Equation For Constant Acceleration
We are able to derive an equation for the acceleration by using force analysis. If we consider a massless, inextensible string and an ideal massless pulley, the only forces we have to consider are: tension force (T), and the weight of the two masses (W1 and W2). To find an acceleration we need to consider the forces affecting each individual mass. Using Newton's second law (with a sign convention of ) we can derive a system of equations for the acceleration (a).
As a sign convention, we assume that a is positive when downward for, and that a is positive when upward for . Weight of and is simply and respectively.
Forces affecting m1:
Forces affecting m2:
and adding the two previous equations we obtain
,
and our concluding formula for 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.
Read more about this topic: Atwood Machine
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