As it plows a parking lot, a snowplow pushes an evergrowing pile of snow in fron
ID: 1977176 • Letter: A
Question
As it plows a parking lot, a snowplow pushes an evergrowing pile of snow in front of it. Suppose a car moving through the air is similarly modeled as a cylinder pushing a growing plug of air in front of it. The originally stationary air is set into motion at the constant speed v of the cylinder. In a time interval t, a new disk of air of mass m must be moved a distance vt and hence must be given a kinetic energy ½(m)v2. Using this model, show that the automobile’s power loss due to air resistance is ½(Av3) and that the resistive force acting on the car is ½(Av2), where is the density of air. Compare this result with the empirical expression ½(DAv2) for the resistive force.
As it plows a parking lot, a snowplow pushes an evergrowing pile of snow in front of it. Suppose a car moving through the air is similarly modeled as a cylinder pushing a growing plug of air in front of it. The originally stationary air is set into motion at the constant speed v of the cylinder. In a time interval delta t, a new disk of air of mass delta m must be moved a distance v delta t and hence must be given a kinetic energy 1/2(delta m)v2. Using this model, show that the automobile?s power loss due to air resistance is 1/2(?Av3) and that the resistive force acting on the car is 1/2(?Av2), where ? is the density of air. Compare this result with the empirical expression 1/2(D?Av2) for the resistive force.