Lumpy Hill 7/31/11

August 1, 2011 at 10:26 pm | Posted in problem of the day solution | Leave a comment

Problem

You slide a spherical ball down a frictionless lumpy hill and trace its bath.

Now you turn on friction and do it again so that the ball rolls down the hill without slipping. (Note that rolling without slipping implies no energy dissipation.)

Does the ball follow the same path as before?

Assume the ball always contacts the hill in exactly one spot.

Solution

I asked this question on Physics.Stackexchange.com, and the thread now has a number of correct answers.