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Natural Science Forum / Physics / General Physics / January 2008Marble Falling Off a Larger Sphere
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? An illustration is at http://home.ca.inter.net/~deniswb/marbleproblem.jpg (I don't know how or even if you can insert pictures into a usenet post) Again I did not get the final answer but got part marks for saying that the acceleration due to gravity was slowed by a factor of cosine theta. When the professor took it up the answer was h = r / 3 Thanks for all your help on these. It's been fascinating. Denny > 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. > An illustration is athttp://home.ca.inter.net/~deniswb/marbleproblem.jpg > [quoted text clipped - 8 lines] > > Denny >> 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 [quoted text clipped - 4 lines] > I don't know how a freshman's knowledge would be used to solve this > problem since this is a classic Lagrangian constraints problem. The marble detaches from the sphere after the force exerted by the sphere on the marble becomes zero. That force can be expressed as mass of the marble times its acceleration minus the gravitational field. IIRC, h is r/3.  SignatureArmy1987 (Replace "NOSPAM" with "email") > > 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 [quoted text clipped - 8 lines] > 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 > > > 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 [quoted text clipped - 15 lines] > > - 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). > > 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 [quoted text clipped - 23 lines] > > - Show quoted text - It was a very tough course and part of a program called Engineering Science at University of Toronto. It was a cut above other Engineering Courses (Electrical, Chemical, Civil etc.) and designed to separate the wheat from the chaff. I did not get high enough grades to continue in Engineering Science and had to transfer to what the professor called "garden variety" engineering. |
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