How can the tension in a wire change on either side of a pulley?

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SUMMARY

The discussion centers on the tension differences in a wire on either side of a pulley when a 12kg box and a 5kg weight are involved, with a pulley mass of 2kg and a diameter of 0.5m. The calculated tensions are 32.7N on the side of the box and 35.4N on the side of the hanging weight. This discrepancy arises due to the pulley having mass, which necessitates a net torque for angular acceleration, as defined by the equations of motion (F = ma and torque = I * angular_acceleration). The analysis confirms that the presence of mass in the pulley alters the tension dynamics compared to an ideal pulley scenario.

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  • Understanding of Newton's second law (F = ma)
  • Knowledge of torque and its relation to angular acceleration (torque = I * angular_acceleration)
  • Familiarity with free body diagrams for analyzing forces
  • Basic principles of rotational dynamics and pulley systems
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  • Study the principles of rotational dynamics in detail, focusing on pulleys with mass.
  • Learn how to construct and analyze free body diagrams for complex systems.
  • Explore the concept of net torque and its effects on angular acceleration in physical systems.
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Students in physics, particularly those studying mechanics, engineers working with pulley systems, and anyone interested in understanding the dynamics of forces in rotational systems.

tey
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Homework Statement



A 12kg box resting on a horizontal, frictionless surface is attached to a 5kg weight (hanging off the side of the table) by a thin, light wire that passes over a frictionless pulley. The pulley has a shape of a uniform solid disk of mass 2kg and a diameter of .5m. After the system is released, find the tension in the wire on both sides of the pulley

The answer gives different tensions in the wire on either side of the pulley. How is that possible?

Homework Equations



F = ma, torque = I*angular_acceleration


The Attempt at a Solution



(a) Tension between 12kg box and pulley = 32.7N, Tension between pulley and 5kg weight is 35.4N.
 
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tey said:

Homework Statement



A 12kg box resting on a horizontal, frictionless surface is attached to a 5kg weight (hanging off the side of the table) by a thin, light wire that passes over a frictionless pulley. The pulley has a shape of a uniform solid disk of mass 2kg and a diameter of .5m. After the system is released, find the tension in the wire on both sides of the pulley

The answer gives different tensions in the wire on either side of the pulley. How is that possible?
For an 'ideal' pulley of negligible friction and mass, the wire tension is the same on both sides of the pulley. Not so for a pulley with mass, because there must be a net torque acting on it to provide it with angular acceleration, per you relevant equation. below.

Homework Equations



F = ma, torque = I*angular_acceleration


The Attempt at a Solution



(a) Tension between 12kg box and pulley = 32.7N, Tension between pulley and 5kg weight is 35.4N.
Please show an attempt at a solution using free body diagrams.
 
I am also having problems understanding this. There is also more parts to the question.

(a) Tensions were correct.

(b) what is the acceleration of the box, after the system is released.

(c)After the system is released, find magnitude of the horizontal and vertical components of the force that the axle exerts on the pulley.

Diagram:
pulleywithrotation.png


Other information:
I = .036
torque = 8.82 N

I really don't know where to start.
 

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