Analyzing Tensions in a Pulley System: Understanding Mechanical Advantage

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Homework Help Overview

The discussion revolves around analyzing the tensions in a pulley system, specifically focusing on how loads are distributed among the wires and the implications of unequal tensions. Participants explore the concept of mechanical advantage and the static nature of the system.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the assumption that pulley loads are split equally and question how this affects the overall tension in the system. There are inquiries about the mathematical representation using vector notation and the implications of unequal tensions on pulley rotation.

Discussion Status

The discussion is ongoing, with participants raising questions about the relationships between different tensions and their effects on the system. Some guidance has been offered regarding the equality of tensions in a static scenario, but multiple interpretations and assumptions are still being explored.

Contextual Notes

There is a mention of the system being static, which influences the discussion on tension equality. Participants also consider the effects of torque and the conditions under which the pulleys operate.

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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