How Does the Ceiling Exert Force on a Pulley System?

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SUMMARY

The discussion focuses on calculating the force exerted by the ceiling on a hook supporting a frictionless pulley system. The system consists of a solid uniform disk pulley with a radius of 0.300 m, supporting two weights: 75 N and 125 N. The calculated force exerted by the ceiling is 249 N. Key equations utilized include the moment of inertia formula, I = 1/2 MR^2, and Newton's second law, F = ma.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with the moment of inertia for solid disks
  • Knowledge of tension in pulley systems
  • Basic principles of dynamics and forces
NEXT STEPS
  • Study the application of Newton's second law in multi-body systems
  • Learn about the dynamics of pulley systems and tension analysis
  • Explore the concept of moment of inertia in different shapes
  • Investigate the effects of friction in pulley systems
USEFUL FOR

Physics students, mechanical engineers, and anyone studying dynamics and forces in pulley systems will benefit from this discussion.

J89
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Homework Statement



Two weights are connected by a very light flexible cord that passes over a 50 N frictionless pulley of radius .300 m. Pulley is a solid uniform disk and is supported by a hook connected to a ceiling. What force does the ceiling exert on the hook? There are two weights around each side of the disk, one is 75 N and the other is 125 N. Answer is 249 N.


Homework Equations



I = 1/2 MR^2
F=ma




The Attempt at a Solution

 

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J89 said:
Two weights are connected by a very light flexible cord that passes over a 50 N frictionless pulley of radius .300 m. Pulley is a solid uniform disk and is supported by a hook connected to a ceiling. What force does the ceiling exert on the hook? There are two weights around each side of the disk, one is 75 N and the other is 125 N. Answer is 249 N.

Hi J89! :smile:

(I assume that "frictionless pulley" means that there is friction between the pulley and the rope, with no slipping)

The tension in the two sections of rope will be different … call them Tm and TM, and call the linear acceleration a …

then apply good ol' Newton's second law three times, ie to each of the weights and the pulley (separately), to get Tm + TM :wink:
 

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