Intuitive Explanation of an Atwood Machine

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SUMMARY

The Atwood Machine requires consideration of both masses to accurately determine the acceleration of the system. The tension in the string is calculated by subtracting the smaller weight from the larger weight, and then dividing by the total weight, which yields the correct acceleration. This method, while effective, may not align with the formal approach of isolating masses and applying Newton's Laws through free body diagrams. Understanding the interaction of opposing forces is crucial for grasping the underlying physics of the Atwood Machine.

PREREQUISITES
  • Understanding of Newton's Laws of Motion
  • Familiarity with free body diagrams
  • Basic knowledge of forces and tension in physics
  • Concept of acceleration in a two-mass system
NEXT STEPS
  • Study the derivation of acceleration in Atwood Machines using Newton's Laws
  • Learn how to construct and interpret free body diagrams for multi-mass systems
  • Explore the concept of tension in strings and its role in pulley systems
  • Investigate real-world applications of Atwood Machines in engineering and physics
USEFUL FOR

Students studying physics, educators seeking to explain mechanics concepts, and anyone interested in understanding the dynamics of pulley systems.

BlackHayze
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So I'm working through a physics a textbook on my own, and because of that don't always have a professor who can help explain concepts I don't understand, so I'm turning to you good folks.

Could someone explain why both masses need to be taken into account when determining the acceleration of one side of an Atwood Machine? And maybe the way I started doing it led me to have a harder time, but I basically found the tension by subtracting the smaller weight from the heavier, then dividing by the total weight got me the correct answer.

I'm fairly certain this way of going about it is wrong, but most of what I see online about the correct way isn't making intuitive sense to me. Could anyone try to explain to me how it works and why the math works out the way it does? Thanks in advance!
 
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The core concept is that the weights are pulling in opposite directions.
The formal approach is to isolate the masses, draw free body diagrams, and apply Newton's Laws to each separately.
 

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