Consider a collection of rigid sticks of length 2r, masses mi, and moments of inertia ?mir2, with m1 >> m2 >> m3 >> .. The CM of each stick is located at the center. The sticks are placed on a horizontal frictionless surface, as shown in Fig. The ends overlap a negligible distance, and the ends are a negligible distance apart. The first (heaviest) stick is given an instantaneous blow (as shown) which causes it to translate and rotate. The first stick will strike the second stick, which will then strike the third stick, and so on. Assume all the collisions are elastic. Depending on the size of ?, the speed of the nth stick will either (1) approach zero, (2) approach infinity, or (3) be independent of n, as n ? ?. Show that the special value of ? corresponding to the third of these three scenarios is ? = 1/3, which happens to correspond to a uniform stick.

Transcribed Image Text:

my M₂ 2r ma