Double Atwood Machine and tension

In summary, the problem involves finding the tension in the string attached to mass 1 and mass 3, as well as the acceleration of all three masses. The free body diagrams are set up and three equations are derived from Newton's 2nd Law. The assumption is made that the massless pulleys do not accelerate and that mass 3 also does not accelerate, resulting in the tension in the string attached to mass 3 being equal to twice the tension in the string attached to mass 1. Any alternate approaches to solving the problem are welcomed.
  • #1
rwx1606
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0

Homework Statement


Find the tension in the string attached to mass 1 and mass 3. Find the acceleration of masses 1,2, and 3. The problem looks similar to the attached image except m1 and m2 are leveled. Express the answers in the given quantities and constants. I will call the tension in the string attached to mass A, F[tex]^{1}[/tex], and the tension attached to mass C, F[tex]_{T3}[/tex].

http://session.masteringphysics.com/problemAsset/1038667/6/YF-05-85.jpg


Homework Equations


[tex]\sum[/tex]F=ma


The Attempt at a Solution


Well aside from setting up the free body diagrams, I've come up with three equations from Newton's 2nd Law.

For mass A, I have the follow:
m[tex]_{1}[/tex]a[tex]_{1}[/tex]= F[tex]_{T1}[/tex]-m[tex]_{1}[/tex]g
For mass B:
m[tex]_{2}[/tex]a[tex]_{2}[/tex]=F[tex]_{T1}[/tex]-m[tex]_{2}[/tex]g
For mass C:
m[tex]_{3}[/tex]a[tex]_{3}[/tex]=F[tex]_{T3}[/tex]-m[tex]_{3}[/tex]g

The first thing that came to mind were the massless pulleys. I assumed both pulleys do not accelerate as a result. So because of this I also assumed mass 3 does not accelerate either or else the bottom pulley would accelerate. In addition I assumed the tension F[tex]_{T3}[/tex] is equal to 2F[tex]_{1}[/tex]. Any help would be appreciated. If my insights are all wrong feel free to direct me towards an alternate way of approaching this problem. Thanks in advance.
 
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  • #2
hmm I can't get the subscripts to work for some reason.
 
  • #3


Dear student,

Your approach to this problem is correct. The double Atwood machine is a classic example of using Newton's laws to solve for tensions and accelerations in a system of connected masses. Your three equations correctly describe the forces acting on each mass.

To solve for the tensions, you will need to use some algebra to eliminate variables and solve for the unknown tensions. For example, you can use the fact that the two masses on either side of a pulley must have equal acceleration, and therefore must have equal tensions in the string attached to the pulley. This will allow you to set up an equation relating F_{T1} and F_{T3}.

You are also correct in assuming that the massless pulleys do not accelerate, and that mass 3 does not accelerate. This is because the two sides of the machine are in equilibrium, meaning that the net force on each side is zero.

Overall, your approach is sound and with some careful algebraic manipulation, you should be able to solve for the tensions and accelerations in the system. Good luck!
 

Related to Double Atwood Machine and tension

1. What is a Double Atwood Machine?

A Double Atwood Machine is a mechanical system that consists of two Atwood Machines connected by a single pulley. It is used to demonstrate and study the principles of tension and acceleration.

2. How does a Double Atwood Machine work?

In a Double Atwood Machine, two masses are suspended from a single pulley. As one of the masses accelerates downwards, the other mass accelerates upwards. This creates a constant tension force in the rope connecting the two masses.

3. What is tension in a Double Atwood Machine?

Tension is a force that is exerted by the rope connecting the two masses in a Double Atwood Machine. It is always equal in magnitude and opposite in direction on both sides of the pulley, and it is responsible for the acceleration of the masses.

4. How is the tension calculated in a Double Atwood Machine?

The tension in a Double Atwood Machine can be calculated using the formula T = (m1*m2*g)/(m1+m2), where T is the tension force, m1 and m2 are the masses of the two objects, and g is the acceleration due to gravity.

5. What factors affect the tension in a Double Atwood Machine?

The tension in a Double Atwood Machine is affected by the masses of the objects, the acceleration due to gravity, and the angle at which the pulley is positioned. Additionally, any external forces acting on the system, such as friction, can also affect the tension.

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