Chapter 16, Problem 16.67CP

If a loop of chain is spun at high speed, it can roll along the ground like a circular hoop without collapsing. Consider a chain of uniform linear mass density μ whose center of mass travels to the right at a high speed υ₀ as shown in Figure P16.67. (a) Determine the tension in the chain in terms of μ and υ₀. Assume the weight of an individual link is negligible compared to the tension, (b) If the loop rolls over a small bump, the resulting deformation of the chain causes two transverse pulses to propagate along the chain, one moving clockwise and one moving counterclockwise. What is the speed of the pulses traveling along the chain? (c) Through what angle does each pulse travel during the time interval over which the loop makes one revolution?