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A photon decays into an electron-positron pair. What is the kinetic energy of the electron if its speed is ?
A mass of 50 g is completely converted into energy. What is the energy that will be obtained when such a conversion takes place?
Show that relativistic kinetic energy becomes the same as classical kinetic energy when .
Relativistic kinetic energy is given as
where
Classical kinetic energy is given as
At low velocities , a binomial expansion and subsequent approximation of gives:
or
Substituting in the expression for gives
Hence, relativistic kinetic energy becomes classical kinetic energy when .
The relativistic energy of a particle in terms of momentum is given by:
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.
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.
We know that the velocity of an object with mass has an upper limit of . Is there an upper limit on its momentum? Its energy? Explain.
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