Inquiry into Physics
8th Edition
ISBN: 9781337515863
Author: Ostdiek
Publisher: Cengage
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Chapter 12, Problem 1C
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The expression for relativistic kinetic energy is similar to classical kinetic energy in the limit of low speeds.
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Consider a highly relativistic particle. Discuss what is meant by the term “highly relativistic.” (Note that, in part, it means that the particle cannot be massless.) Construct a problem in which you calculate the wavelength of such a particle and show that it is very nearly the same as the wavelength of amassless particle, such as a photon, with the same energy.Among the things to be considered are the rest energy of the particle (it should be a known particle) and its total energy, which should be large compared to its rest energy.
(a) Prepare a graph of the relativistic kinetic energy and the classical kinetic energy, both as a function of speed, for an object with a mass of your choice. (b) At what speed does the classical kinetic energy underestimate the experimental value by 1%? (c) By 5%? (d) By 50%?
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Chapter 12 Solutions
Inquiry into Physics
Ch. 12 - Prob. 1AACh. 12 - Prob. 2AACh. 12 - Prob. 1PIPCh. 12 - Prob. 1MIOCh. 12 - Prob. 2MIOCh. 12 - Prob. 1QCh. 12 - Prob. 2QCh. 12 - Prob. 3QCh. 12 - Prob. 4QCh. 12 - Prob. 5Q
Ch. 12 - Prob. 6QCh. 12 - Prob. 7QCh. 12 - Prob. 8QCh. 12 - Prob. 9QCh. 12 - (Indicates a review question, which means it...Ch. 12 - Prob. 11QCh. 12 - Prob. 12QCh. 12 - (Indicates a review question, which means it...Ch. 12 - Prob. 14QCh. 12 - Prob. 15QCh. 12 - Prob. 16QCh. 12 - Prob. 17QCh. 12 - Prob. 18QCh. 12 - Prob. 19QCh. 12 - Prob. 20QCh. 12 - Prob. 21QCh. 12 - Prob. 22QCh. 12 - Prob. 23QCh. 12 - Prob. 24QCh. 12 - Prob. 25QCh. 12 - Prob. 26QCh. 12 - Prob. 27QCh. 12 - Prob. 28QCh. 12 - Prob. 29QCh. 12 - Prob. 30QCh. 12 - Prob. 31QCh. 12 - Prob. 32QCh. 12 - Prob. 33QCh. 12 - Prob. 34QCh. 12 - Prob. 35QCh. 12 - Prob. 36QCh. 12 - Prob. 37QCh. 12 - Prob. 38QCh. 12 - Prob. 39QCh. 12 - Prob. 40QCh. 12 - Prob. 41QCh. 12 - Prob. 42QCh. 12 - Prob. 43QCh. 12 - Prob. 44QCh. 12 - Prob. 1PCh. 12 - How fast would a muon have to be traveling...Ch. 12 - The lifetime of a free neutron is 886 s. If a...Ch. 12 - Prob. 4PCh. 12 - The formula for length contraction gives the...Ch. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - Prob. 8PCh. 12 - Prob. 9PCh. 12 - . In a particular beam of protons, each particle...Ch. 12 - . A particle of rest energy 140 MeV moves at a...Ch. 12 - . If the relativistic kinetic energy of a particle...Ch. 12 - Prob. 13PCh. 12 - Prob. 14PCh. 12 - Prob. 15PCh. 12 - . How many years would you have to wait to observe...Ch. 12 - Prob. 17PCh. 12 - Prob. 18PCh. 12 - . A compact neutron star has a mass of kg (about...Ch. 12 - Prob. 20PCh. 12 - Prob. 21PCh. 12 - Prob. 22PCh. 12 - Prob. 23PCh. 12 - Prob. 24PCh. 12 - Prob. 25PCh. 12 - Prob. 26PCh. 12 - Prob. 27PCh. 12 - Prob. 28PCh. 12 - Prob. 29PCh. 12 - Prob. 30PCh. 12 - Prob. 31PCh. 12 - . If the average lifetime of a proton was 1033...Ch. 12 - Prob. 1CCh. 12 - Prob. 2CCh. 12 - Prob. 3CCh. 12 - Prob. 4CCh. 12 - Prob. 5CCh. 12 - Prob. 6CCh. 12 - Prob. 7CCh. 12 - Prob. 8CCh. 12 - Prob. 9CCh. 12 - Prob. 10C
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- Check Your Understanding A particle is traveling through Earth’s atmosphere at a speed of 0.750c. To an earthbound observer, the distance it travels is 2.50 km. How far does the particle travel as viewed from the particle’s reference frame?arrow_forwardOne cosmic ray neuron has a velocity of 0.250c relative to the Earth. (a) What is the neutron's total energy in MeV? (b) Find its momentum. (c) Is in this situation? Discuss in terms of the equation given in part (a) of the previous problem.arrow_forward. If the relativistic kinetic energy of a particle is 9 times its rest energy, at what fraction of the speed of light must the particle be traveling?arrow_forward
- 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.arrow_forwardA yet-to-be-built spacecraft starts from Earth moving at constant speed to the yet-to-be-discovered planet Retah, which is 20 lighthours away from Earth. It takes 25 h (according to an Earth observer) for a spacecraft to reach this planet. Assuming that the clocks are synchronized at the beginning of the journey, compare the time elapsed in the spacecraft’s frame for this one-way journey with the time elapsed as measured by an Earth-based clock.arrow_forwardCheck Your Understanding What is the kinetic energy of an electron if its speed is 0.992c?arrow_forward
- Is it possible for an external force to be acting on a system and relativistic momentum to be conserved? Explain.arrow_forwardA spaceship, 200 m long as. seen on board, moves by the Earth at 0.970c. What is its length as measured by an earthbound observer?arrow_forwardCheck Your Understanding a. A particle travels at 1.90108m/sand lives 2.10108swhen at rest relative to an observer. How long does the particle live as viewed in the laboratory? b. Space craft A and B pass in opposite directions at a relative speed of 4.00107m/s . An internal clock in space craft A causes it to emit a radio signal for 1.00 s. The computer in spacecraft B corrects for the beginning and end of the signal having traveled different distances, to calculate the time interval during which ship A was emitting the signal. What is the time interval that the computer in spacecraft B calculates?arrow_forward
- What happens to the relativistic Doppler effect when relative velocity is zero? Is this the expected result?arrow_forwardSame two observers as in the preceding exercise, but now we look at two events occurring in spaceship A. A photon arrives at the origin of A at its time and another photon arrives atat in the frame of ship A. (a) Find the coordinates and times of the two events as seen by an observer in frame B. (b) In which frame are the two events simultaneous and in which frame are they are not simultaneous?arrow_forwardSuppose our Sun is about to explode. In an effort to escape, we depart in a spaceship at v = 0.80c and head toward the star Tau Ceti, 12 lightyears away. When we reach the midpoint of our journey from the Earth, we see our Sun explode and, unfortunately, at the same instant we see Tau Ceti explode as well. (a) In the spaceship’s frame of reference, should we conclude that the two explosions occurred simultaneously? If not, which occurred first? (b) In a frame of reference in which the Sun and Tau Ceti are at rest, did they explode simultaneously? If not, which exploded first?arrow_forward
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