What is the tension force acting on the block?

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SUMMARY

The discussion focuses on calculating the tension force acting on a block connected to a uniform spherical shell and a pulley system. The spherical shell has a mass of Ms and radius R, while the pulley has a mass Mp and radius r. Key equations include the moment of inertia for the sphere, Isphere = (2/5) Ms R^2, and for the disk, Idisk = 0.5 Mp r^2. The tension force on the block and the sphere can be derived using torque and net force equations.

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  • Familiarity with moment of inertia calculations
  • Basic knowledge of Newton's second law (F=ma)
  • Ability to analyze free body diagrams (F.B.D.)
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1. A uniform sperical shell of mass Ms and radius R rotates about a vertical axis on frictionless bearings. A light cord passes around the equator of the shell over a pulley (a disk of mass Mp and radius r) and is attached to a small block of mass m that is otherwise free to fall under the influence of gravity.
A. What is the acceleration of the block?
B. What is the tension force acting on the block?
C. What is the tension force acting on the sphere?




Homework Equations


Isphere=(2/5) Ms R^2 Idisk=.5Mpr^2


3. Torque =rxf=Is(angular a)
RF=Is(angular a)
F=(2/5)MsR(ang. a)
Fnet=ma
Fs-mg=ma

 
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