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.
•• A mad scientist claims to have observed the decay of a particle of mass M into two identical particles of mass m with M < 2m. In response to the objection that this violates conservation of energy, he retorts that if M was traveling fast enough, it could easily have energy greater than 2mc2 and hence could decay into the two particles of mass m. Show that he is wrong. (He has forgotten that momentum as well as energy must be conserved. You can analyze this problem in terms of these two conservation laws, but it is much easier to view the proposed reaction from the rest frame of the particle M.)
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