What Is the Acceleration Constraint in This Pulley System?

[ezp0004]

Homework Statement

Hello. I need help with a problem that deals with the acceleration constraint of a system (URL below is to an image of the system):

http://s3.amazonaws.com/answer-board-image/e8ee7c74-664f-4220-a394-fc2b3d5bc269.jpeg

The questions asked in the problem are as follows:

1) Find the acceleration constraint for this system. It should be a single equation relating a1y, a2y, and a3y. Hint: yA is not a constant.

2) Find an expression for the tension in string "A".

3) Using m1 = 2.5kg, m2 = 1.5kg, and m3 = 4kg, find a1y, a2y, and a3y.

Homework Equations

I need to find equation for a1y in terms of a2y and a3y. I know that a1y should be equal to -a2y. However, I do not understand how a3y relate to these. Newton's second law (force=mass*acceleration) should be the only other equation needed to solve this problem.

The Attempt at a Solution

Other than recognizing that a1y = -a2y, I am complete stuck on this problem. I would appreciate any and all help that you may be able to provide. Thanks in advance.

 

[Andrew Mason]

Homework Statement

Hello. I need help with a problem that deals with the acceleration constraint of a system (URL below is to an image of the system):

http://s3.amazonaws.com/answer-board-image/e8ee7c74-664f-4220-a394-fc2b3d5bc269.jpeg

The questions asked in the problem are as follows:

1) Find the acceleration constraint for this system. It should be a single equation relating a1y, a2y, and a3y. Hint: yA is not a constant.

2) Find an expression for the tension in string "A".

3) Using m1 = 2.5kg, m2 = 1.5kg, and m3 = 4kg, find a1y, a2y, and a3y.

Homework Equations

I need to find equation for a1y in terms of a2y and a3y. I know that a1y should be equal to -a2y. However, I do not understand how a3y relate to these. Newton's second law (force=mass*acceleration) should be the only other equation needed to solve this problem.

The Attempt at a Solution

Other than recognizing that a1y = -a2y, I am complete stuck on this problem. I would appreciate any and all help that you may be able to provide. Thanks in advance.

I am not clear on the variables you are using. Please explain what you mean by a1y, a2y, a3y etc. That is an acceleration x distance.

Assume that m2=m3 and m1=m2+m3. What would the tension be on the ropes? Then change the masses slightly and analyse the change.

AM

 

[ezp0004]

I am not clear on the variables you are using. Please explain what you mean by a1y, a2y, a3y etc. That is an acceleration x distance.

Assume that m2=m3 and m1=m2+m3. What would the tension be on the ropes? Then change the masses slightly and analyse the change.

AM

I believe that a1y, a2y, and a3y are referring to the accelerations of blocks m1, m2, and m3 in the 'y' direction. Other than that, all variables should be represented in the figure that I linked.

Using m2=m3 and m1=m2+m3, does this meant that the tensions on the ropes for m2 and m3 are the same and that the tension for the rope connected to m1 is twice that of the tension for ropes connected to m2 and m3? I'm not really sure what you are trying to get at. Since the masses are given in the third question (m1+m2=m3 but m1 does not equal m2).

 

[Andrew Mason]

I believe that a1y, a2y, and a3y are referring to the accelerations of blocks m1, m2, and m3 in the 'y' direction. Other than that, all variables should be represented in the figure that I linked.

Using m2=m3 and m1=m2+m3, does this meant that the tensions on the ropes for m2 and m3 are the same and that the tension for the rope connected to m1 is twice that of the tension for ropes connected to m2 and m3? I'm not really sure what you are trying to get at. Since the masses are given in the third question (m1+m2=m3 but m1 does not equal m2).

If m1 = (m2+m3) and m2=m3, the system is in balance. Doing a free body diagram you can see that: 1. the tension in the rope through A is just m₂g and the tension in the rope through B is m₁g = (m2+m3)g

Now change it so that m2 and m3 differ by \Delta m and analyse that. (Hint: think of m2 on each side with an added mass \Delta m added to the one on the right (m3).

AM