A large number (n) of identical beads, each of mass m and radius r are strung on a thin smooth rigid horizontal rod of length L (L r) and are at rest at random positions. The rod is mounted between two rigid supports (see figure). If one of the beads is now given a speed v, the average force experi…

Question

A large number (n) of identical beads, each of mass m and radius r are strung on a thin smooth rigid horizontal rod of length L (L r) and are at rest at random positions. The rod is mounted between two rigid supports (see figure). If one of the beads is now given a speed v, the average force experienced by each support after a long time is (assume all collisions are elastic)

Accepted Answer

(2) (mv²)/(L-2nr). Identical beads exchange velocities in elastic collisions, so the motion passes from bead to bead as if one bead travelled the free length of the rod. The beads occupy n×2r of the rod, leaving a free path L-2nr; a round trip takes (2(L-2nr))/v. Each hit gives a support impulse 2mv: F=(2mv)/(2(L-2nr)/v)=(mv²)/(L-2nr).

Step-by-step solution

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