String through hole - central forces

AI Thread Summary
The discussion revolves around a physics problem involving two particles connected by a string, where one moves on a table and the other hangs below a hole. The goal is to derive a specific equation using conservation of energy and angular momentum. A participant initially struggles with the derivation, particularly with an extra factor of 2 and the presence of 8 in the denominator of a term. Ultimately, the participant believes they have found the solution to the problem. The conversation highlights the complexities of applying conservation principles in dynamic systems.
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Homework Statement



Two particles of mass m are connected by a light inextensible string of length l. One of the particles moves on a smooth horizontal table in which there is a small hole. The string passes through the hole so that the second particle hangs vertically below the hole. Use the conservation of energy and angular momentum to show that:

r(dot)^2 = (gl+v^2)/2 - (lv)^2/(8r^2) - gr

where r(t) is the distance of the first particle from the hole.

Homework Equations





The Attempt at a Solution



I tried to solve this question using the expression linking angular momentum and the conservation of energy, namely:

E = U(r) + J^2/(2mr^2) + 1/2*m*r(dot)^2

However, i cannot show the result that they want me to derive. There's a factor of 2 extra that I keep ending up with and I don't see how they have 8 in the denominator of one of the terms.

Any help would be appreciated.
 
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Just bumping this -- any help at all would be great.
 
Never mind -- I think I have the answer now.
 
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