Understanding Different Accelerations in Constrained Pulley Motion

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SUMMARY

The acceleration of masses m1 and m2 in a constrained pulley system can differ due to the motion of the pulley itself, which is influenced by mass m3. When one mass moves upward, its acceleration is augmented, while the downward-moving mass experiences diminished acceleration. This phenomenon is best understood through free-body diagrams, which illustrate the forces acting on each mass and the pulley. Analyzing these diagrams reveals the relationship between the masses and their respective accelerations.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with free-body diagrams
  • Basic knowledge of pulley systems
  • Concept of inertial frames of reference
NEXT STEPS
  • Study the mechanics of pulley systems in detail
  • Learn how to draw and analyze free-body diagrams
  • Explore the effects of different mass distributions on acceleration
  • Investigate the role of inertial frames in classical mechanics
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the dynamics of pulley systems and acceleration differences in constrained motion.

anigeo
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could you please tell me how can the accelaration of masses m1 and m2 can be different.
i am in a great necessity.so please explain me how can the two strings of the two sides of the lower pulley have different accelarations?
 

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A good start: draw some free-body diagrams.
 
The lower masses have different accelerations due to the fact that the pulley they are attached to is itself moves due to the mass m3. So the mass moving upward will have an augmented acceleration while the mass moving downward will have a diminished acceleration. (Everything being viewed from an inertial frame like the constant surroundings.)
 

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