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.

•• Consider the decay A → B + C shown in Fig. 2.13 (Problem 1). Suppose that both B and C are mass- less and that θB = θC. Use conservation of energy and momentum to prove that cos θB = β where β is the dimensionless “velocity” (u/c) of particle A.

Problem 1

•• A particle A moving with momentum pA ≠ 0 decays into two particles B and C as in Fig. 1. (a) Prove that the three momenta pA, pB, pc lie in a plane. (b) If mB = mc and if it is found that θB = θC, prove that particles B and C must have equal energies. (c) If it is found that θB = 0, prove that θC = 0 or 180°.

FIGURE 1