Acceleration in an Atwood's Machine

In summary, we are trying to find the acceleration of two masses connected by a string over a pulley. The equation for this is a=g*m1-m1/m1+m2, but it is incorrect because it does not take into account the mass of the pulley. To incorporate the mass of the pulley, we need to use the moment of inertia formula, which for a disk is 1/2M*r^2. We can then treat the pulley as a point mass with the same moment of inertia and ignore its rotation.
  • #1
eagles12
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Homework Statement



An Atwood's machine consists of two masses, m1 and m2, connected by a string that passes over a pulley.
If the pulley is a disk of radius R and mass M, find the acceleration of the masses.
Express your answers in terms of variables m1,m2, M, R, and appropriate constants

Homework Equations




The Attempt at a Solution



I got the equation a=g*m1-m1/m1+m2 but it said this was incorrect because i need to function in M, the mass of the pulley. I am not sure how to incorporate that though.

I also tried a=g*m1-m2/m1+m2+I/r^2
it said this was incorrect also
 
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  • #2
You need the moment of inertia of the pulley. For a disk it's 1/2M r^2 .
Note that for a point mass rotating around an axis the MoI is mr^2
A trick then is to treat the pulley as if it were a point mass with the same moment of inertia. You can then ignore the fact it rotates and treat it as an added mass.
 

1. What is an Atwood's Machine?

An Atwood's Machine is a simple mechanical device used to demonstrate the principles of acceleration and force. It consists of two masses connected by a string or pulley system, with one mass hanging on each side of the pulley. The machine was named after George Atwood, an English mathematician who first described it in the late 1700s.

2. How does acceleration occur in an Atwood's Machine?

In an Atwood's Machine, acceleration occurs due to the difference in the masses on each side of the pulley. The heavier mass will experience a greater force of gravity, causing it to accelerate downwards. At the same time, the lighter mass will experience a smaller force of gravity, causing it to accelerate upwards. This creates a net force and acceleration in the direction of the heavier mass.

3. How is acceleration calculated in an Atwood's Machine?

The acceleration in an Atwood's Machine can be calculated using the formula a = (m1 - m2)g / (m1 + m2), where m1 and m2 are the masses on each side of the pulley and g is the acceleration due to gravity (9.8 m/s^2). This formula assumes that the pulley and string have negligible mass.

4. Can the acceleration in an Atwood's Machine be greater than the acceleration due to gravity?

No, the acceleration in an Atwood's Machine cannot be greater than the acceleration due to gravity. The acceleration due to gravity is a constant value and the maximum acceleration that can be achieved in the machine is equal to the acceleration due to gravity, when one of the masses is infinitely greater than the other.

5. How does changing the masses affect the acceleration in an Atwood's Machine?

The acceleration in an Atwood's Machine is directly proportional to the difference in masses on each side of the pulley. This means that increasing the difference in masses will result in a greater acceleration. However, the total mass of the system also affects the acceleration, with a larger total mass resulting in a smaller acceleration. Therefore, changing the masses on each side of the pulley can affect the acceleration in different ways.

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