In this example we will add friction to an inclined ramp. Of course, friction does work and we will need to determine its contribution to Wother. A crate full of machine parts sits on the floor; the total mass is 8.0 kg. The crate must be raised to the floor of a truck by sliding it up a ramp 2.5 m long, inclined at 30∘. The shop foreman, giving no thought to the force of friction, calculates that he can get the crate up the ramp by giving it an initial speed of 5.0 m/s at the bottom and letting it go. Unfortunately, friction is not negligible; the crate slides 1.6 m up the ramp, stops, and slides back down. (Figure 1) shows the situation.
Question: Suppose the foreman had released the box from rest at a height of 0.25 m above the ground. What would the crate's speed be when it reaches the bottom of the ramp?