Solving for Speed of Blocks in Uniform Pulley System

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SUMMARY

The speed of the blocks (m1 and m2) in a uniform pulley system can be calculated using the formula v = √(4gd/5). This formula derives from equating the change in gravitational potential energy of the blocks to the sum of their kinetic energy and the rotational kinetic energy of the pulley disk. The analysis assumes no friction and constant tension in the string, leading to the conclusion that the speeds of m1 and m2 are equal, with v(m1) = v(m2) = rw, where r is the radius of the disk and w is the angular velocity.

PREREQUISITES
  • Understanding of gravitational potential energy
  • Knowledge of kinetic energy concepts
  • Familiarity with rotational dynamics
  • Basic principles of pulley systems
NEXT STEPS
  • Study the principles of energy conservation in mechanical systems
  • Learn about rotational kinetic energy and its applications
  • Explore the dynamics of pulley systems in more complex scenarios
  • Investigate the effects of friction on pulley systems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators seeking to explain pulley systems and energy conservation principles.

Littlemstrouble
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Homework Statement


A pulley is a uniform cylindrical disk of mass m and radius r. The strings are massless and there is no friction. If the system is initially at rest, find the speed of the blocks (m1 and m2) after they have moved a distance d.

m1----------0
**********l
**********l
**********l
**********m2

Homework Equations





The Attempt at a Solution


The answere should be v = square root(4gd/5)

 
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You'll need to look at the change in the gravitational potential energy of m1 and m2 and equate that to the kinetic energy of m1 and m2 plus the rotational kinetic energy of the disk. I don't believe your answer unless there is a special relation between m1, m2 and m.
 
If there is no friction, then tension in the string is constant and the speed of m1=m2. Now, v(m1)=v(m2)=rw where r is the radius of the disk and w is the angular velocity.
 

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