Relativity, Momentum, and Kinetic Energy

William Bertozzi (as described in an article published in American Journal of Physics, vol 32, p 551, 1964) accelerated electrons with a van de Graff generator to very high speed. He sent the electrons past a gate, then through a tube 8.4 meters long, and into a target. His device was able to measure the time it took for electrons to fly down the tube.

By varying the voltage of the electron gun, he could set the amount of kinetic energy given to the electrons. So, his experiment allowed him to see how kinetic energy varied with speed. In the classical world,


                    1         2
            KE  =  --- * m * v
                    2

So, let's see the results. Below, I've filled in the quantities that Bertozzi actually measured. You should calculate the speed (in meters per second), the kinetic energy via 0.5*m*v^2, and also the "gamma" factor for each run.


                                                2
  time        KE              speed      0.5*m*v       gamma
  (ns)      (Joules)          (m/s)      (Joules)   
---------------------------------------------------------------
  32.3     0.8 x 10^(-13)

  30.8     1.6 x 10^(-13)

  29.2     2.4 x 10^(-13)

  28.4     7.2 x 10^(-13)

Recall that



                                      -1/2
                       [           2 ] 
             gamma  =  [  1 - (v/c)  ]  
                       [             ]

Viewgraph 1

Viewgraph 2

Viewgraph 3

Viewgraph 4

For example, consider a solar panel on a satellite in orbit around the Earth. At the location of the Earth, sunlight provides about 1 kiloWatt per square meter of power. If a solar panel is about 2 meters on a side, and absorbs all the light which strikes it, estimate the momentum transferred to the panel over the course of one minute.



     a)  about  8        kg*m/s

     b)  about  0.08     kg*m/s

     c)  about  0.0008   kg*m/s

Viewgraph 5