A number n of identical balls, each of mass m and radius r, are stringed like beads at random and at rest along a smooth, rigid horizontal rod of length L mounted between immovable supports. $$\frac{r}{L}$$ is small but not negligible. Collision between balls, or between balls and supports, are perfectly elastic. One of the balls is struck horizontally so as to acquire a speed v. Resulting outward force felt by supports, averaged over a long time, is