An electron and a proton are separately accelerated by accelerators that point at each other. The particles then approach each other as shown below. In each case the particle is accelerated from rest and an amount of work equal to 10mc2 is done, where m is the rest mass (the mass) of the particle.
a) Show (turn off the calculator) using relativity that each particle will emerge from its respective accelerator with exactly the same speed as measured by an observer at rest with both accelerators. Determine that speed as a multiple (fraction) of c.
b) Which particle has gained more energy through the acceleration process or is this also the same for the two particles? Explain how you know.
c) Imagine that the accelerators are linear (i.e. straight evacuated tubes) with electric fields, directed so as to do positive work on the particle in question. that are uniform and of equal magnitude. Which accelerator is longer? How do you know? Find the ratio of the proper lengths of the accelerators.
