Mechanics Physics: Pulley w/ 2 Blocks - Determine T, T3, Tl, I1

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The discussion focuses on a mechanics physics problem involving a pulley with two blocks. The key tasks include determining the tension T in the cord and analyzing the system when one block is removed. The solution requires applying Newton's second law and rotational dynamics, specifically using the equations of motion for the blocks and the relationship between linear and angular acceleration. The final answers are expressed in terms of mass m, pulley radius R1, and rotational inertia I1.

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  • Understanding of Newton's second law of motion
  • Familiarity with rotational dynamics and moment of inertia
  • Knowledge of kinematic equations for linear motion
  • Basic grasp of tension in cords and pulleys
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  • Learn about the relationship between linear and angular acceleration
  • Explore the concept of moment of inertia for different shapes
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A pulley of radius R1 and rotational inertia I1 is mounted on an axle with negligible friction. A light cord passing over the pulley has two blocks of mass m attached to either end, as shown above. Assume that the cord does not slip on the pulley. Determine the answers to parts (a) and (b) in terms of m, R1, I1, and fundamental constants.
a. Determine the tension T in the cord.
b. One block is now removed from the right and hung on the left. When the system is released from rest, the three blocks on the left accelerate downward with an acceleration g/3 . Determine the following.
i. The tension T3 in the section of cord supporting the three blocks on the left
ii. The tension Tl in the section of cord supporting the single block on the right
iii. The rotational inertia I1 of the pulley
 
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