Analyzing Tensions in a Pulley System: Understanding Mechanical Advantage

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E2dad
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Homework Statement
How will the tensions/load be distributed between each wire section (4 sections)?
Relevant Equations
Not sure
I asume the upper right pulley wire loads will be split in two equally. Therefore, the sum of the loads above pulley equal T1+T2?.

To me it appears as if the setup is almost like a 2 to 1 ratio. However, the wires on the left side which are anchored, split the load of the other half of the 2 to 1 (half of half).

Therefore, top right pulley (T1+T2 = 50lbs)? T3=25lbs? T4=25lbs?

How would I see this mathematically solved using vector notation?

Note that the bottom pulleys are bonded together.
 

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Your help would be appreciated. I am so confused.
 
E2dad said:
Homework Statement: How will the tensions/load be distributed between each wire section (4 sections)?
Homework Equations: Not sure

I asume the upper right pulley wire loads will be split in two equally. Therefore, the sum of the loads above pulley equal T1+T2?.

To me it appears as if the setup is almost like a 2 to 1 ratio. However, the wires on the left side which are anchored, split the load of the other half of the 2 to 1 (half of half).

Therefore, top right pulley (T1+T2 = 50lbs)? T3=25lbs? T4=25lbs?

How would I see this mathematically solved using vector notation?

Note that the bottom pulleys are bonded together.
Suppose that, e.g., T2 and T3 are not equal. What would happen to the middle pulley?
 
haruspex said:
Suppose that, e.g., T2 and T3 are not equal. What would happen to the middle pulley?

Great question. Not sure.
 
haruspex said:
What happens when you apply opposing but unequal torques to an object that is free to rotate?

In this case that should not happen. All "legs" are anchored with a dedicated load not in motion (static).
 
E2dad said:
In this case that should not happen. All "legs" are anchored with a dedicated load not in motion (static).
That's not what I asked.
Forget the current problem for a moment. If a rope goes around a pulley (which is free to rotate) and the tensions are different in the two sections of rope, what will happen? Think about torque.
 
haruspex said:
That's not what I asked.
Forget the current problem for a moment. If a rope goes around a pulley (which is free to rotate) and the tensions are different in the two sections of rope, what will happen? Think about torque.

I believe the pulley shall torque or "rotate" freely towards the leg/section that has the highest tension?
 
haruspex said:
So what does that tell you about the tensions in your diagram?
 
Because of pulley torque:

T1 tension pointing up
T2 tension pointing down
T3 tension pointing up
T4 tension pointing up

?
 

Because of pulley torque:

T1 tension pointing up
T2 tension pointing down
T3 tension pointing up
T4 tension pointing up

?
 
E2dad said:
Because of pulley torque:

T1 tension pointing up
T2 tension pointing down
T3 tension pointing up
T4 tension pointing up

?
Not what I meant.
Take T2 and T3 for example. As you stated, if they are not equal then the pulley they both connect to will rotate. Does it?
 
haruspex said:
Not what I meant.
Take T2 and T3 for example. As you stated, if they are not equal then the pulley they both connect to will rotate. Does it?
In this case I believe NO. However, if there was slack YES until it stops or becomes static. The pulley torques I would imagine remains.
 
haruspex said:
You can safely assume it is now static.
So what can you say about T2 and T3?
T2 and T3 equal each other?
 
haruspex said:
Right.
What about all the other tensions?
All tensions are equal. Each leg is a 1/4 of 100LB load?