Assignment 10

Problem 1:

Find the speed of an electron that has been accelerated from rest by an electric field through a potential increase of
(a) 20.0 kV and
(b) 5.00 MV, typical of a high-voltage x-ray machine.
Give your answers in units of the speed of light.

Problem 2:

Spaceship A moving with speed v = 0.5 c with respect to earth is chased by spaceship B, moving with speed v = 0.6 c with respect to earth. When ship A passes earth at tearth = tA = 0, ship B is 10-3 ly behind ship A, as measured by an observer on earth?
(a)  When, as measured on earth, will ship B catch up with ship A.  What is the ships' distance from earth at that time?
(b)  What is the speed with which ship B is approaching ship A, as measured by ship A?
(c)  When, as measured on ship A, will ship B catch up with ship A?

Problem 3:

A rocket with a proper length of 700 m is moving in the positive x-direction at a speed of 0.9c.  It has two clocks, one in the nose and one in the tail, that have been synchronized in the frame of the rocket.  A clock on the ground and the nose clock on the rocket both read t = 0 as they pass, i.e. have the same x-coordinate.
(a)  At t = 0, what does the tail clock on the rocket read in the frame of an observer on the ground? 
(b)  When the tail clock on the rocket passes the ground clock,
  i.  what does the tail clock read in the frame of an observer on the ground?
  ii.  what does the nose clock read in the frame of an observer on the ground?
  iii.  what does the nose clock read in the frame of an observer on the rocket?
(c)  At t = 1 h, as measured on the rocket, a light signal is sent from the nose of the rocket to an observer standing by the ground clock.  What does the ground clock read when the observer receives this signal?  (Assume distances perpendicular to the x-axis are negligibly small compared to distances along the x-axis.)
(d)  When the observer on the ground receives the signal, he sends a return signal to the nose of the rocket.  When is this signal received at the nose of the rocket as seen on the rocket?

Problem 4:

The space ship leaving Earth is constructed to make the occupants feel comfortable as it accelerates.  It has an acceleration g = 10 m/s2 in its own rest frame.
(a)  How long does it take the ship to reach a speed v = 0.1 c in its own rest frame and in the Earth frame?
(b)  How long does it take the ship to reach a speed v = 0.5 c in its own rest frame and in the Earth frame?

Problem 5:

Consider the decay Λ0 --> n + π0, followed by π0 --> 2γ.
(a)  Given the masses MΛ, Mn and Mπ, find the energy of the decay products n and π0 in the rest frame of the Λ0.
(b)  The two gamma rays from the decay of the π0 are observed to have equal energies in the rest frame of the Λ0.  Find the angle between the two gamma rays in this frame, in terms of the particle masses.