Friction on Inclines

1. A wooden block slides down a ramp at a constant speed. If the ramp were made of a different material that provides twice as much friction, how would the angle of the ramp need to change to maintain the same constant speed? Explain your answer using the relationship between the angle, friction, and gravitational force.

2. Imagine you are designing a system to lower packages gently down a ramp. Describe how you could use different materials (with varying coefficients of kinetic friction) and ramp angles to control the speed of the packages. What trade-offs would you need to consider?

3. A box slides down a ramp with an initial velocity. The ramp has friction. Describe how the box's velocity changes over time. How does friction affect the box's acceleration, and what eventually happens to the box if the ramp is long enough?