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

[ago01]

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.

 

[jbriggs444]

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.

 

[ago01]

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!

 

[jbriggs444]

he's effectively getting "pulled twice", once by the arm, and once by the chair

Yes, "pulled twice" captures the idea nicely.

 

[Lnewqban]

 

[Lnewqban]

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:

 

[hutchphd]

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.