Using Forces and Torques to solve a pulley problem

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SUMMARY

The discussion focuses on solving a pulley problem using forces and torques, emphasizing the application of Newton's 2nd law. Participants suggest creating four equations to address the problem: one for the net torque on the pulley, two for the masses using Newton's 2nd law, and one for the pulley’s rotation without slipping. This method contrasts with using mechanical energy conservation, which simplifies the solution to a single equation. The detailed approach provides a comprehensive understanding of the dynamics involved in pulley systems.

PREREQUISITES
  • Newton's 2nd Law of Motion
  • Understanding of torque and rotational dynamics
  • Basic principles of mechanical energy conservation
  • Knowledge of pulley systems and their mechanics
NEXT STEPS
  • Study the application of Newton's 2nd Law in multi-body systems
  • Learn about torque calculations in rotational motion
  • Explore mechanical energy conservation in complex systems
  • Investigate the dynamics of non-slipping pulleys
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the mechanics of pulley systems and rotational dynamics.

kepherax
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Homework Statement
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Relevant Equations
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I am able to solve this easily using energy conservation, but I'm curious how one would go about solving this using forces and torques?

pulleytorque.JPG


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I see you have already make one equation with the net torque on the pulley. You can make two more equations by applying Newton's 2nd law on each of the masses. Then one more equation by the fact that the pulley rotates without slipping. So in total you ll have 4 equations with 4 unknowns (The two tensions, the (common) acceleration of the masses and the angular acceleration of the pulley).
 
Alternatively, you can use mechanical energy conservation and get the answer with a single equation.
 

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