How to draw pulley system diagram to find the relationship between two objects?

In summary, the acceleration in block A is related to the acceleration in block B, but the direction of the forces is irrelevant.
  • #1
theBEAST
364
0

Homework Statement


Here is the diagram and I need to find a relationship between the acceleration in block A and the acceleration in block B.
http://dl.dropbox.com/u/64325990/HW%20Pictures/datum2.PNG

The Attempt at a Solution


Here is my diagram, which is wrong:
http://dl.dropbox.com/u/64325990/HW%20Pictures/Photo%202012-04-08%209%2039%2025%20PM.jpg

It is wrong in that there shouldn't be a negative sign in front of aB. Instead 3aA=2aB is the correct answer. However I do not know how to derive that answer and where to put my datum. I need help with the diagram, thanks!
 
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  • #2
If A moves downward B will move to the left and SB will decrease. You supposed aB in the direction of growing sA.ehild
 
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  • #3
ehild said:
If A moves downward B will move to the left and SB will decrease. You supposed aB in the direction of growing sA.ehild

I am still confused... So do you mean that with what I did, I can still get the correct answer? This is really confusing because one object is moving up/down while the other is left/right so I don't know how to set up the signs and how to define the directions.

I forgot to mention in the question that block A accelerates downwards and block B is to the left according to the question. I did the problem with 3a_A=-2a_B and I go the wrong answer. When I used 3a_A=2a_B I got the right answer.
 
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  • #4
OH I just had an epiphany, so are you saying that the way I drew my diagram would be wrong in that s_B is pointing to the right when it should be pointing to the left since the question tells me a_B is pointing to the left?
 
  • #5
It depends what you mean on S. If it is the length of a piece of thread, 3SA+2SB =L is right. If it is displacement of a block in the "natural direction of moving) 3SA=2SB.

When the motion goes on along a thread, it can be considered one-dimensional. The actual direction (horizontal, vertical, along a slope... ) is irrelevant. Fit the direction of forces to the supposed direction of the accelerations.

ehild
 
  • #6
ehild said:
Fit the direction of forces to the supposed direction of the accelerations.

ehild

This is what I am doing now and it has been working great so far! Thanks for your help!
 
  • #7
You are welcome. :smile:

ehild
 

1. How do I draw a pulley system diagram?

To draw a pulley system diagram, first identify the two objects that are connected by the pulley. Draw a rectangle to represent each object, and label them with their respective masses. Then, draw a circle or oval to represent the pulley. Draw a line connecting the two objects to the pulley, and label it with the tension force acting on the objects. Finally, add arrows to represent the direction of the forces and label any other relevant information.

2. How do I find the relationship between two objects in a pulley system?

To find the relationship between two objects in a pulley system, you can use the equation F1 = F2. This means that the force acting on one object is equal and opposite to the force acting on the other object. You can also use this equation to determine the acceleration of the objects, as the force is equal to the mass times the acceleration (F=ma).

3. Can I use a pulley system to lift objects of different masses?

Yes, a pulley system can be used to lift objects of different masses. By using multiple pulleys and changing the direction of the rope, you can distribute the weight of the load among multiple ropes and make it easier to lift.

4. How does the number of pulleys affect the relationship between two objects in a pulley system?

The number of pulleys does not affect the relationship between two objects in a pulley system. The relationship is still based on the equation F1 = F2, regardless of how many pulleys are in the system. However, using more pulleys can make it easier to lift heavier objects.

5. What is the difference between a fixed and movable pulley in a pulley system diagram?

A fixed pulley is attached to a stationary object, while a movable pulley is attached to the object being moved. In a pulley system diagram, a fixed pulley is represented by a circle or oval that is attached to a fixed object, whereas a movable pulley is represented by a circle or oval that is attached to the object being moved.

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