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.Explanation / Answer
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
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.