Find Accelerations for Double Atwood Homework

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In summary, the conversation is about finding the equation for the accelerations of masses on a double Atwood apparatus using the formula F=ma. The person has created a free body diagram and has three equations for the forces, with the tension on the top rope being twice that of the lower rope. They also mention that the average of the accelerations for A and B is the opposite of A. They are having trouble solving the system of equations and are seeking help. The correct solution is given as AccelA = (MassB+MassC-2*MassA)*g/2T, AccelB = (2*MassA+MassC-MassB)*g/2T, and AccelC = (2
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MeMoses
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Homework Statement



I need to find the equation for the accelerations of the masses on a double atwood apartatus.

Homework Equations



F=ma

The Attempt at a Solution


Ok, I made a free body diagram and I think I figure the first part out. The tension on the top rope is twice the lower rope. I get 3 eqations for the forces.
Note: MassA is on the top pull with B and C on the lower
2T - MassA * g = MassA * AccelA
T - MassB * g = MassB * AccelB
T - MassC * g = MassC * AccelC
I also get AccelA = -((AccelB+AccelC)/2) because the average of A and B is simply the opposite of A.
I hope this is all clear and sorry about the formatting. Somehow I'm drawing a blank on solving this system of equations. I am pretty sure I have all that I need but I just can't get it started. Any help is greatly appreciated. Thank you
 
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  • #2
. The correct solution is AccelA = (MassB+MassC-2*MassA)*g/2TAccelB = (2*MassA+MassC-MassB)*g/2TAccelC = (2*MassA+MassB-MassC)*g/2T
 

Related to Find Accelerations for Double Atwood Homework

1. What is the purpose of the "Find Accelerations for Double Atwood Homework"?

The purpose of this homework is to practice using the Atwood machine to find the acceleration of a system of two masses connected by a string over a pulley.

2. How do I set up the equations for this homework?

To set up the equations, you will need to use Newton's second law of motion and the formula for the acceleration of an Atwood machine: a = (m1-m2)g/(m1+m2).

3. What information do I need to solve this homework?

You will need the masses of the two objects, the value of gravity (9.8 m/s^2), and the direction of motion for each mass (up or down).

4. How do I know if I have the correct answer?

You can check your answer by plugging it back into the equation and making sure it balances out. Also, check your units to make sure they are consistent.

5. Are there any common mistakes to watch out for when solving this homework?

Some common mistakes include not properly setting up the equations, not using the correct units, and not considering the direction of motion for each mass. It is also important to double check your calculations to avoid any errors.

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