How Does Pulley Torque Affect Wire Tension in a Frictionless System?

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SUMMARY

The discussion focuses on calculating the horizontal tension in a wire connecting a 12.0 kg box and a 5.00 kg weight over a frictionless pulley, which is modeled as a uniform solid disk with a mass of 1.70 kg and a diameter of 0.600 m. The approach involves analyzing the system as if the pulley were massless initially, but acknowledges that the pulley’s mass introduces different tensions on either side. The net torque on the pulley, influenced by the two tensions, is crucial for determining the angular acceleration, which is linked to the linear acceleration of the masses. The inextensible nature of the wire ensures uniform acceleration across the system.

PREREQUISITES
  • Understanding of Newton's Second Law of Motion
  • Familiarity with torque and moment of inertia concepts
  • Knowledge of angular acceleration and its relationship to linear acceleration
  • Basic principles of frictionless systems in physics
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  • Study the relationship between torque and angular acceleration in rigid bodies
  • Learn about the moment of inertia for different shapes, particularly disks
  • Explore the dynamics of systems with multiple masses connected by strings
  • Investigate the effects of friction in pulley systems for comparative analysis
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Physics students, educators, and anyone interested in understanding the dynamics of pulley systems and the interplay between tension, torque, and acceleration in frictionless environments.

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Homework Statement



A 12.0kg box resting on a horizontal, frictionless surface is attached to a 5.00kgweight by a thin, light wire that passes without slippage over a frictionless pulley (the figure ). The pulley has the shape of a uniform solid disk of mass 1.70kg and diameter 0.600 m.
After the system is released, find the horizontal tension in the wire.

http://session.masteringphysics.com/problemAsset/1037926/6/YF-10-44.jpg

Homework Equations





The Attempt at a Solution


I'm thinking of approaching it as I would if the pulley was massless by setting m1a= Thorz and m2a=m2g-Tvert, but I don't know where the pulley would come in
 
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There will be different tensions on either side of the pulley. The net torque on the pulley will be due to the actions of the two tensions. The angular acceleration of the pulley will be dictated by the net torque and its moment of inertia. The horizontal tension determines the acceleration of M1. The vertical tension, in concert with force due to gravity on M2, determines the acceleration of M2. The inextensible wire endures that all the accelerations are the same.

Relate the angular acceleration of the pulley to the acceleration of the wire in order to tie everything together.
 

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