# Work done by friction and change in mechanical energy

We want to slide a 12-kg crate up a 2.5-m-long ramp inclined at . A worker, ignoring friction, calculates that he can do this by giving it an initial speed of 5 m/s at the bottom and letting it go. But friction is not negligible; the crate slides only 1.6m up the ramp, stops, and slides back down (Fig. 7.11a). (a) Find the magnitude of the friction force acting on the crate, assuming that it is constant. (b) How fast is the crate moving when it reaches the bottom of the ramp?

So I'm mainly confused about part b. I know how to get the answer, but I'm confused about why I include the distance traveled up the ramp as well as down the ramp when finding the work done by friction. If I set the starting position at to be the top of the ramp to solve the problem, the block only travels a distance of 1.6 meters not 1.6*2 meters so why do I include the entire path traveled? Also wouldn't work done by friction be zero if you do include the entire distance traveled because Work = Force * displacement and since the stating position is the same as the ending position, the displacement is zero?

Oh. I read the solution incorrectly. But I'm still curious if work done by friction is zero if the initial and final position is the same.

jbriggs444