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| Time dilation | |
| Lorentz factor | |
| Length contraction | |
| Galilean transformation | |
| Lorentz transformation | |
| Inverse Lorentz transformation | |
| Space-time invariants | |
| Relativistic velocity addition | |
| Relativistic Doppler effect for wavelength | |
| Relativistic Doppler effect for frequency | |
| Relativistic momentum | |
| Relativistic total energy | |
| Relativistic kinetic energy |
How are the classical laws of conservation of energy and conservation of mass modified by modern relativity?
What happens to the mass of water in a pot when it cools, assuming no molecules escape or are added? Is this observable in practice? Explain.
Because it loses thermal energy, which is the kinetic energy of the random motion of its constituent particles, its mass decreases by an extremely small amount, as described by energy-mass equivalence.
Consider a thought experiment. You place an expanded balloon of air on weighing scales outside in the early morning. The balloon stays on the scales and you are able to measure changes in its mass. Does the mass of the balloon change as the day progresses? Discuss the difficulties in carrying out this experiment.
The mass of the fuel in a nuclear reactor decreases by an observable amount as it puts out energy. Is the same true for the coal and oxygen combined in a conventional power plant? If so, is this observable in practice for the coal and oxygen? Explain.
Yes, in principle there would be a similar effect on mass for any decrease in energy, but the change would be so small for the energy changes in a chemical reaction that it would be undetectable in practice.
We know that the velocity of an object with mass has an upper limit of c . Is there an upper limit on its momentum? Its energy? Explain.
Given the fact that light travels at c , can it have mass? Explain.
Not according to special relativity. Nothing with mass can attain the speed of light.
If you use an Earth-based telescope to project a laser beam onto the moon, you can move the spot across the moon’s surface at a velocity greater than the speed of light. Does this violate modern relativity? (Note that light is being sent from the Earth to the moon, not across the surface of the moon.)
What is the rest energy of an electron, given its mass is Give your answer in joules and MeV.
0.512 MeV according to the number of significant figures stated. The exact value is closer to 0.511 MeV.
Find the rest energy in joules and MeV of a proton, given its mass is
If the rest energies of a proton and a neutron (the two constituents of nuclei) are 938.3 and 939.6 MeV, respectively, what is the difference in their mass in kilograms?
to two digits because the difference in rest mass energies is found to two digits
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