SPH4U: Relativity Problems | 1. 10. 1]. 12. A cosmic ray (a muon) enters Earth's atmosphere 60 km above Earth's surface. It reaches a detector on the ground after travelling 400 as (u = 10'?) in the atmosphere, as measured by experimenters on the ground. How long does the journey take according to the muon? You and your friends here on Earth are watching a live video showing a clock onboard a fast moving rocket (more popular than replace videos). At one moment the clock in the video reads 10:23 am and at another moment it reads 10:29 am. You noticed that 12 minutes elapsed on your own clock. What speed was the rocket moving at? An astronaut travels to a star system 4.5 ly away as measured by Mission Control at a speed of 0.9 1:. Assume the times needed to speed up and slow down are negligible. (a) How much time does the journey take according to Mission Control on Earth? (b) How long does the journey take according to the astronaut? An astronaut travels on a journey to a distant star, leaving Earth at the age of 46 years and arriving at the star when she is 61 years old. Scientists at mission control on Earth measured that the trip takes 120 years. What was the speed of the rocket? According to the scientists, how far away is the star? Jill claims that her new rocket is 100 m long. As she ies past your house, you measure the rocket's length and nd that it is only 80 In. What is Jill's speed? A muon travels 60 km through the atmosphere (similar to question #1) at a speed of 0.9997 c. According to the muon, how thick is the atmosphere? Our Milky Way galaxy is 100,000 ly in diameter. A spaceship crossing the galaxy measures the galaxy's diameter to be a mere 100 1y. (a) What is the speed of the spaceship relative to the galaxy? (b) How long is the crossing time as measured in the galaxy's frame of reference? A muon (1.883 x 10'28 kg) enters the atmosphere with a speed of 0.8 c. When it reaches the ground, it is traveling at 0.7 c. How much energy (in joules) did it lose? During radioactive beta-decay, a neutron (1.6749x10'27 kg) at rest decays into a very slow moving proton (1 .6726x10'17 kg) and a fast electron (9.1091t10'31 kg). What is the speed of the electron? (Hint: nd the total energy of the electron) In an attempt to reduce the extraordinarily long travel times for voyaging to distant stars, some people have suggested travelling close to the speed of light. Suppose you wish to visit the red giant start Betelgeuse, which is 430 1y away, and that you want your 20 000 kg rocket to move so fast (0.99892 c) that you age only 20 years during the journey. (a) What is the distance between Earth and Betelgeuse according to an observer in the rocket? (b) How much energy is needed to accelerate the rocket to this speed? (c) Compare this amount of energy to the total used by the United States in the year 2010, which was roughly ].01:1020 I. The nuclear reaction that powers the sun involves the fusion of four protons (mp = 1.673x10'17 kg) into a helium nucleus (mm = 6.645111027 kg). The process involves several steps, but the net reaction is simply: 4p > He + energy. How much energy is released overall in each fusion process? Give your answer in J and MeV. Consider the inelastic collision: e' + e+> e' + e+ + e' + e+ in which an electron-positron pair is produced in a head-on collision between an electron and positron moving in opposite directions at the same speed. All the particles are moving very slowly after the collision. (a) What is the total kinetic energy of the electron and positron before the collision? (b) What is the speed of an electron with this energy? 1. 347 us 5. 0.6 c 9. 0.918 c 2. 0.866 c 6. 1.47 km 10. (a) 19.981y (b).'i.691c1022 J, (c) 3. (a) 5 yr, (b) 2.18 yr 7. (a) 0.9999995e, (b) 100 000.05 yr 369 times greater! 4. 0.992 c, 1191y 8. 4.52 x 10-12 J 11. 4.22;;10-12 J, 26.4 MeV 12. (a) 1.022 Mev, (b) 0.866 c From R. Knight, Physicsfor Scientists and Engineers. A Strategic Approach. Pearson Education, 2013 111