Double Atwood Machine Question

In summary: I've looked online and people say to use "integrate" but I don't know how to do that. In summary, the person is having difficulty solving an equation for the acceleration of mass. They are trying to use the equation given by the picture, but they are not getting it correct. They have also tried doing it without using the picture, but that has also not worked. They are lost and need help from someone who knows what they are doing.
  • #1
JoeBargo
3
0

Homework Statement



I've tried and tried and can't solve this to look like this equation. Please Help!

http://i233.photobucket.com/albums/ee237/biggyjoe210/IMAG0175.jpg

1. Show that the Acceleration of Mass A is given by : (look at picture)

IMAG0175.jpg


Homework Equations



F = ma

The Attempt at a Solution



So far all I have is a = g(mA-mB)/(mA+mB)

Im lost
 
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  • #2
Did you draw any free-body diagrams?
 
  • #3
Yeah all have tension going up and mg going down except the pulley which has tension up and tension down as well *** mg. The tension of string attaching a and b are the same and c and d are the same.
 
  • #4
Does the following look like I'm on the right track? Six equations in six unknowns.
 

Attachments

  • atwood057.jpg
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  • #5
Yeah, I have that down. I solved for the smaller system(mA, mB, mD) for acceleration and tension. I'm guessing x is acceleration. If so that's exactly what I have. I can't get the algebra right or something when I solve for a1 and a2(the two separate accelerations of the strings). I keep getting close to the given formula but I'm messing up somewhere.
 
  • #6
hey do you go to tech??
m having problem with the same question...did you solved it??
 
  • #7
the trick is displace one body and see the motion of other bodies eg.if u displace the "Mc" body then the other two bodies(Ma and Mb) will as a whole go down but one of them will go up and other down relative to each other.then draw the free body diagram on each.NOTE: tension in the Mc body will be 2times that of ropes of other two.then write the equations involving T and g.gud luck
 
  • #8
I'm also at Tech. I get some of it, but there are like 3 parts to the final equation that I'm missing. I'm still not exactly sure on how to do this.
 

1. What is a Double Atwood Machine?

A Double Atwood Machine is a simple mechanical device that consists of two pulleys and a string connecting them. It is commonly used in physics experiments to demonstrate concepts related to forces and motion.

2. How does a Double Atwood Machine work?

The Double Atwood Machine works by using the principles of tension and gravity to transfer the force applied on one end of the string to the other. As one mass moves down, the other mass moves up, creating a continuous cycle of motion.

3. What is the purpose of a Double Atwood Machine?

The purpose of a Double Atwood Machine is to demonstrate the relationship between forces, masses, and acceleration using a simple and visual experiment. It can also be used to calculate and measure physical quantities such as tension and acceleration.

4. What are some examples of real-life applications of a Double Atwood Machine?

A Double Atwood Machine has various real-life applications, such as in elevators where the counterweight acts as the second mass, reducing the force needed to lift the elevator. It is also used in cranes, where the pulleys help to lift heavy objects with less effort.

5. What are some factors that can affect the operation of a Double Atwood Machine?

Some factors that can affect the operation of a Double Atwood Machine include the mass and weight of the objects used, the length and tension of the string, and the presence of friction. These factors can affect the accuracy of the experiment and should be carefully controlled for reliable results.

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