Simple Pulley System: Accelerations Equation Explained

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SUMMARY

The discussion focuses on the acceleration relationship in a simple pulley system, specifically the equation a1 = 2*a2. This relationship is derived from the geometric constraints of the system, where the displacement of mass m2 (x2) directly influences the displacement of mass m1 (x1) such that x1 = 2x2. The key takeaway is that understanding the geometry of the pulley system is essential for deriving acceleration equations.

PREREQUISITES
  • Basic understanding of kinematics
  • Familiarity with pulley systems
  • Knowledge of differentiation in calculus
  • Concept of geometric relationships in physics
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  • Study the principles of kinematics in one-dimensional motion
  • Learn about the mechanics of pulley systems and their applications
  • Review differentiation techniques in calculus
  • Explore geometric relationships in physics problems
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Students studying physics, particularly those focusing on mechanics and kinematics, as well as educators looking for clear explanations of pulley systems and acceleration relationships.

asi123
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Homework Statement



Hey guys.
I have the following pulley system (in the pic).
I wrote down all the equations.
The thing I don't get is the accelerations equation (a1 = 2*a2). I understand that I can get to this equation somehow by the length of the rope, but how?
Thanks.

Homework Equations





The Attempt at a Solution

 

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asi123 said:
The thing I don't get is the accelerations equation (a1 = 2*a2). I understand that I can get to this equation somehow by the length of the rope, but how?

Hi asi123! :smile:

You get it by double-differentiating x1 = 2x2

and that is simple geometry … when m2 moves a distance x2, m1 moves a distance x1 = 2x2. :smile:
 

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