a girl and her bicycle have a total mass od 40kg. At the top of the her speed is 3m/s...?

Question

the hill is 30m high and 100m long and makes an angle of 40degrees with the horizontal. The coefficient friction between the tires of the bicycycle and the hill is .30. what is the work done by friction on the girl and her bicycle at the bottom of the hill. I think the answer is -9009J. I know W=f*d cos theta but im just having trouble (especially drawing the picture)

Answer 1

Well, the only information we need is

W_fr = -µ N d

µ = 0.3

We can get N through a free body diagram
N = mg cos 40º = 300.3N

d = 100 m

W_fr = -0.3 * 300.3 * 100 = -9008.68 J, or -9009 J like you have.

You did the problem corectly. The negative sign is because friction is taking energy out from the system. The theta in your equation is not 40º. Rather, it is the angle made between the force of friction and the direction the bike is traveling. Since friction opposes this motion, the angle is 180º. Cos 180º = -1. This is where the negative sign comes from.