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Chapter 37: Q27P (page 1147)
A particle moves along the x' axis of frame S' with velocity 0.40c. Frame S' moves with velocity 0.60c with respect to frame S. What is the velocity of the particle with respect to frame S?
The velocity of the particle with respect to frame S is 0.81c.
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Continuation of Problem 65. Let reference frame C in Fig. 37-31 move past reference frame D (not shown). (a) Show that
(b) Now put this general result to work: Three particles move parallel to a single axis on which an observer is stationed. Let plus and minus signs indicate the directions of motion along that axis. Particle A moves past particle B at . Particle B moves past particle C at . Particle C moves past observer D at . What is the velocity of particle A relative to observer D? (The solution technique here is much faster than using Eq. 37-29.)
What is the speed parameter for the following speeds: (a) a typical rate of continental drift (1 in./y); (b) a typical drift speed for electrons in a current-carrying conductor (0.5 mm/s); (c) a highway speed limit of 55 mi/h; (d) the root-mean-square speed of a hydrogen molecule at room temperature; (e) a supersonic plane flying at Mach 2.5 (1200 km/h); (f) the escape speed of a projectile from the Earth’s surface; (g) the speed of Earth in its orbit around the Sun; (h) a typical recession of a distant quasar due to the cosmological expansion .
Question:A 5.00-grain aspirin tablet has a mass of 320 mg. For how many kilometers would the energy equivalent of this mass power an automobile? Assume 12.75 km/L and a heat of combustion of for the gasoline used in the automobile.
The premise of the Planet of the Apes movies and books is that hibernating astronauts travel far into Earth’s future, to a time when human civilization has been replaced by an ape civilization. Considering only special relativity, determine how far into Earth’s future the astronauts would travel if they slept for 120 y while traveling relative to Earth with a speed of 0.9990c, first outward from Earth and then back again?
Quite apart from effects due to Earth’s rotational and orbital motions, a laboratory reference frame is not strictly an inertial frame because a particle at rest there will not, in general, remain at rest; it will fall. Often, however, events happen so quickly that we can ignore the gravitational acceleration and treat the frame as inertial. Consider, for example, an electron of speed v =0.992c, projected horizontally into a laboratory test chamber and moving through a distance of 20 cm. (a) How long would that take, and (b) how far would the electron fall during this interval? (c) What can you conclude about the suitability of the laboratory as an inertial frame in this case?
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