Atwood's Machine: Finding Acceleration & Tension Magnitudes

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SUMMARY

The discussion focuses on solving the dynamics of Atwood's machine, where two masses, m_A and m_B, are connected by a string over a wheel. The key equations derived include m_A*a = m_A*g - T_A and m_B*a = T_B - m_B*g, which relate the linear acceleration of the blocks to the tensions in the cord. Additionally, the angular acceleration of the wheel is expressed as I(alpha) = T_A*R - T_B*R, with the relationship a = R(alpha) linking linear and angular accelerations. The discussion emphasizes the need for clarity in calculating tensions T_A and T_B under the condition of no slipping between the cord and the wheel.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Familiarity with rotational dynamics and moment of inertia
  • Knowledge of linear and angular acceleration relationships
  • Basic grasp of tension in strings and pulleys
NEXT STEPS
  • Study the derivation of equations of motion for Atwood's machine
  • Learn about the principles of rotational dynamics and torque
  • Explore the concept of moment of inertia in various shapes
  • Investigate real-world applications of Atwood's machine in physics
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Physics students, educators, and anyone interested in classical mechanics, particularly in understanding the dynamics of systems involving pulleys and tension forces.

Tonyt88
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There is an Atwood's machine. The masses of blocks A and B are m_A and m_B, respectively, the moment of inertia of the wheel about its axis is I, and the radius of the semicircle in which the string moves is R.

Known: m_A > m_B

a)Find the magnitude of the linear acceleration of the block A.
b)Find the magnitude of the linear acceleration of the block B.
c)What is the magnitude of the angular acceleration of the wheel C?
d)Find the magnitude of the tension in the left side of the cord if there is no slipping between the cord and the surface of the wheel.
e)Find the magnitude of the tension in the right side of the cord if there is no slipping between the cord and the surface of the wheel.

Okay, so I have:

m_A*a = m_A*g - T_A

m_B*a = T_B -m_B*g

I(alpha) = T_A*R - T_B*R

a = R(alpha)

Am I missing something, or...
 
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