Monday, September 9, 2013

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 )

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