Masses on Pullies, equal weights on both sides but still rotating

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SUMMARY

The discussion centers on the mechanics of a double Atwood machine, specifically analyzing a system with a mass of 4m suspended from a pulley and a second pulley supporting masses of 3m and m. Upon release, the mass 4m accelerates downwards at g/7. The top pulley rotates despite having equal weights on both sides due to the net forces acting on the second pulley, where the forces from the masses do not balance out, leading to a net force that causes rotation.

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  • Understanding of Newton's laws of motion
  • Familiarity with pulley systems and tension forces
  • Basic knowledge of acceleration and gravitational force
  • Concept of net force and its role in motion
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Homework Statement


Consider a double Atwood machine constructed as follows: A mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. The other end of this string supports as second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. Find the acceleration of the mass 4m when the system is released.

Explain why the top pulley rotates even though it carries equal eights on each side.


Homework Equations





The Attempt at a Solution


The mass 4m accelerates downwards with an acceleration of g/7.

Can anyone explain why, though, the pulley rotates at all, since it has equal weights on both sides?
 
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In the second pulley, m is going up and 3 m is going down. If net force on m is f1 and that on 3m is f2, the net force on the second pulley is f2 - f1. And f1 and f2 are not the weights. So 4mg on the right is greater than f2 - f1. Hence the first pulley rotates.
 

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