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 respectively.

Forces affecting m1 Forces affecting m2

The Atwood machine is sometimes used to illustrate the Lagrangian method of deriving equations of motion.

See also

Notes

External links

• 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.

• Professor Greenslade's account on the Atwood Machine

• Atwood's Machine by Enrique Zeleny, The Wolfram Demonstrations Project