Frictionless Ramp to Rough Surface: Energy Conservation | Symbolic Physics (AP Free Response 1975B1)
This video is slightly based on the following AP problem from 1975, modified to reflect the current trend (and sticking point for students) of algebraic solutions instead of numerical ones. The solutions here turn out to be surprisingly simple in their format.
1975B1. A 2-kilogram block is released from rest at the top of a curved incline in the shape of a quarter of a circle of radius R. The block then slides onto a horizontal plane where it finally comes to rest 8 meters from the beginning of the plane. The curved incline is frictionless, but there is an 8-newton force of friction on the block while it slides horizontally. Assume g = 10 meters per second^2.
a. Determine the magnitude of the acceleration of the block while it slides along the horizontal plane.
b. How much time elapses while the block is sliding horizontally?
c. Calculate the radius of the incline in meters.