Analyzing Tensions in a Pulley System: Understanding Mechanical Advantage

AI Thread Summary
The discussion centers on analyzing the tension distribution in a pulley system, where the upper right pulley wires are assumed to split loads equally. The user proposes that the setup resembles a 2:1 ratio, leading to calculations suggesting T1 + T2 equals 50 lbs, with T3 and T4 each at 25 lbs. The conversation explores the implications of unequal tensions on pulley rotation, concluding that in a static scenario, T2 and T3 must be equal, resulting in all tensions being equal at a quarter of the total load. The final understanding is that each wire section carries an equal share of the load due to the static nature of the system.
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.
 
E2dad said:
Great question. Not sure.
What happens when you apply opposing but unequal torques to an object that is free to rotate?
 
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?
 
E2dad said:
I believe the pulley shall torque or "rotate" freely towards the leg/section that has the highest tension?
So what does that tell you about the tensions in your diagram?
 
  • #10
haruspex said:
So what does that tell you about the tensions in your diagram?
 
  • #11
Because of pulley torque:

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

?
 
  • #12

Because of pulley torque:

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

?
 
  • #13
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?
 
  • #14
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.
 
  • #15
E2dad said:
if there was slack YES until it stops or becomes static.
You can safely assume it is now static.
So what can you say about T2 and T3?
 
  • #16
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?
 
  • #17
E2dad said:
T2 and T3 equal each other?
Right.
What about all the other tensions?
 
  • #18
haruspex said:
Right.
What about all the other tensions?
All tensions are equal. Each leg is a 1/4 of 100LB load?
 
  • #19
E2dad said:
All tensions are equal. Each leg is a 1/4 of 100LB load?
Yes..
 

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