A man I met the other day found out I am studying physics and asked me a question about energy, namely kinetic energy. Below in the box is an edited version of what he postulated to me.(adsbygoogle = window.adsbygoogle || []).push({});

He seems to want to determine his speed compared to a universal reference frame, which is silly, but I haven't been able to reason out an interesting question that occurred to me in listening to him...

Imagine you are at rest in a reference frame (S). You have a spaceship with 16 units of potential chemical energy (E_chem). You use E_chem to accelerate your spaceship to a velocity (v) of 5.66. Your spaceship now has 16 units of kinetic energy (K).

In a completely different scenario, you are at rest in reference frame (S') which is moving at a velocity of 4 (V') relative to the reference frame of the first situation, S. in S' you use 8 units of E_chem to accelerate your ship to a velocity of 4 relative to S'. Given that you were moving initially with respect to S with a velocity of 4 and a kinetic energy of 8, and seeing that your final velocity is now 8 compared to S after using 8 units of E_chem (V' + v), it seems, by comparing the scenarios that kinetic energy is linearly related to velocity.

but K = .5*m*v^2.

Okay, either I just haven't done energy equations in too long, or I'm missing something, but something is wrong here. care to explain?

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0) I am in a space ship.

1) I am at rest relative to a buoy that I will take to be my reference point.

2) I accelerate the first time, using 8 units of energy, and measure a

velocity of 4 relative to the buoy.

3)I launch another buoy (whose mass is negligible relative to the mass of my space ship) so that it is at rest with respect to me (and thus moving at a velocity of 4 relative to the first buoy).

4) I accelerate the second time, using 8 units of energy and measure a velocity of 1.66 relative to the second buoy, and 5.66 to the first.

Finally, in view of the above, it seems to that I can distinguish

between being at rest, and being in motion. The method (given in the

box below) is simple, although it *differs* from the modified

scenario just explained above... however, were the method given in the

box below to fail, it seems to me that the failure would force a

contradiction to what was said above.

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I am adrift in space, so very far away from everything that I have no

reference points whatsoever. What do I do to determine my speed? Simple.

I launch a *single* bouy (whose mass is negligible relative to the mass of my

space ship), so that it is at rest relative to myself,

and then accelerate using 8 units of energy. Next, I measure my

velocity relative to the bouy!

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If I happened to be at rest, my velocity relative to the bouy will be

different that it would have been if I happened to be in motion...

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# Energy enigma in uniformly moving reference frames (I hope this doesn't double post)

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