Someone wants to load a 12 kg crate into a truck by sliding it up a ramp 2.5 m long, inclined at 30o. A physics student, giving no thought to friction, calculates that she can get the crate up the ramp by giving it an initial speed of 5.0 m/sec at the bottom. But friction is not negligible; the crate slides 1.6 m up the ramp, stops, and then slides back down.

(a) Assuming that the frictional force acting on the crate is constant, find the magnitude of the frictional force.

(b) How fast is the crate moving when it reaches the bottom of the ramp?

(c) What is the minimum initial speed she must give the crate for it to make it up the ramp?