Understanding the physics of a bosun's chair and mechanical advantage

In summary, In the problem, a person is weighting themselves down with a 10 kg Bosun Chair while another person is pulling on a rope. The rider has a mechanical advantage because they are pulling twice the weight of the chair. If help is given by a coworker, the help only gives 1T of assistance.
  • #1
ago01
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I had a homework question recently where I had gotten a bosun chair question wrong. It is the exact question found in this youtube video (with the values changed).



I am struggling to understand the way 2T is arrived at here (though I do understand this is an example of mechanical advantage). In my analysis the only difference I had was I had simply assumed that the tension was the same throughout, arriving at exactly T force being needed to lift the chair (no mechanical advantage).

But there is a reaction force I apparently forgot. When the bosun chair rider pulls the cable down it imposes a force (obviously). Then it also imposes a force on the chair. I had wrapped these all up into tension under the (bad) assumption that it was only the tension causing the bosun chair to lift up, and the force being applied to pull the chair up was making the rope taut, therefore transferring that force directly to the bosun chair. So under this (wrong) assumption the pull force imposed a tension in the line, the reaction force was the "pull tension" felt by the chair. Since the rope is massless and the pulley is deal the tension is the same throughout. I hope you can see how I am puzzled.

But in the analysis in this youtube video there is in fact two forces at play here. One tension and one push force each of them having a pivotal role in lifting the chair with mechanical advantage.

Even more confusing is how the mechanical advantage is eliminated if a coworker instead lifts the chair. It appears all the mechanical advantage is derived from lifting yourself!

Do I misunderstand tension? In other problems, such as boxes pulling each other on inclines, or pulling a string of boxes together and calculating their individual cable tensions, or two masses on a pulley with one falling under gravity I assumed it was the tension doing the moving here because if the string went limp nothing would move. This was reinforced by tension being sufficient to solve these problems, I suppose. But it appears not to be the case here and I am trying to differentiate them in my head.
 
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  • #2
ago01 said:
But there is a reaction force I apparently forgot. When the bosun chair rider pulls the cable down it imposes a force (obviously). Then it also imposes a force on the chair.
It is nothing as magical as what you are contemplating. It is entirely mundane.

The supporting force on the chair is only equal to ##T##. Not ##2T##. So that part of your analysis was correct.

But the supporting force on the person in the chair... There is the supporting force from the chair itself. Plus the supporting force from the person's grip on the cable. The rider is supporting half of his own weight with his hands.
 
  • #3
jbriggs444 said:
It is nothing as magical as what you are contemplating. It is entirely mundane.

The supporting force on the chair is only equal to ##T##. Not ##2T##. So that part of your analysis was correct.

But the supporting force on the person in the chair... There is the supporting force from the chair itself. Plus the supporting force from the person's grip on the cable. The rider is supporting half of his own weight with his hands.

I see so I think I see my mistake. To be clear:

When the man pulls on the rope he induces a tension in the rope, which by Newton's 3rd law induces a tension on the other side lifting the chair. There's no extra force, just tension. The extra tension force comes from the rope also pulling up on him via the connection he makes with his arm.

This is why when his coworker helps, it's just 1T, no mechanical advantage. But because he's effectively getting "pulled twice", once by the arm, and once by the chair he has some mechanical advantage. I had mistakenly treated the man as completely separate from the rope which is how I made my mistake. Makes sense!
 
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  • #4
ago01 said:
he's effectively getting "pulled twice", once by the arm, and once by the chair
Yes, "pulled twice" captures the idea nicely.
 
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Ex4.17.gif
 
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  • #6
ago01 said:
This is why when his coworker helps, it's just 1T, no mechanical advantage. But because he's effectively getting "pulled twice", once by the arm, and once by the chair he has some mechanical advantage.
The amount of mechanical advantage he has is exactly 2.
You can see that if you make the chair your fixed point of reference and analyze the performed work.

Then, the fixed pulley becomes and acts as a mobile pulley, which approaches the chair at exactly half the speed with which the hands-rope move respect to the chair.

Try turning the attached diagram upside down and imagine that the black line is the chair and that 10 kgf is the weight of the chair plus the rider:

cub_simple_lesson05_fig6.jpg
 
  • #7
Lnewqban said:
You can see that if you make the chair your fixed point of reference and analyze the performed work.
Personally I find this a very confusing analysis. To each his own I guess.
 

1. What is a bosun's chair and how does it work?

A bosun's chair is a type of seat that is commonly used by workers in high places, such as on ships or in construction sites. It is typically made of canvas or rope and is suspended from a single point, allowing the user to be raised or lowered. The chair works by utilizing the principles of mechanical advantage, where a small force applied over a long distance can lift a heavier load over a shorter distance.

2. What is the purpose of a bosun's chair?

The main purpose of a bosun's chair is to provide a safe and efficient way for workers to access high places. It is commonly used for tasks such as painting, window cleaning, and maintenance work on tall structures. The chair allows the user to be lifted to the desired height and provides a stable and secure platform for them to work from.

3. How does the mechanical advantage of a bosun's chair work?

The mechanical advantage of a bosun's chair is achieved through the use of a pulley system. The chair is suspended from a single point, which is connected to a rope that runs through a series of pulleys. This arrangement allows for the force applied by the user to be multiplied, making it easier to lift heavier loads. The mechanical advantage is determined by the number of pulleys in the system.

4. What are the benefits of using a bosun's chair?

One of the main benefits of using a bosun's chair is that it provides a safe and stable platform for workers to perform tasks at high places. It also allows for efficient and precise movement, as the user can be easily raised or lowered to the desired height. Additionally, the use of a bosun's chair reduces the physical strain on the user, making it easier to perform tasks that would otherwise be difficult or impossible to do without the chair.

5. Are there any safety precautions to keep in mind when using a bosun's chair?

Yes, it is important to follow proper safety precautions when using a bosun's chair. This includes checking the chair and all its components for any signs of damage before each use, wearing appropriate safety gear such as a harness, and ensuring that the chair is properly secured and stable. It is also important to have a trained and experienced operator who can properly operate the chair and monitor the safety of the user at all times.

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