## 08 February 2011

### Relativity

Problem 1.1.

Calculate the velocity of an electron with kinetic energy of 100 keV, 1MeV and 10 MeV.

Problem 1.2.

Calculate the relativistic masses and momenta of the electrons in the three cases in Problem 1.1.

Problem 1.5.

Calculate the velocities at which the electron and proton masses are 2 percent greater than their rest energies.

Problem 1.7.

Two spaceships approach each other, one traveling at 0.3c and the other at 0.6c. What is their relative velocity of approach as seen by an observer on either ship?

Problem 1.9.

Event 1 occurs at x1 = 10m at time t1 = 0. Event 2 occurs at x2 = 600 000 010m at time t2 = 1.8 s. Is there any reference frame where these two events can be reversed so that event 2 occurs before event 1? Prove your answer.

Problem 1.11.

A space shuttle that is 20m long in its rest frame is passing a space docking station which is 110m long in the docking station rest frame. If the space shuttle is moving at 0.6c relative to the station, what will be the length of the docking station to the person on the shuttle? How long will it take the shuttle from the time the front tip of the shuttle reaches one end of the station until the front tip is seen by the person on the shuttle to reach the other end of the station?

Problem 1.13.

An object from outer space moves past the Earth at 0.8c. You measure the length of the object as 3.3m in the Earth’s frame. In the object’s rest frame, what is its length?

Problem 1.15.

A 30-year-old female astronaut makes a trip from the Earth to a star that is 6 light years away at an average velocity of 0.9c. Neglecting the time it takes to turn the spaceship around for the return, how old is the woman when she returns to Earth? How old is her boss, who was 40 when she left? Explain which one aged more than the other and why it was that person who aged more.

Problem 1.17.

Suppose you see that light from a particular type of atom in a distant star that should be at 950nm actually occurs at 525 nm. What is the velocity of the star relative to you, including the direction of the velocity?

Problem 1.19.

Suppose the Concorde flies from Paris to New York, a flying distance of about 3800 miles at a supersonic velocity of 1200 miles/hour. Neglecting the time and distance to reach that velocity, what is the distance as measured by an observer on the plane? What is the time to cover the 3800 miles as measured by a ground observer for a clock on the ground? What is the time as measured by the observer on the ground for the clock on the Concorde?