Re: Marble Falling Off a Larger Sphere
- From: Denny <nudest@xxxxxxxxxxxx>
- Date: Wed, 30 Jan 2008 14:07:00 -0800 (PST)
On Jan 30, 4:41 pm, Randy Poe <poespam-t...@xxxxxxxxx> wrote:
On Jan 30, 3:32 pm, Eric Gisse <jowr...@xxxxxxxxx> wrote:
On Jan 30, 10:46 am, Denny <nud...@xxxxxxxxxxxx> wrote:
I want to thank everyone who replied to my "bowling ball" post. On
that same freshman exam was this problem: a marble sits atop a larger
sphere of radius r. The marble starts falling off and when it loses
contact with the sphere, it has fallen a vertical distance h. The
question is: what proportion of r is h?
I can't believe I remember this, but as I recall the angle at which
the marble would fall off the sphere is 57.3 degrees - assuming I'm
remembering correctly. You can work out the proportion from there.
I don't know how a freshman's knowledge would be used to solve this
problem since this is a classic Lagrangian constraints problem.
It's a Halliday & Resnick problem which can be solved
through energy and centripetal force considerations. I
suspect the bowling ball problem was from a similar
text.
- Randy
The professor was Donald G. Ivey (1922 - ) at University of Toronto.
He and Patterson Hume wrote several physics textbooks in the 1960s as
well as producing films and TV show (incl. The Nature of Things).
.
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- From: Denny
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