An Atwood Machine is a simple physics laboratory maker often supplied to demonstrate simple principles the dynamics and also acceleration. The device typically involves a pulley, a string, and also a device of masses. Tricks to resolving Atwood an equipment problems are recognizing that the force transmitted by a string or rope, known as tension, is constant throughout the string, and also choosing a constant direction as positive. Let’s walk through an instance to demonstrate.
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Question: two masses, m1 and m2, space hanging through a massless string indigenous a frictionless pulley. If m1 is better than m2, identify the acceleration the the 2 masses once released indigenous rest.
Answer: First, determine a direction as positive. Since you can quickly observe the m1 will certainly accelerate downward and also m2 will accelerate upward, since m1 > m2, speak to the direction the motion about the pulley and down towards m1 the hopeful y direction. Then, you can create complimentary body diagrams because that both thing m1 and also m2, as displayed below:
Using this diagram, create Newton’s second Law equations for both objects, taking care to keep in mind the positive y direction:
Next, integrate the equations and also eliminate T by resolving for T in equation (2) and also substituting in for T in equation (1).
Finally, fix for the acceleration that the system.
Alternately, you might treat both masses as component of the same system.
Drawing a dashed line approximately the system, girlfriend can straight write an ideal Newton’s 2nd Law equation for the whole system.
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Note that if the string and pulley were not massless, this problem would end up being considerably more involved.