Calculate Acceleration of an Atwood Machine Using Mechanical Energy

Solve for the velocity and acceleration of a hanging Atwood machine using the conservation of mechanical energy.
This problem is typically solved using force and Newton's Laws, however in this problem we use the conservation of mechanical energy, or the work energy theorem to look at the loss of gravitational potential energy and relate it to the increase in kinetic energy.
This problem comes up in physics courses including AP Physics 1 and AP Physics C Mechanics.

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