physics
posted by ajo .
A bicyclist rides 5.0km due east, while the resistive force from the air has a magnitude of 3.0N and points due west. The rider then turns around and rides 5.0km due west, back to her starting point. The resistive force from the air on the return trip has a magnitude of 3.0N and points due east. (a) Find the work done by the resistive force during the round trip. (b) Based on your answer to part (a), is the resistive force a conservative force? Explain.
In part a, I got 3.0*10^4J, but I don't understand what it means by a conservative force. Can anyone please explain to me? Thanks a lot!

Say it were a conservative force like gravity.
As you went down from the top of a hill to the bottom, gravity would push down in your direction and you would get a positive amount of work done by gravity.
When you go back up the hill, gravity is pushing down still but you are going up, so force times distance is negative and the work done by gravity is negative.
By the time you get back to the starting point at the top of the hill, gravity has done just as much negative work coming back up as it did positive work on the way down.
That is NOT what happened with your air resistance. By the time you got back to your starting point, the air resistance force had done nonzero work on you. Therefore it is not conservative. 
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