Unequal Accelerations in Double Atwood Machine

In summary, the conversation discusses the accelerations of block A and block B in a Double Atwood machine. The reason for the unequal accelerations is due to the pulley being attached to a second pulley, causing an additional term to be added to both accelerations.
  • #1
id the sloth
67
0
I have a simple question about the Double Atwood machine.


220px-DoubleAtwood.jpg


I am able to follow the solution but one thing makes no sense to me. The accelerations for block A and block B are:

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Why aren't these equal? If they aren't, doesn't that mean the rope stretches? Or is this just an effect of assuming a massless rope?
 
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  • #2
In the few minutes since posting this, I have realized my mistake.

a_b and a_a are not equal because that pulley is attached to a second pulley. When that pulley A and B are attached to moves up and down, it will add a term to both a_b and a_a, making them unequal.
 

Related to Unequal Accelerations in Double Atwood Machine

1. What is a Double Atwood Machine?

A Double Atwood Machine is a simple mechanical device that consists of two masses connected by a string or rope that passes over a pulley. It is used to study the effects of unequal accelerations on the masses due to varying forces.

2. Why are the accelerations of the masses unequal in a Double Atwood Machine?

The accelerations of the masses in a Double Atwood Machine are unequal because the forces acting on each mass are different. The net force on a mass is equal to its mass multiplied by its acceleration, so if the forces are unequal, the accelerations will also be unequal.

3. How do you calculate the accelerations of the masses in a Double Atwood Machine?

The accelerations of the masses can be calculated by using the equation a = (m1-m2)/(m1+m2) * g, where m1 and m2 are the masses and g is the acceleration due to gravity. This equation takes into account the unequal forces and masses of the two masses.

4. How does the angle of the pulley affect the accelerations in a Double Atwood Machine?

The angle of the pulley does not affect the accelerations in a Double Atwood Machine as long as the pulley is frictionless. This is because the forces acting on the masses are still the same, regardless of the angle of the pulley.

5. What factors can cause the accelerations to be unequal in a Double Atwood Machine?

The accelerations can be unequal due to varying forces on the masses, different masses of the two masses, and friction in the pulley. In real-life situations, other factors such as air resistance and the strength of the string or rope can also affect the accelerations.

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