My physics book claims that if two identical disks moving at the same velocity travel up nearly identical hills, with the second hill not having friction, then the disk rolling up the first hill will travel to a greater height. Given that the disks started with the same kinetic energy while rolling at the base of the hill, shouldn't they reach the same height (i.e. same potential energy) as a result?
[Physics] Conservation of energy of 2 identical Rolling Disks with and without friction
energy-conservationfrictionnewtonian-mechanicsrotational-dynamicsrotational-kinematics
Best Answer
First, let's assume that no slipping occurs on the hill with friction and that both disks are rolling without slipping before they get to their respective hills.
You are forgetting to consider that the disk on the frictionless incline will still be spinning when it gets to it's maximum height. Therefore, it will still have some of its initial kinetic energy that can't be converted into potential energy. This means it can't go as high as the disk on the hill with friction.
Thinking just about the forces, the static friction force points up the incline as the disk rolls up it, so this force counters the acceleration down the incline due to gravity which allows disk to go farther before it stops, as well as providing a torque that causes the disk to eventually stop rotating at the top of it's trajectory.