35. Special Relativity

What is the speed of a pion if its average lifetime is measured to be 4.80 x 10^-8 s? At rest, its average lifetime is 2.60 x 10^-8 s.

Tell It to the Judge. (a) How fast must you be approaching a red traffic light (λ = 675 nm) for it to appear yellow (λ = 575 nm)? Express your answer in terms of the speed of light. (b) If you used this as a reason not to get a ticket for running a red light, how much of a fine would you get for speeding? Assume that the fine is \$1.00 for each kilometer per hour that your speed exceeds the posted limit of 90 km/h.

A star is 23.5 light-years from Earth. How long would it take a spacecraft traveling 0.950c to reach that star as measured by observers on the spacecraft?

Rocket A passes Earth at a speed of 0.65c. At the same time, rocket B passes Earth moving 0.90c relative to Earth in the same direction. How fast is B moving relative to A when it passes A?

(II) You travel to a star 115 light-years from Earth at a speed of 2.90 x 10⁸ m/s. What do you measure this distance to be?

A distant quasar is found to be moving away from the earth at 0.80c. A galaxy closer to the earth and along the same line of sight is moving away from us at 0.20c. What is the recessional speed of the quasar, as a fraction of c, as measured by astronomers in the other galaxy?

A quasar emits familiar hydrogen lines whose wavelengths are 8.5% longer than what we measure in the laboratory.

(a) Using the Doppler formula for light, estimate the speed of this quasar.

(b) What result would you obtain if you used the “classical” Doppler shift discussed in Chapter 16?

A healthy astronaut’s heart rate is 60 beats/min . Flight doctors on Earth can monitor an astronaut’s vital signs remotely while in flight. How fast would an astronaut be flying away from Earth if the doctor measured her heart rate as 52 beats/min?

What minimum amount of electromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this process. See Section 37–5.)

An electron (m = 9.11 x 10⁻³¹ kg) is accelerated from rest to speed v by a conservative force. In this process, its potential energy decreases by 7.20 x 10⁻¹⁴ J . Determine the electron’s speed, v.

A proton is accelerated to 0.999c. By what factor does the proton's momentum exceed its Newtonian momentum?

A source of electromagnetic radiation is moving in a radial direction relative to you. The frequency you measure is 1.25 times the frequency measured in the rest frame of the source. What is the speed of the source relative to you? Is the source moving toward you or away from you?

Electrons pass through the parallel electrodes shown in FIGURE EX37.9 with a speed of 5.0×10⁶ m/s. What magnetic field strength and direction will allow the electrons to pass through without being deflected? Assume that the magnetic field is confined to the region between the electrodes.

Calculate the maximum kinetic energy of the electron when a muon decays from rest via μ⁻ ⟶ e⁻ + vₑ + vμ. [Hint: In what direction do the two neutrinos move relative to the electron in order to give the electron the maximum kinetic energy? Both energy and momentum are conserved; use relativistic formulas.]