Modeling the Motion of a Car Against Constant Frictional Resistance

[grae]

Homework Statement

A motor car with a power output of 2500W is moving against a constant frictional resistance of 180N. What distance does it travel in 1 minute on a horizontal road?
P = 2500W
F_F = 180N
t = 60s
s = ?

Homework Equations

P = W/t
W = Fs
F_net = F_A - F_F

The Attempt at a Solution

P = W/t
2500= Fs/60
s = 150000/F
??I don't know where to go from here as I only know the frictional force??

 

[NascentOxygen]

Hi grae. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

s = 150000/F looks right.

The data seems to imply that the car is traveling at a constant speed. (If this were not the case, you would need to know the car's weight so you could determine its acceleration.)

You don't happen to know the text-book's answer?

 

[grae]

Yes, my teachers answer and working is attached to this msg however he often gets these questions wrong. He has assumed that the net force is 180N which is where I am lost

 

[NascentOxygen]

It's traveling at a constant speed. Its engine has to overcome only friction.

The question should have stated that it's a constant speed situation.

Are you okay now?

 

[grae]

Doesn't that make the net force equal to 0?

 

[Arcani]

Yes, the net force on the car would be 0 if it's moving at a constant velocity and the net work done on the car is therefore also equal to 0. However, the motor has to apply a force to counter the frictional resistance which puts a limit on the maximum speed of the car (P=Fv)

Essentially, the problem having you solve for the distance traveled by the car when it's moving at its maximum speed for the power output listed.

 

[NascentOxygen]

Homework Statement

A motor car with a power output of 2500W is moving against a constant frictional resistance of 180N. What distance does it travel in 1 minute on a horizontal road?

If you are into differential equations, it might be instructive to work out the DE describing this scenario. Let the mass of the car be m. You can then follow the speed of the vehicle from a standing start, right up until it approaches terminal velocity.

Hint: The energy from the power unit equates to kinetic energy of the vehicle + work done against friction.