# Relative velocity and work done

1. Jul 31, 2010

### werunom

Consider the usual example of relativity - train and the observer on the platform. Now, the observer is moving according to the train and the train is moving according to the observer.
But we know that it is the train which is spending the energy to move forward. We can neglect the friction and just consider the ideal linear motion of the train on the tracks. So, if we consider two systems: train and the observer, then it is only the train which is doing the work.
So going by this, why cannot we say that the statement "observer is moving wrt train" is false and it is only the train which is moving wrt the observer since the observer is not doing any work?

2. Jul 31, 2010

### Fredrik

Staff Emeritus
Work is only performed during the acceleration phase. During that time, there is a difference. The proper acceleration of the platform is zero while the proper acceleration of the train is non-zero.

Proper acceleration is a coordinate-independent concept. The easiest way to define it is however coordinate-dependent: it's equal to the object's coordinate acceleration in its comoving inertial frame.

3. Jul 31, 2010

### Al68

Because neglecting friction, no work is being done. Energy is only required to either speed up or slow down the train.

That's why the "usual example" is a train with no net force applied, and therefore in uniform motion.

4. Jul 31, 2010

### Ken Natton

The thing is weronum that your argument is nothing new, it has been argued by people struggling with relativity’s counter intuitive concepts ever since Einstein first introduced them. Einstein himself talks about the arguments that were put to him that it is clear that you have to lubricate and maintain the train, you don’t have to lubricate or maintain the railway station. In the case of a modern electric train, it is equally clear that the drive motors are sized to have a sufficient power output to drive the train, they do not have the power output required to knock planet earth off its axis. But all of these arguments are completely irrelevant. Relativity is not interested in how the motion is produced. It only makes assertions about the nature of the resulting motion. And a moments logical thought brings you to the realisation of its simple truth. If you are stood on the station platform, it is abundantly clear that it is the platform that stays where it is and the train that moves. If you are sat on the train, it is just as clear that the seat you are sat in does not move, nor does the book on the table in front of you. It is the outside world that moves in the opposite direction. If you and a friend stood on the station platform before the train left tossing a ball back and forth, then got on the train before it departed and sat there tossing the same ball back and forth as the train drew out of the station, in the reference frame of the moving railway carriage, the ball will behave no differently than it did when you were stood on the station platform.

5. Jul 31, 2010

### werunom

@Ken Natton - I think you got my intention wrong. I not trying to disprove something. The only way I can understand something better is by questioning. By being doubtful I can patch the gap in my understanding. Anyways ... thanks for replying.
For relative velocity, it doesnt matter how the motion is produced - i do agree. But I had this doubt because when we say relative velocity between the participating objects, if one of the objects [the train] stops spending energy, then there would be no relative velocity. So if it is the case, then somehow [I dont know how - thats why I asked the question] it is only the energy spent by train which matters - not that of the platform.

@Al68 - I never knew I would get into trouble by mentioning the word "friction" there. Thanks for correcting.

@Fredrik - Thanks for answering the question.

But with the correction provided by Fedrick & AI68, comes a doubt of mine.
When the train is not in accelerated state, then at least to maintain its constant velocity, it would be doing work at a constant rate. But in this situation, it is the train system which is expending energy and not the platform.
Or are you guys saying that the work done in any natural processes [day to day activities] is always to overcome the friction and to bring out the relative velocity - which is got only by accelerating first?
But then the question arises that in order to maintain the relative velocity, I have to keep spending the energy at a uniform rate. [And I came back to where I started the question :D].
Just correct where I am going wrong.

Thanks!

6. Jul 31, 2010

### DrGreg

The train needs energy to accelerate from rest up to a constant velocity. In the real world it also needs energy to work against friction to maintain a constant velocity. But if we imagine there is no friction at all, then it needs no energy and no force just to continue coasting along at constant velocity. This is Newton's First Law of Motion, already known for a few centuries before Einstein.

7. Jul 31, 2010

### yossell

But only because it's supplying the energy to work against the frictional forces. This is so whatever frame you work in, and the forces are there whatever frame you work in. The forces arise from an interaction between the train and the platform, and can be analysed equally well from any inertial frame, the train's and the platform's. But none of this points to any need to revise the relativity of velocity.

8. Jul 31, 2010

### werunom

Oh ok. Got it! Thanks all for correcting me.

Can you guys suggest any book which explains these basic notions of motion, etc., from philosophical point of view rather than pedagogical approach? The book may not be particularly focused on relativity only... But expounds all kind of nuances of these concepts.