35. Special Relativity

A firecracker explodes in reference frame S at t = 1.0 s. A second firecracker explodes at the same position at t = 3.0 s. In reference frame S', which moves in the x-direction at speed v, the first explosion is detected at x' = 4.0 m and the second at x' = -4.0 m. What is the speed of frame S' relative to frame S?

The star Alpha goes supernova. Ten years later and 100 ly away, as measured by astronomers in the galaxy, star Beta explodes. An alien spacecraft passing through the galaxy finds that the distance between the two explosions is 120 ly. According to the aliens, what is the time between the explosions?

The nuclear reaction that powers the sun is the fusion of four protons into a helium nucleus. The process involves several steps, but the net reaction is simply 4p → ⁴He + energy. The mass of a proton, to four significant figures, is 1.673 x 10^-27 kg, and the mass of a helium nucleus is known to be 6.644 x 10^-27 kg. What fraction of the initial rest mass energy is this energy?

How many electrons, protons, and neutrons are contained in the following atoms or ions: (a) ¹⁰B, (b) ¹³N⁺, and (c) ¹⁷O⁺⁺⁺?