College Physics
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Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Is the relativistic rule consistent with the fact that light can have only one speed in all uniformly moving reference frames?
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- What is the classical and relativistic momentum of an object with a mass of 5 kg moving at a speed of 0.8c?arrow_forward4. Relativistic Doppler shift: A spaceship with speed v close to c is moving away from Earth. At regular intervals of time, At', (as measured in the ship's frame), it sends out a light pulse. (a) In the inertial reference frame in which Earth is at rest, give the equation for the time interval between successive pulses being emitted? (b) In the inertial reference frame in which Earth is at rest, what give the equation for the time interval between successive pulses arriving at Earth? Give the answer in terms of v, c and At'. (c) If we convert the arrival time interval into a frequency, via f = 1/At, show that 1 - fs, farrival 1+v/cs» where f = 1/Ať. (This is the formula for the relativistic Doppler shift, by which the light from distant galaxies, moving at relativistic speeds away from us, is red-shifted.) (d) Use the formula from part (c) to find the speed v at which blue light with frequency 650 x 1012 Hz, emitted by the spaceship, will be received on Earth as red light with…arrow_forwardHINT (a) What is the momentum (in kg · m/s) of a proton moving at 0.886c? |kg · m/s (b) At what speed (in m/s) will a particle's relativistic momentum equal twice its classical momentum? |m/sarrow_forward
- Calculate the relativistic energy of a proton moving at 0.9c.arrow_forwardAt what speed (in m/s) is the magnitude of a particle's relativistic momentum 20.8% larger than its classical value? HINT m/sarrow_forwardAn elementary particle of mass 9.5 x 10-27 kg is moving at speed 9 x 107 m/s. (A) Its relativistic momentum in terms of its classical momentum (B) Its KE = . (C) Its rest energy = . (D) Its total energyarrow_forward
- Starting with the definitions of relativistic energy and momentum, show that E2 =P2c2 +m2c4 (Eq. 26.13).arrow_forwardIn a proton linear accelerator, protons are accelerated to have a kinetic energy of 520 Me. What is their relativistic momentum? (The rest mass of a proton is 1.67 × 10-2 kg.). Needs Complete typed solution with 100 % accuracy.arrow_forward12. (a) A particle is traveling through the Earth's atmosphere at a speed of 0.750c. To an earth bound observer, the distance it travels is 2.5km. How far does the particle travel in the particle's frame of reference? (b) Calculate the momentum of an electron traveling at a speed 0.985c? The rest mass of the electron is 9.11 X 10-31 kg.arrow_forward
- A rocket ship carrying passengers blasts off to go from New York to Los Angeles, a distance of about 5000 km. (a) How fast must the rocket ship go to have its own length shortened by 1%? (b) Ignore effects of general relativity and determine how much time the rocket ship’s clock and the ground-based clocks differ when the rocket ship arrives in Los Angeles.arrow_forwardConsider a general equation for the ratio the relativistic length to the proper length. Find an algebraic expression for v/c in terms of, ΔL/ΔLo Show the algebraic form of the equation that you apply and the final final expression.arrow_forwardWhen pions are brought to rest their lifetime is 1.77´10-8 s. A beam of pions is produced in an accelerator and moves at a speed of 0.99c relative to the laboratory. After moving 39 m as measured in the la, half the pions have decayed. a) from the viewpoint of an observer in the lab frame and b) from an observer at rest in the frame of the moving pions that the two numerical results given in the problem for the half-life of the pions are consistent.arrow_forward
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