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

AI Thread Summary
The discussion centers on determining the velocity of a particle moving in a vertical circle when a force acts on it as a function of angle. The force is given by F=(Mmg(1+cosα))/(M+m), where M and m are masses with M greater than m. It is noted that while determining velocity from a time-dependent force is straightforward, the challenge arises when the force is expressed as a function of angle. However, it is suggested that knowing F(α) allows for the calculation of potential energy, which can then be used to find velocity through energy conservation principles. This approach provides a viable method to analyze the motion of the particle in the given scenario.
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\alpha))/(M+m)

(m is moving in on the surface of a verticle 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 (\alpha;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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