Exam 26: Relativity

The time of flight (TOF) technique is routinely used to distinguish between different particle species in a particle detector. Calculate the difference in time interval required for a proton (mass 938 MeV/c²) and a muon (mass 106 MeV/c²) to travel 2.5 m, assuming each particle has a momentum of 255 MeV/c.

At what speed would an astronaut need to travel so that he would age 4.20 years while traveling a distance (as measured by an Earth observer) of 4.20 ly?

A pair of observers moving relative to one another will always agree upon all but which of the following?

How tall is Mount Everest from the perspective of a cosmic ray muon traveling straight down toward the Earth at 0.99c? Observers at rest relative to the ground measure the height of Mt. Everest to be 8848 m.

A spaceship is observed by a stationary observer to be moving at 0.600 c. A laser beam is directed straight ahead from the front of the spaceship. How fast does the laser beam travel relative to the stationary observer?

Relative to a stationary observer, a moving clock

If a proton has a kinetic energy of 1.000 GeV, what is its speed? (m_p = 938 MeV/c²)

How does the kinetic energy of a proton change when its total energy doubles?

Which of the following is a postulate of special relativity?

If the velocity of a nonrelativistic object is doubled, its energy is quadrupled. This is only true for velocities that are very small compared with the speed of light. At what velocity would a doubling of velocity result in a doubling of energy?

The Sun radiates energy at a rate of 3.8 × 10²⁶ W. Assuming that rate is constant, approximately how long does it take for the Sun to lose an amount of mass equal to the mass of the Earth (6.0 × 10²⁴ kg)?

An electron has a rest energy of 0.511 MeV. At what speed would its kinetic energy equal 1.022 MeV?

What are the minimum and maximum values for the Lorentz factor γ, respectively?

A rocket speeding by the Earth at 0.917c is roughly cylindrical in shape and oriented such that its axis is parallel to its velocity. At rest, it is measured to have a radius of 15 m and a length of 150 m. When speeding by, what is its volume as measured by observers on Earth?

The conclusion of the Michelson-Morley experiments was that

At what speed is the relativistic momentum five times the value calculated classically?

How much energy is released in a nuclear reactor if the total mass of the fuel decreases by 1.0 g?

The front of a spacecraft forms a point (like the tip of a cone) with an interior opening angle of 60°. As the spacecraft increases speed relative to Earth, what happens to this angle as observed in the Earth frame?

Protons are sent at 0.900 c down a tube of length 27.0 m. How long does it take for the protons to travel this distance as measured in the lab?

An electron is accelerated from rest through a potential difference of 1.0 MV. If the rest energy of the electron is 0.511 MeV, how fast is the electron moving?