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Chapter 33: Problem 65
At what speed are a particle's kinetic and rest energies equal?
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A spaceship travels at \(0.80 c\) from Earth to a star 10 light years distant, as measured in the Earth-star reference frame. Let event A be the ship's departure from Earth and event B its arrival at the star. (a) Find the distance and time between the two events in the Earth-star frame. (b) Repeat for the ship's frame. (Hint: The distance in the ship frame is the distance an observer has to move with respect to that frame to be at both events-not the same as the Lorentz- contracted distance between Earth and star.) (c) Compute the square of the spacetime interval in both frames to show explicitly that it's invariant.
A spaceship passes by you at half the speed of light, and you determine that it's \(35 \mathrm{m}\) long. Find its length as measured in its rest frame.
Two stars are 50 ly apart, measured in their common rest frame. How far apart are they to a spaceship moving between them at \(0.75 c ?\)
The quantity \(\vec{E} \cdot \vec{B}\) is invariant. What does this say about how different observers will measure the angle between \(\vec{E}\) and \(\vec{B}\) in a light wave?
You're designing a Michelson interferometer in which a speedof-light difference of \(100 \mathrm{m} / \mathrm{s}\) in two perpendicular directions is supposed to shift the interference pattern so a bright fringe of \(550-\) nm light ends up where the adjacent dark fringe would be in the absence of a speed difference. How long should you make the interferometer's arms?
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