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For my physics assignment, I have to determine the equation of motion for an Atwood machine....

For my physics assignment, I have to determine the equation of motion for an Atwood machine. The final equation is only supposed to include m1,m2,g, and acceleration. I then have to use this equation to create a straight line graph with acceleration as the y axis, and the x-axis as the other variable (which I do not know yet as I have to figure it out from the equation)

I just need help figuring out the equation please.

fnet=?

Expert Solution

Equation of motion for an Atwood machine:

An Atwood machine consists of two weights, of mass m1 and m2, connected by a light inextensible cord of length l, which passes over a pulley of radius a<<l, and moment of inertia , as shown in below figure:

Referring to the diagram, we can see that this is a one degree of freedom system whose instantaneous configuration is specified by the coordinate x. Assuming that the cord does not slip with respect to the pulley, the angular velocity of pulley is .

Hence, the kinetic energy of the system is given by:

The potential energy of the system takes the form:

It follows that the Lagrangian is written as:

The equation of motion,

thus yields,

genius_generous answered 2 years ago

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