Acceleration of two pulleys help

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SUMMARY

The relationship between the accelerations of two masses, m1 and m2, in a pulley system is defined as a1 = 2*a2. This conclusion is derived from a practical demonstration using a string wrapped around a coffee cup, where pulling the string a distance x results in the cup moving a distance of x/2. This visualization effectively illustrates the mechanics of the system, confirming the acceleration relationship. Understanding this concept is crucial for solving problems related to pulley dynamics.

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  • Basic understanding of Newton's laws of motion
  • Familiarity with pulley systems and their mechanics
  • Knowledge of acceleration and its relation to force
  • Ability to interpret diagrams related to physics problems
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Homework Statement



If a1 and a2 are the accelerations of m1 and m2, respectively, what is the relation between these accelerations?

Homework Equations



Link to the diagram :
http://www.webassign.net/serpop/p4-38.gif

The Attempt at a Solution



The answer is a1 = 2*a2, but I'm having trouble visualizing/understanding how it was gotten. Is there a specific way to do this?
 
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Get a string or shoe lace and wrap it around a coffee cup. Hold one end of the string still and pull the other end of the string up some distance x, the coffee cup will move x/2.
 

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I get it now; thanks a lot! I can't believe I didn't even see that in the first place.
 

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