Two small rings each of weight w can slide on a fixed rough horizontal rod. the rings are attached one to each end of a uniform chain of weight 4w and length 4a so that the chain hangs freely from the rings. if the coefficient of friction between each ring and the rod is 1/2, find the distance between the rings when they are in limiting equilibrium. prove that the lowest point of the chain is then at a depth a below the rod.

Aball is thrown from the top of a building with an initial velocity of 21.9 m/s straight upward, at an initial height of 51.6 m above the ground. the ball just misses the edge of the roof on its way down, as shown in the figure. (a) determine the time needed for the ball to reach its maximum height. (b) determine the maximum height. (c) determine the time needed for the ball to return to the height from which it was thrown, and the velocity of the ball at that instant. (d) determine the time needed for the ball to reach the ground. (e) determine the velocity and position of the ball at t = 5.35 s.