Mechanics 1
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Science for Fun :: Level 1 , 2 and 3 :: Olympiad :: Physics
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Mechanics 1
by Infinity squared Tue Oct 07, 2008 10:38 pm
i kno Latex won't work here rite now--but a try
We have a wire, which is made into a circle of radius R. The circle is in the horizontal plane. We put a small pearl of mass m on it. The pearl can only move on the wire, round and round. The coefficient of friction between the pearl and the wire is [tex]\mu[/tex]. How big initial velocity should we give the pearl so that it goes around the circle exactly once, and stops at the initial position (There is gravity of course)? (Hint: we only need the [tex]v(\phi)[/tex] function not the [tex]v(t)[/tex] function. So try simplifying the second order equation into a simple first order DE. The Problem is NOT hard, and can be solved on olympiad level)
We have a wire, which is made into a circle of radius R. The circle is in the horizontal plane. We put a small pearl of mass m on it. The pearl can only move on the wire, round and round. The coefficient of friction between the pearl and the wire is [tex]\mu[/tex]. How big initial velocity should we give the pearl so that it goes around the circle exactly once, and stops at the initial position (There is gravity of course)? (Hint: we only need the [tex]v(\phi)[/tex] function not the [tex]v(t)[/tex] function. So try simplifying the second order equation into a simple first order DE. The Problem is NOT hard, and can be solved on olympiad level)
- Spoiler:
- [tex]v_0=\sqrt{gR\sinh(4\pi\mu)}[/tex] :na:
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Science for Fun :: Level 1 , 2 and 3 :: Olympiad :: Physics
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