A 4.5kg box slides down a 4.1-m -high frictionless hill, starting from rest, across a 1.7-m -wide horizontal surface, then hits a horizontal spring by spring constant 550N/m. The other end of the spring is anchored against a wall. The ground under the spring is frictionless; however the 1.7-m-long horizontal surface is rough. The coefficient of kinetic friction of the box on this surface is 0.24.
1. How far is the spring compressed?
2. What is the speed of the box just before hitting the spring?
3. What is the speed of the box just before reaching the rough surface?
4. Including the first crossing, how many complete trips will the box make across the rough surface before coming to rest?