Forest UCM NLM AtwoodMachine

Simple Atwood's machine

[math]\displaystyle{ \Rightarrow T = \frac{2m_1m_2}{m_1+m_2} g }[/math]

Double Atwood's machine

The problem

Determine the acceleration of each mass in the above picture.

Step 1: Identify the system

Each block is a separate system with two external forces; a gravitational force and the rope tension.

Step 2: Choose a suitable coordinate system

A coordinate system with one axis that defines the posive direction as up is one possible orientation.

Step 3: Draw the Free Body Diagram

File:TF UCM FBD DoubleAtwoodMach.png

Step 4: Define the Force vectors using the above coordinate system

for mass 1

[math]\displaystyle{ T_1 - m_1 g = m_1 a_1 }[/math]

for mass 2

[math]\displaystyle{ T_2 - m_2 g = m_2 a_2 }[/math]

for mass 3

[math]\displaystyle{ T_3 - m_3 g = m_3 a_3 }[/math]

Step 5: Use Newton's second law

Forest_UCM_NLM#Atwoods_Machine