Contradictory FBD's for simple pulley problem

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    Pulley pulley problem
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SUMMARY

The discussion centers on a basic pulley problem involving a massless pulley and a suspended mass. The user initially misinterprets the free-body diagrams (FBDs) by cutting at different points, leading to contradictory conclusions about the tension in the ropes. Upon reevaluation, the user realizes that the tension in the top rope must account for the weight of the mass, confirming that it is indeed twice the tension in the bottom rope, represented as 2mg. This highlights the importance of correctly applying the principles of physics in analyzing pulley systems.

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  • Understanding of basic physics concepts, particularly forces and tension.
  • Familiarity with free-body diagrams (FBDs) and their application in mechanics.
  • Knowledge of Newton's laws of motion, especially in static systems.
  • Ability to analyze simple pulley systems and their mechanical advantages.
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  • Study the principles of tension in ropes and pulleys in static equilibrium.
  • Learn how to construct and analyze free-body diagrams for various mechanical systems.
  • Explore the effects of mass and gravity on tension in pulley systems.
  • Investigate more complex pulley systems and their applications in real-world scenarios.
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Students of physics, educators teaching mechanics, and anyone interested in understanding the dynamics of pulley systems and free-body diagram analysis.

mordechai9
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I have a basic pulley problem which has been troubling me.

Consider the system as shown in the attached picture. We have a massless pulley attached to the ceiling and a mass suspended from one side of the pulley.

If we take the free-body-diagram by 'cutting' where the red box is, we find the tension in the bottom rope is equal to the tension in the top rope. But if we take the free-body-diagram by 'cutting' at the green box, then we find the tension in the top rope is twice the tension in the bottom rope, since the tension in the rope is everywhere the same.

What is going wrong here?
 

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Nevermind. I just forgot for the red-box FBD you still have to include the weight of the mass, so actually it just says the tension in the top rope is equal to twice mg again. Doh. Too long since I did basic physics.
 

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