Potential Energy of 2 Masses Connected by a String - Find Theta

AI Thread Summary
The discussion focuses on finding the equilibrium point of two masses connected by a string in terms of the angle theta. Participants emphasize the need to express potential energy as a function of theta to identify its minimum. The vertical distances of the masses from a reference point are calculated using trigonometric functions, specifically L*cos(theta) for mass M1 and L*sin(theta) for mass M2. The potential energy is derived from the formula mgh, where h represents the vertical distance. The conversation concludes with a realization that determining these distances simplifies the problem significantly.
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Homework Statement



A figure is attached.
A string with length L connects two beads with masses M1,M2.
what is the equilibrium point?(in terms of the angle theta,as in the figure)

The Attempt at a Solution



well I know that I need to find the potential energy as a function of theta,and then find the minimum.

but I don't know how to express the potential energy in terms of theta
 

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You know the distance between m1 and m2 is L. To get started, find the distances of m1 and m2 from the rightangle in terms of L and theta.
 
well this is easy

for m1 : l*cos(theta)
for m2 : l*sin(theta)

I can't see how this is helping me
(by the way,this is not homework,I'm doing extra problems from the book)
 
The potential energy of a mass = mgh where h is the vertical distance from some point.

From those lengths, finding the vertical distance of the masses below the right angle (using alpha) is also easy.
 
can't believe I didnt see it..really easy

thanks :)
 

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