Air resistance of a high speed car

AI Thread Summary
Ignoring air resistance significantly impacts calculations for high-speed cars, as air resistance is proportional to the square of speed. To analyze the forces acting on the car, a free body diagram (FBD) should include gravity, normal force, air resistance, and motor force, leading to the equation F = F_ar when traveling at constant speed. The power required to overcome air resistance is proportional to the cube of speed, which can be derived from the relationship between power, force, and velocity. For a car consuming 20 horsepower at 30 mph, the power needed to maintain 60 mph can be calculated using this cubic relationship. Understanding these principles is crucial for accurately assessing a car's performance at varying speeds.
tomrule007
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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
 
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Do you know the relation between the power force and velocity?
 
after looking it up i found power = force x velocity (is this what your talking about ? it was never mentioned in my class)
 
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.
 
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