As it plows a parting lot. a snowplow pushes an ever - growing pile of snow in f
ID: 1976067 • Letter: A
Question
As it plows a parting lot. a snowplow pushes an ever - growing pile of snow in front of it. Suppose a car moving trough 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 deltat a new disk of air of mass deltam must be moved a distance vdeltat and hence must be given a kinetic energy 1/2(deltam)v2 Using this model, show that the automobile's power loss due to air resistance is 1/2(rhoAV2) and that the resistive force acting on the car is 1/2(rhoAV2), where rho is the density of air. Compare this result with the empirical expression 1/2(DrhoAV2) for the resistive forceExplanation / Answer
when the car is moving work done is equal to change in kinetic energy w = k = mv^2/2 but work = power x time = pt pt = mv^2/2 .......(1) the density is = m/v = m/ Ax subsituting this ino the first equation and solving for p since x/t = v for constant speed we get = m/ A vt m = A vt from the equation (1) p = mv^2/ 2t =Av3/2 since p = Fv F= Av2 /2 for D = 1 for the drag coefficient . air actually slips around the moving object instead of accumulating infront of it for this reason the drage coefficient not necessarly unity. it is typically less than one for a streamlined object and can be greater than one i fthe air flow around the object is complicated.Related Questions
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