Re: [Phys-l] Force and potential

[curtis osterhoudt <flutzpah@yahoo.com>]

To be fair, motion along a _constrained_ surface often shows such "problems" (one is NOT allowed to "penetrate" the bowl's surface at all, and raising off of it infinitesimally means no force whatsoever).






> ________________________________
> From: "LaMontagne, Bob" <RLAMONT@providence.edu>
> To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu> 
> Sent: Wednesday, April 4, 2012 1:11 PM
> Subject: [Phys-l] Force and potential
>
> Deep in the sugar shock of eating too many Easter "Peeps", I came up with the following:
>
> Consider a bowl formed from the lower half of a sphere. In 2D I can write the equation for the bowl as x^2 + (y-1)^2 = 1. 
>
> This gives y = 1 - sqrt(1-x^2)
>
> If I place a marble at the inside rim (x=1, y=1) of the bowl and release it, the marble will oscillate back and forth, repeatedly coming back to the release point.
>
> The potential energy is given by U=mgh=mgy = mg[1 - sqrt(1-x^2)]
>
> Using F_x = - dU/dx , then we have F_x = -x/sqrt(1-x^2) which implies that F_x is infinitely strong when x = 1 (the release point).
>
> :-(
>
> Bob at PC
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