Atwood machine

The Atwood machine (or Atwood's machine) was invented in 1784 by the English mathematician George Atwood as a laboratory experiment to verify the mechanical laws of motion with constant acceleration. Atwood's machine is a common classroom demonstration used to illustrate principles of classical mechanics.

The ideal Atwood machine consists of two objects of mass and , connected by an inextensible massless string over an ideal massless pulley.

Both masses experience uniform acceleration. When , the machine is in neutral equilibrium regardless of the position of the weights.

Equation for constant acceleration

An equation for the acceleration can be derived by analyzing forces.
Assuming a massless, inextensible string and an ideal massless pulley, the only forces to consider are: tension force (), and the weight of the two masses ( and ). To find an acceleration, consider the forces affecting each individual mass.
Using Newton's second law (with a sign convention of derive a system of equations for the acceleration ().

As a sign convention, assume that ''a'' is positive when downward for $m_1$ and upward for $m_2$. Weight of $m_1$ and $m_2$ is simply $W_1 = m_1 g$ and $W_2 = m_2 g$ respectively.

Forces affecting m₁: $m_1 g - T = m_1 a$
Forces affecting m₂: $T - m_2 g = m_2 a$
and adding the two previous equations yields $m_1 g - m_2 g = m_1 a + m_2 a,$
and the concluding formula for acceleration $a = g \frac$

The Atwood machine is sometimes used to illustrate the Lagrangian method of deriving equations of motion. Section 1-6, example 2

See also

*
*
*
*

Notes

External links

{{commons category, Atwood's machine
A treatise on the rectilinear motion and rotation of bodies; with a description of original experiments relative to the subject
by George Atwood, 1764. Drawings appear on page 450.
Atwood's Machine
by Enrique Zeleny, The Wolfram Demonstrations Project

Mechanics
Physics experiments