Physics - Atwood's Machine

Atwood's Machine is a simple experiment that verifies the mechanical laws of motion under constant acceleration. As shown below two masses are attached to the ends of one pulley.

If the weight of m₁ and m₂ are equal then there is no acceleration. However if they are unequal their acceleration would be as follows. We can define the forces acting on m₁ as T the tension force of the rope and W1 the force due to the weight of the block. The forces acting on m₂ are T the tension force and W₂ the weight of the second block. As you can see the tension force has the same magnitude on each block and all that is left is to solve for our acceleration.

m₁ g - T = m₁ a

T - m₂ g =  m₂ a

We then combine this system of equations by adding them together to get

m₁ g - m₂ g = m1 a + m2 a

This is the same as distributing g and a over m1 and m2 so our acceleration is

a = g(m₁ - m₂ )/(m₁ + m₂ )