What are the forces and torques acting on the masses and pulley in this system?

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SUMMARY

The discussion focuses on analyzing the forces and torques acting on a system involving two masses, m1 and m2, connected by a light cord over a pulley with moment of inertia I and radius R0. The equations of motion are derived using Newton's second law, where the net force on m2 is affected by the tension T and the kinetic friction force, while the tension in the cord is also influenced by the gravitational force acting on m1. The key equations include ΣF = ma for linear motion and Στ = Iα for rotational motion.

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  • Familiarity with free-body diagrams
  • Concept of kinetic friction and its effects on motion
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Homework Statement


A mass m_{1} is hanging from a light cord which is strung over a pulley of moment of inertia, I, and radius R_{0} and connected to a mass m_{2} which is sliding on a rough horizontal surface with coefficient of friction \mu_{k}.

a) What is the acceleration of the system?
b) What are the tensions in each part of the cord?

All help is appreciated! :)

pulley.jpg




Homework Equations


\SigmaF = ma
\Sigma\tau = mR^{2}\alpha

The Attempt at a Solution


I started by trying to sum up all the forces and torques but I don't know where to go from there.

\Sigma F_{x} = T - \mu m_{1}g = (\mu m_{1} + m_{2})g = ma
\Sigma F_{y} = T = m_{2}g
\Sigma \tau = rF_{x} + rF_{y}
 
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Always start by drawing a free-body diagram on each object, including the pulley, and writing out Newton's second law for each object.
 

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