Question

Continuation of Problem 8: The mysterious sliding stones. Along the remote Racetrack Playa in Death Valley, California, stones sometimes gouge out prominent trails in the desert floor, as if the stones had been migrating (see the figure). For years curiosity mounted about why the stones moved. One explanation was that strong winds during occasional rainstorms would drag the rough stones over ground softened by rain. When the desert dried out, the trails behind the stones were hard-baked in place. According to measurements, the coefficient of kinetic friction between the stones and the wet playa ground is about 0.75. Now assume that equation Upper D equals StartFraction 1 Over 2 EndFraction Upper C rho Upper A v Superscript 2 gives the magnitude of the air drag force on a typical 17 kg stone, which presents to the wind a vertical cross-sectional area of 0.045 m2 and has a drag coefficient C of 0.78. Take the air density to be 1.21 kg/m3. (a) What wind speed V along the ground is needed to maintain the stone's motion once it has started moving? Because winds along the ground are retarded by the ground, the wind speeds reported for storms are often measured at a height of 10 m. Assume wind speeds are 1.7 times those along the ground. (b) For your answer to (a), what wind speed would be reported for the storm? (Story continues with Problem 65.)