Do all masses in a pulley have the same acceleration?

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SUMMARY

In pulley systems, all masses experience the same acceleration due to the constraints of the connecting cable. The net force of the system can be calculated using the formula F=ma, where 'm' is the total mass and 'a' is the acceleration. However, specific scenarios may result in differing accelerations for individual masses, such as when the pulley system is configured to allow one mass to accelerate at a different rate than another. A free body diagram is essential for analyzing the forces acting on each mass and determining their respective accelerations.

PREREQUISITES
  • Understanding of Newton's Second Law (F=ma)
  • Basic knowledge of pulley systems and mechanics
  • Ability to create and interpret free body diagrams
  • Familiarity with the concept of tension in strings
NEXT STEPS
  • Study the principles of tension in pulley systems
  • Learn how to derive acceleration equations for multiple masses in a pulley system
  • Explore advanced pulley configurations and their effects on acceleration
  • Practice solving problems involving free body diagrams in mechanics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and pulley systems, as well as educators teaching these concepts in a classroom setting.

Balsam
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Homework Statement


The way my teacher makes us solve for accelleration in pulley problems is by calculating the net force of the system as a whole and then using F=ma, with the total mass and total net force. Are you supposed to solve for something like accelleration separately for each mass or do all masses in a pulley have the same accelleration?

Homework Equations


F=ma

The Attempt at a Solution


Does it make sense to solve for the accelleration of the system as a whole or of the separate masses? I'm not sure.
 
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All the mass have the same acceleration, if not that would mean that the cable connecting 'em would change it's lenght
 
Balsam said:

Homework Statement


The way my teacher makes us solve for accelleration in pulley problems is by calculating the net force of the system as a whole and then using F=ma, with the total mass and total net force. Are you supposed to solve for something like accelleration separately for each mass or do all masses in a pulley have the same accelleration?
If all masses have the same acceleration, depends on the problem.
In the figure on the left, the masses have the same acceleration, A upward and B downward. On the right, the accelerations are not the same. The upward acceleration of A is twice the downward acceleration of B. Make a free body diagram for each mass and find the relation of their accelerations from the condition that the length of the string must be constant.

upload_2016-3-20_6-36-41.png
 

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