How Does Torque Affect Tensions in an Atwood's Machine with a Massive Pulley?

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SUMMARY

The discussion centers on the dynamics of an Atwood's machine, specifically analyzing the effects of torque on tensions in a system with a massive pulley. The masses involved are m1 = 8.4 kg and m2 = 20.7 kg, with the pulley having a mass M = 7.40 kg and radius r = 0.200 m. It is established that the tension T2 must be greater than T1 due to the need for net torque to produce angular acceleration in the pulley. The acceleration of the system can be calculated assuming a frictionless pulley axis, and the tensions T1 and T2 can be derived using the principles of rotational dynamics.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Familiarity with rotational dynamics and torque
  • Knowledge of free body diagrams (FBDs)
  • Basic principles of Atwood's machine mechanics
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  • Study the derivation of tension equations in Atwood's machines
  • Learn about the moment of inertia for solid cylinders
  • Explore the relationship between linear acceleration and angular acceleration
  • Investigate the effects of friction on pulley systems
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Physics students, educators, and engineers interested in mechanics, particularly those studying systems involving pulleys and rotational motion.

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An Atwood's machine consists of blocks of masses m1 = 8.4 kg and m2 = 20.7 kg attached by a cord running over a pulley as in the figure below. The pulley is a solid cylinder with mass M = 7.40 kg and radius r = 0.200 m. The block of mass m2 is allowed to drop, and the cord turns the pulley without slipping.

(a) Why must the tension T2 be greater than the tension T1?

(b) What is the acceleration of the system, assuming the pulley axis is frictionless?

(c) Find the tensions T1 and T2.

Does anyone have idea how pully w/ mass works?
 
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Treat the pulley as a third body and draw three FBDs. Since the cord does not slip on the pulley, you have the tensions acting on the two sides of the pulley acting to give it an angular acceleration.
 

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