# Relative movement and agreement about an object's speed

1. May 12, 2015

### Quarlep

I am confused about Relative Motion.Lets suppose we have one train and two observer.One of them inside the train and the other one is outside.Lets think the outside observer see the train moves a constant velocity v.The observer in the train will be think it is not moving cause of Galileo Principle(It means you cannot prove your are moving or not moving).The outside observer will think kinetic energy will be 1/2mv^2 but the inside observer cant say anything(or will say zero cause he will think its not moving).Now lets think a special situation which two observer can agree the speed.(I know its not possible but lets think thats possible).In this case Can two observers agree on kinetic energy of train(In this case again its violets galileo principle cause the observer in the train know its moving but he cant proof)here I am started to confused.What can be solution Can they agree on kinetic energy cause of the observer inside the train no proof of movement ?

2. May 12, 2015

### A.T.

3. May 12, 2015

### Quarlep

Thank you thats the thing what I want

4. May 12, 2015

### Quarlep

I didnt understand something.Total kinetic energy will be A momentum energy and normal relative kinetic energy ? How can we calculate momentum energy ? (My main language is not english so I am getting trouble to understand logic)

5. May 12, 2015

### Staff: Mentor

There is no such thing as "momentum energy". I think you misread/mistranslated.

6. May 13, 2015

### Quarlep

Whats Ei snd MV^2/2 can someone explain me this simpler just what these things mean and whats the COM frame please
Thanks

Last edited: May 13, 2015
7. May 13, 2015

### Staff: Mentor

The COM frame is the frame where the total momentum is 0. The mv^2/2 is just the non relativistic formula for kinetic energy.

I have no idea what Ei might be referring to. Perhaps you could provide a citation or some context.

Last edited: May 13, 2015
8. May 13, 2015

### Ibix

Assuming you are talking about the formula in the "Frame of reference" section of the Wikipedia article linked above, Ei is the kinetic energy measured by observers at rest in frame i, which is the Center Of Mass (COM) frame. Ek is the kinetic energy measured by observers at rest in some other frame which is moving with speed V with respect to frame i.

Note that the formulae in that web page are non-relatisistic ones. There may be a relativistic section - I haven't read the whole thing.

9. May 13, 2015

### Quarlep

So in my sitatuion The observer in the train will measure a kinetic energy Ei plus the outside observer kinetic energy (which observer i see that objects moves a velocity v) ,that will be his (the observer in the train) total kinetic energy.If thats true how can we calculate Ei.

Last edited: May 13, 2015
10. May 13, 2015

### Ibix

In your case, since there's only one thing (the train) it is stationary in its Center Of Mass frame, so Ei=0. Its kinetic energy in a frame moving at speed v with respect to the train is just $\frac{1}{2}mv^2$, where the mass of the train is m. Or $(\gamma-1)mc^2$, where $\gamma=1/\sqrt{1-v^2/c^2}$ if we're going for the full relativistic treatment.

11. May 13, 2015

### Quarlep

Inside the observer will detect train kinetic energy 1/2mv2 isnt it. You said something different I guess.Just I wanna be sure I have bad english.If you write me again I will be very happy.
Thanks

12. May 13, 2015

### Staff: Mentor

That's not how it works. Since KE is a square function of speed, you have to do your speed transformation first to calculate how fast the observer on the train is moving with respect to the chosen reference. Then you plug that speed into the KE equation.

13. May 13, 2015

### Quarlep

In my question, I asked what we get ,If the observer in the train calculates train kinetic energy.Now the observer inside the train things train speed is zero so train kinetic energy will be zero.But it cant be.The observer which its outside the train call A and the observer which inside the train call B.Train total energy for B will be ET=Ei+1/2Mv2 now our referance frame will be train or B (they are in the same referance frame) russ said I need to calculate speed of observer (B) to referance frame thats zero so we get zero energy (again its not possible) here what I am trying to say .
B will thing" I see A observer moves velocity v " so train kinetic energy will be 1/2mv2 or train is not moving so v is zero . Then Ei is not zero so total energy will be Ei.
Thanks

14. May 13, 2015

### Staff: Mentor

Zero. If an object is not moving, it has no kinetic energy. Kinetic energy is frame-dependent.

If you're just looking at a single object, or a system that has all of its parts at rest relative to each other, then $E_i$ is zero, and since $v$ is also zero in the train frame, the train's total kinetic energy is zero. That does not mean its total energy is zero; it still has its rest energy, $Mc^2$.

No. $E_i$ is only nonzero if the system consists of internal parts that are moving relative to its center of mass. For example, suppose there is a merry-go-round inside the train, whose center is anchored to the train, and it is rotating. Then the merry-go-round will have some rotational kinetic energy relative to the train's center of mass; this energy will appear as a nonzero $E_i$ in the equation you see on the Wikipedia page. But this energy has nothing to do with the velocity $v$ of the train as a whole relative to something else.

15. May 13, 2015

### Staff: Mentor

Kinetic energy requires that you define a frame of reference against which to measure it. What is that frame?
Well, it can be, but only if he defines a frame of reference in which the train is stationary. He can do that, but why would he if what he is really looking for is the train's KE with respect to the ground?
So again: you can't use three different reference frames in different parts of the problem. Pick a rest frame, pick an observer and do the whole problem using only those two things. The consistency will eliminate the logical contradictions you are creating.

16. May 13, 2015

### Quarlep

The observer inside the train

I am defining that stationary referance frame observer in the train.

Referance frame is B observer is also B.

17. May 13, 2015

### Staff: Mentor

OK, so since the train is stationary with respect to that frame, the kinetic energy with respect to that frame is zero.

18. May 13, 2015

### Quarlep

So If I change referance frame to A, B will se 1/2Mv^2 and If I pick referance frame to ground also its 1/2Mv^2 .If these things are rhen true thanks for help I understand the idea.

19. May 13, 2015

### Staff: Mentor

Yes, it is true that kinetic energy is frame dependent, just like (because) velocity is frame dependent. As long as you recognize that asking about the kinetic energy with respect to an additional frame results in a different answer and the two answers don't have to match, then you should be fine.

20. May 13, 2015

### Quarlep

I ll will check that If I found correct answer and I ll post it.For now thanks