A particle of mass , initially moving with a speed v, collides head on ELASTICALLY with an identical particle initially at rest.

a. Do you expect the total mass of the particles after the collision to be greater than 2m, less than 2m, or equal to 2m? Why?

b. What are the total energy and momentum of the two particles after the collision, in terms of m, v, and c?

(Little Physics Phun with algebra) Using the relativistic expression for total energy E and the magnitude p of the momentum of a particle,

a. show that the two quantities are related by

b. Use this expression to determine the linear momentum of a proton with a kinetic energy of 1000MeV.

The operator of a linear particle accelerator tells a tour group that it is used to give protons an energy of 600MeV.

a. This 600MeV must refer to the proton's total, kinetic, or rest energy? (Why did you pick your particular answer?)

b. What are the values of these three proton energies?

c. What is the proton's speed?

d. What is the proton's momentum?

Referring to problem above, let's try a generalization. Experimental evidence suggests the existence of a huge black hole at the center of the Milky Way Galaxy. This black hole is absorbing stars and increasing in mass and radius. Assuming this black hole has a mass of solar masses,

Determine its current Schwarzschild Radius. Compare this to the radius of our galaxy (about 300 ly). Does this black hole take up a significant portion of our galaxy?

Suppose it is "gobbling" up stars, each with a mass of our Sun at one per Earth-year. At what rate is its Schwarzschild radius increasing?

Assuming it could "swallow" all of the stars-about 200 billion-in the galaxy, each with the mass of our Sun, how long would this process take and what would be the eventual Schwarzschild radius of the black hole?