Can Velocity be Determined from Force as a Function of Angle in Mechanics?

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SUMMARY

The discussion centers on determining the velocity of a particle moving in a vertical circle under the influence of a force defined as a function of angle, specifically F=(Mmg(1+cosα))/(M+m). The participants conclude that while direct velocity determination from force as a function of angle may not be straightforward, it is possible to derive the velocity using energy conservation principles. By calculating the potential energy associated with the force F(α), one can subsequently find the velocity v(α) at any point described by the coordinates (α; R).

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Gloyn
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Hello!

I've been doing some excercises in mechanics and stopped for a moment over the thing that sometimes bothers me. I have a set of particles of masses M and m, M>m. If I have force acting on m particle as a function of angle:

F=(Mmg(1+cos[itex]\alpha[/itex]))/(M+m)

(m is moving in on the surface of a vertical circle of radius R, powered by the falling M particle, both particles are connected by a string)

is there a way to determine the velocity of particle in a point described by coordinates ([itex]\alpha[/itex];R)? If force was in funtction of time, that would be obvious, but what about the function of the coordinate?
 
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Hmm, your force looks strange. However, if you know F(alpha), you can determine a potential and get v(alpha) via energy conservation.
 

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