Halliday, Resnick & Walker — Force and Motion–II: Problem 65_FCP

Continuation of Problems 8 and 37. Another explanation is that the stones move only when the water dumped on the playa during a storm freezes into a large, thin sheet of ice. The stones are trapped in place in the ice. Then, as air flows across the ice during a wind, the air-drag forces on the ice and stones move them both, with the stones gouging out the trails. The magnitude of the air-drag force on this horizontal “ice sail” is given by \(D_{ice} = 4 C_{ice} \rho A_{ice} v^2\), where \(C_{ice}\) is the drag coefficient (\(2.0 \times 10^{-3}\)), \(\rho\) is the air density (\(1.21 \text{ kg/m}^3\)), \(A_{ice}\) is the horizontal area of the ice, and \(v\) is the wind speed along the ice. Assume the following: The ice sheet measures \(400 \text{ m}\) by \(500 \text{ m}\) by \(4.0 \text{ mm}\) and has a coefficient of kinetic friction of \(0.10\) with the ground and a density of \(917 \text{ kg/m}^3\). Also assume that 100 stones identical to the one in Problem 8 are trapped in the ice. To maintain the motion of the sheet, what are the required wind speeds (a) near the sheet and (b) at a height of 10 m? (c) Are these reasonable values for high-speed winds in a storm?