different carts he made. (Film at 11! ) Remember how positive everyone was he would never make one?

And if you or anyone has time, there's still my question above about the FoRs applicable for deceleration?

18. Jan 1, 2012

### rcgldr

Although off topic from the orignal DDWFTTW thread ... ignoring any losses due to aerodynamic drag, rolling resistance, conversion of energy, ... , then considering a car and earth as a closed system, then energy (and momentum) of this closed system is conserved.

KERS - extracts energy from earth + car closed system and adds that energy to a device that stores energy (kinetic or potential).

Usage of fuel - extracts chemical potential energy from fuel and adds that energy to the kinetic energy of earth + car closed system.

For both of these cases, the amount of energy converted is independent of the frame of reference, as long as the frame of reference is inertial.

Getting back on topic from the original DDWFTTW thread, someone was wondering if a DDWFTTW vehicle was somehow extracting it's own kinetic energy (wrt ground). The responses that followed tried to explained that a DDWFTTW vehicle extracts energy by slowing down air (wrt ground), and that a DDWFTTW vehicle requires a true wind (wrt ground) in order to operate.

19. Jan 1, 2012

### Humber

KE is the work of acceleration.
http://en.wikipedia.org/wiki/Kinetic_energy
"The kinetic energy of an object is the energy which it possesses due to its motion.[1] It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest."
The accleration of a 640kg car, cannot be equated with the acceleration of the Earth.

Your first statement is correct, because KE is related to the square of velocity, but then again, momentum isn't. There is certainly -p and +p. That allows conservation to work.

If it were necessary for there to be "-ve KE" to "recover +ve KE," then no transfer could ever take place under any circumstances. The answer is the the KE does not need to be negative, because all cases lie between zero and some non-zero number.

Momentum transfer to the ground is necessary to force, but not to the motion itself, but wheels do need that force, so momentum is indeed transferred as the car gains KE via acceleration.
The car gains momentum p, and the Earth -p.
total energy = p^2/2mcar+ p^2/2mearth
mearth = 6e24Kg, so the second term is negligible.

ETA:
It is not a matter of arbitrarily choosing frames because changes in momentum are not frame dependent. One would be at a loss to explain how the battery in an electric car loses charge, if it where just a matter of choosing which frame it lost it in.

Last edited: Jan 1, 2012
20. Jan 2, 2012

### Ken G

Sure, but the statements you objected to did not say anything about either the acceleration or the fuel, they talked about recovering energy from the Earth, which is perfectly correct in the frame of the car's velocity.
No, nor is there any need to justify that, because no one thinks the Earth is being accelerated as much as the car. That comes from a=F/m, the F is an action/reaction pair so is the same on the car and the Earth. Not the "a." There is only a very small "a" for the Earth, but it suffices to remove exactly the correct amount of kinetic energy from the Earth to make the problem work out in any reference frame.

What is happening here is that you are confused about the differences between energy, momentum, and acceleration, and your confusion is causing you to contradict the statements made by people who do understand these differences. I'm not sure you can move forward until you understand those basic concepts better, and then you can get to the point where you understand that stories about what energy is doing always depend on the reference frames from which they are told. This is all elementary to us.