Physics problem Fairly simple but I keep getting wrong? Help please?

[jcfor3ver]

1. Homework Statement

The dominant form of drag experienced by vehicles (bikes, cars, planes, etc.) at operating speeds is called form drag. It increases quadratically with velocity (essentially because the amount of air you run into increases with and so does the amount of force you must exert on each small volume of air). Thus
Fdrag=C_dA_*v^2....where A is the cross-sectional area of the vehicle and C_d is called the coefficient of drag.


Consider a vehicle moving with constant velocity . Find the power dissipated by form drag?

P=?

Homework Equations

P=(delta Work)/ (delta time)

or P= F*v

The Attempt at a Solution

Fdrag=C_dA_*v^3 <----- how is this wrong? Maybe I am misinterpreting the problem?

 

[PhanthomJay]

You have the wrong drag equation, the power dissipated is P_drag = C_dA*p*v³, where p is the mass density of air . As long as you are ignoring other dissipative forces, at constant velocity the power dissipated by the drag is equal to the power delivered by the car or bike or aeroplane. (The drag factor for a car is a bit more complex than just C_d; an equivalent 'C_dA' factor is often used).

 

[jcfor3ver]

You have the wrong drag equation, the power dissipated is P_drag = C_dA*p*v³, where p is the mass density of air . As long as you are ignoring other dissipative forces, at constant velocity the power dissipated by the drag is equal to the power delivered by the car or bike or aeroplane. (The drag factor for a car is a bit more complex than just C_d; an equivalent 'C_dA' factor is often used).

The online problem told me that P=C_d*A*v^2 and to only express my answer using the terms C_d, A, and v. So then how would I express this? I thought I was correct the first time but this seemingly simple problem is causing me trouble now.

 

[PhanthomJay]

Well, actually both me and your online problem had it wrong, the drag force is
F_ drag = 1/2(C_d)A(p)v^2 (I forgot the 1/2) , and and P_drag = 1/2(C_d)A(p)v^3, so I don't know what to tell you. Perhaps they lumped the 1/2 and p terms together as an equivalent C_d factor, but I don't know. In which case, I don't know why your answer is wrong if that's the equation they told you to use.