Analyzing Tensions in a Pulley System: Understanding Mechanical Advantage

[E2dad]

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.

 

[E2dad]

Your help would be appreciated. I am so confused.

 

[haruspex]

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?

 

[E2dad]

Suppose that, e.g., T₂ and T₃ are not equal. What would happen to the middle pulley?

Great question. Not sure.

 

[haruspex]

Great question. Not sure.

What happens when you apply opposing but unequal torques to an object that is free to rotate?

 

[E2dad]

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).

 

[haruspex]

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.

 

[E2dad]

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]

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?

 

[E2dad]

So what does that tell you about the tensions in your diagram?

 

[E2dad]

Because of pulley torque:

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

?

 

[E2dad]

Because of pulley torque:

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

?

 

[haruspex]

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?

 

[E2dad]

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]

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?

 

[E2dad]

You can safely assume it is now static.
So what can you say about T₂ and T₃?

T2 and T3 equal each other?

 

[haruspex]

T2 and T3 equal each other?

Right.
What about all the other tensions?

 

[E2dad]

Right.
What about all the other tensions?

All tensions are equal. Each leg is a 1/4 of 100LB load?

 

[haruspex]

All tensions are equal. Each leg is a 1/4 of 100LB load?

Yes..