- #1
davidbenari
- 466
- 18
In class we had a conceptual problem:
There will be a race between two springs. Both will receive the same initial impulse, but one has been agitated and is therefore oscillating in some way, the other is just still. Who arrives first?
The answer is that the still spring arrives first because it has less energy.
However I don't really get this. I know of the mass energy equivalence, but my understanding is that you actually have to consider the relativistic total energy, not just ##E=mc^2##. The spring has more energy, right, but this because each particle in the system has a kinetic energy. The rest energy is left unaltered. Namely, the total energy of the oscillating system would be ##E_{tot}=\sum_i \frac{\gamma m_i c^2}{\sqrt{1-u^2/c^2}} = \frac{\gamma M c^2}{\sqrt{1-u^2/c^2}}## … ##M## is still the original inertial mass.
An oscillating system hasn't more inertial mass, this is nonsense to me. The same analysis could be done in the case of a hot body. People say that a hot coffee is more massive than a cold one, but because of a similar analysis as above I would say that's wrong.
Places where inertial mass could be changed, though, are nuclear processes and other things I have no knowledge of.
Obviously I am the one who is wrong. But I want to know why.
Thanks.
There will be a race between two springs. Both will receive the same initial impulse, but one has been agitated and is therefore oscillating in some way, the other is just still. Who arrives first?
The answer is that the still spring arrives first because it has less energy.
However I don't really get this. I know of the mass energy equivalence, but my understanding is that you actually have to consider the relativistic total energy, not just ##E=mc^2##. The spring has more energy, right, but this because each particle in the system has a kinetic energy. The rest energy is left unaltered. Namely, the total energy of the oscillating system would be ##E_{tot}=\sum_i \frac{\gamma m_i c^2}{\sqrt{1-u^2/c^2}} = \frac{\gamma M c^2}{\sqrt{1-u^2/c^2}}## … ##M## is still the original inertial mass.
An oscillating system hasn't more inertial mass, this is nonsense to me. The same analysis could be done in the case of a hot body. People say that a hot coffee is more massive than a cold one, but because of a similar analysis as above I would say that's wrong.
Places where inertial mass could be changed, though, are nuclear processes and other things I have no knowledge of.
Obviously I am the one who is wrong. But I want to know why.
Thanks.