SR, Spring '10

Homework 9 (covers Mermin Chapter 11)

1. Do the math that Mermin describes in the surrounding text to derive Equation 11.21. Summarize in a sentence or two why this result is relevant/important.

2. A particle of mass m = 1 (in some units) flies with a velocity v = 4/5 c. It collides with another particle of mass m = 1 that was at rest. The two stick together and move off as one. Use equations 11.37 and 11.38 to calculate the energy and momentum of each of the two particles prior to the sticky collision. Now use energy and momentum conservation to calculate the mass and velocity of the "new particle" which moves off. For fun, draw a reasonably accurate spacetime diagram of the collision.

3. This one has nothing to do with this chapter, really, but is something that should be covered in this course. Take Alice and Bob as usual, with Alice at rest and Bob moving to the right with velocity v. Suppose for simplicity that the origins of Alice's and Bob's spacetimes coincide; that is, suppose that the event to which Alice assigns spacetime coordinates X=0, T=0, Bob assigns X'=0, T'=0. So setup a spacetime diagram with Alice's x and t axes and Bob's x' and t' axes, remembering for example that Bob's x' axis is an "equitemp" for Bob and that his t' axis is an "equiloc" and so they should be slanted in the way that's appropriate for such things. OK, that's all just setup; here's the real problem. Draw a big dot at some random point in spacetime, and call its x- and t-coordinates (for Alice) X and T. Now the question is: what coordinates X' and T' will Bob assign to this same event? See if you can develop explicit formulas for X' and T'. (Each will depend on things like X, T, v, and c.) In principle there are several ways of doing this. You could approach it "purely geometrically" as in Chapter 10. Or you could go through the "narrative" that Alice would tell about how Bob (from her point of view, erroneously) measures the coordinates of the event.