The Atwood machine (or Atwood's machine) was invented in 1784 by Rev. George Atwood as a laboratory experiment to verify the mechanical laws of uniformly accelerated motion. Atwood's machine is a common classroom demonstration used to illustrate principles of physics, specifically mechanics.
The ideal Atwood Machine consists of two objects of mass m1 and m2, connected by an inelastic massless string over an ideal massless pulley.
When , the machine is in neutral equilibrium regardless of the position of the weights.
When both masses experience uniform acceleration.
forces affecting m1 :
forces affecting m2 :
Using Newton's second law we can derive an equation for the system's acceleration.
Conversely, the acceleration due to gravity, g, can be found by timing the movement of the weights, and calculating a value for the uniform acceleration a: .
The Atwood machine is sometimes used to illustrate the Lagrangian method of deriving equations of motion.
For example substituting into , we get
The tension can be found in a similar manner from
In that case, the total torque for the system becomes:
An elevator with a counterbalance approximates an ideal Atwood machine and thereby relieves the driving motor from the load of holding the elevator car — it has to overcome only weight difference and inertia of the two masses. The same principle is used for funicular railways with two connected railway cars on inclined tracks.
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