12.1 Pulley Problems - Part I, Set up the Equations

In the figure, pulley A is fixed to the ceiling. An ideal rope is attached at one end to block 1 of mass \(m_1\), it passes around a second pulley, labelled B, and its other end is fixed to the ceiling. A second ideal rope attaches pulley B to a second block of mass \(m_2\). As a result, pulley B and block 2 move together.

The goal of the problem is to calculate the accelerations of blocks 1 and 2.

A diagram of two blocks hanging from two pulleys attached to the ceiling.

The solution of this problem is divided into four parts:

  • Part I : Set up the system of equations.
  • Part II: Constraint condition - find the relationship between the accelerations.
  • Part III: Constraint condition using a virtual displacement argument.
  • Part IV: Solving the system of equations.


The video below will help you to set up the equations needed to answer the question.

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