Suppose you are running with speed of 5m/s (with respect to ground, mass=20kg)

and there is a mechanism by which all of your kinetic energy is converted to electrical energy which is used to light a bulb of constant power

Case 1: 'L' who is at rest on ground reports the duration for which the bulb has glowed

Case 2: 'M' who is running opposite to you with speed 5m/s also reports the duration for which the bulb has glowed

Do both the cases have same answer???

How much amount of energy will be converted to electrical energy in both the frame??

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## Comments

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TopNewestI agree with @Shashwat Shukla , if you look into the mechanism of the process, suppose you press a spring and the energy stored in spring is converted to electrical energy,

Then the spring is only compressed by the relative motion of your hand and spring. if the spring's tip was moving as fast as you, Then the energy is not stored in spring and instead simply remains as the kinetic energy of the particles as seen from the frame forever.

But ofcourse, this simply means that our assumption that a device can exist which converts the whole kinetic energy in

all framesinto electric energy is impossible.Suppose it is his pedalling that does the job, then only the circular motion of the pedals affects the energy stored and any free translation of all particles causes no change.

Another perhaps more rigorious statement would be to state that energy is stored or removed when the body is

deformedand deformity requires relative motion between its various particles.Now you might ask, when we throw a stone, energy is stored as kinetic energy but no deformity occurs? Well consider the whole system, We are throwing the stone, it is moving forward, so we are actually pushing it and hence our hand is actually moving slightly faster than the stone at each instant to provide the stone its extra energy and hence there is relative motion here as well.

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Thank you @shashwat shukla and @Mvs Saketh

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I agree. However the term \(deform\) for non-contact forces must be extended to mean relative motion (and not just change in the shape of the body).

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Yes, both cases have same answer. And in both the ground frame and in the frame of 'M', the amount of energy converted is identical and equal to \(1/2*20*25=250J\)

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Then what about the other 250 joules in frame of M?? Do the efficiency of mechanism changes just by changing the reference frame???

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Hmm. I thought you might have done that too. check out these links 1

wiki

3

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B)The ambiguity arises because you haven't really defined this 'mechanism'.

As I understand it, what you are saying is this: Look at the man in a particular reference frame, calculate his kinetic energy and convert it all into electrical energy. And your question is, why it isn't the same in all frames.

That's precisely because the mechanism is \(frame \quad dependent\) (meaning that you have one machine corresponding to each frame, and not one unique machine) and this 'mechanism' cannot actually exist(because if it did exist, then as you said, the amount of light emitted will be the same in every frame).

So why can't it exist? We have to analyse this 'mechanism'. Well, while this may not be perfectly rigorous reasoning, look at it this way:

One possible machine is as follows: Make the man push against a big spring which is coupled to a dynamo. It is immediately obvious as to why the duration of the bulb glowing will be the same in all frames: the \(relative\) velocity between the spring and the man at all times and in all frames will be the same.

Yet a more general way to say the same is to note that the way in which energy is converted/transferred from one form to another is via an interaction of bodies through forces. The important point is that these \(forces \quad are \quad frame \quad independent\)(if we are working with inertial frames of reference) as this is just Einstein's equivalence principle. And thus, as the forces remain the same, the work done by the man on the device is also the same(this work appears as electrical energy).

C)The total energy is also not conserved under a change of reference frame simply because the K.E is not. If you're wondering if some 'other' form of energy like P.E can change so that the net effect is that total energy is a constant, my explanation remains the same: Any form of potential energy exists only by virtue of the body having done work against a force (like gravity or electrostatic force),which as mentioned before, is frame invariant. But is there any other form of energy apart from K.E and P.E?

Not that I know of; as vibrational, rotational energy etc. are also just other forms of K.E

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@Azhaghu Roopesh M @Mvs Saketh @Shashwat Shukla , help us out here?

To tell you the truth, I don't know how to explain it to you. That means that i don't understand it well either.Log in to reply

So does it really come out to be so? Does total energy of the isolated system depends upon the frame?

Or I have done some mistake ?

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@Raghav Vaidyanathan ,@Mvs Saketh ,@Shashwat Shukla ,@uddeshya upadhyay

How about anyone of you make a question on this just to check the conceptual clarity of others , what say ?

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We can also say that energy or energy transformations require the presence of matter(Einstein)(vaguely). Since some properties of matter(like kinetic energy) depend upon the frame of reference,,we can say that energy transformations (in this case) will depend upon the relative motion of the runner and the device(which has to be some form of matter).

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The question itself is incomplete ... When you say " there is a mechanism by which

all of your kinetic energyis converted to electrical energy" Then kinetic energy in which frame you are talking about..??Log in to reply