Re: Rolling AP Problem

[Maurice Barnhill <mvb@UDel.Edu>]

Ron Curtin wrote:
> Some students and I in my AP C-level high school course are trying a
> problem from the 1994 mechanics test.  A ball, rolling along a level
> surface, encounters an incline.  In the first case, we have no trouble
> calculating the velocity of the ball at the top of the incline.  Then,
> the
> question asks how fast the ball would be going if the incline was
> frictionless.  Would it be faster, slower, or the same speed as if it
> did
> pure rolling up the incline in the first part of the problem?  Thanks.

If the incline is frictionless, the ball will slide up the incline
instead of rolling. It will continue rotating at the rate it had when it
reached the bottom of the incline.  At the top, if it gets there, it
will be rotating faster, and its center of mass will have a lower
velocity, than when it rolled up.  

I am assuming that on the level surface and going up the incline with
friction, the ball rolls without slipping, and that the transition from
level to incline is sufficiently smooth that no energy is lost in the
transition. [You have to be careful about such things in this forum, and
no doubt somebody will find another assumption that I haven't listed]. 

-- 
Maurice Barnhill, mvb@udel.edu                
http://www.physics.udel.edu/~barnhill/          
Physics Dept., University of Delaware, Newark, DE 19716