Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.

•• Many problems in relativity are best solved by viewing them first in a cleverly chosen reference frame. Here is an example: A K° meson (see Problem 1) traveling at 0.9c decays into a π+ and π−, sending the π+ exactly forward and the π− exactly backward. Using the results of Problem 1, find the velocities of the two pions. [Hint: Let S be the frame of this problem and S′ the K° rest frame. You can use the results of Problem 1 in S′ and then use the velocity transformation to find the velocities in S.]

Problem 1

•• The K° meson is a subatomic particle of rest mass mK = 498 MeV/c2 that decays into two charged pions, K° → π+ + π−. (The π+ and π− have opposite charges but exactly the same mass, mπ = 140 MeV/c2.) A K° at rest decays into two pions. Use conservation of energy and momentum, to find the energies, momenta and speeds of the two pions. (Give algebraic answers, in terms of the symbols mK and mπ first; then put in numbers.)