As it plows a parking lot, asnowplow pushes an evergrowingpile of snow infront of it

Chapter 8, Problem 54

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As it plows a parking lot, asnowplow pushes an evergrowingpile of snow infront of it. Suppose a carmoving through the airis similarly modeled as acylinder of area A pushinga growing disk of airin front of it. The originallystationary air is set into motion at the constantspeed v of the cylinder as shown in Figure P8.54. In atime interval Dt, a new disk of air of mass Dm must bemoved a distance v Dt and hence must be given a kineticenergy 121Dm2v2. Using this model, show that the carspower loss owing to air resistance is 12rAv3 and that theresistive force acting on the car is 12rAv2, where r is thedensity of air. Compare this result with the empiricalexpression 12DrAv2 for the resistive force.