Air resistance of a high speed car

[tomrule007]

Homework Statement

Ignoring air resistance is a large error when dealing with cars, especially when they are traveling at high speeds. Remember that air resistance depends on the speed squared F_ar=-Av^2.

A) draw a "FBD" for the car. show that the power required to keep a car going at a constant speed on a flat road against air resistance alone is proportional to the speed to the third power.

B)If your car consumes 20hp when traveling at a constant speed of 30mph. how much more power would it need to travel at a constant speed of 60mph under the same conditions?

Homework Equations

Not really sure what i should even start with for part A i used
Newtons second law and that's all i pretty much used so far

The Attempt at a Solution

A) For the free body diagram ill list the forces i included: Gravity(down), Normal force(up), Air resistance(left),Motor force=F(right)

so i can set F-F_ar=M*A (but it says the is traveling at a constant speed so i can just a=0 and then get

F=F_ar
So i think i did this part right but i don't know were to go from here to prove that the force is 3x the velocity


Any help would be appreciated -Thanks Tom

 

[mukundpa]

Do you know the relation between the power force and velocity?

 

[tomrule007]

after looking it up i found power = force x velocity (is this what your talking about ? it was never mentioned in my class)

 

[denverdoc]

Well another way to think about it from simpler principles is that work if force times distance, and power is the rate at which work is performed, so dividing by time=force times velocity.