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Mechanical advantage of a crane

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Consider the following picture, where the same platform and man is being lifted by a crane and by the man standing the platform, who can pull on a rope connected to a pulley in the ceiling. My question is: Does the scenario in which the man has the pulley have a mechanical advantage over the other? i.e. Does he have to supply half the force over twice the length to lift the platform?

If yes, how can I realize that he must pull twice the amount of rope through the pulley?
 

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  • #2
Doc Al
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If yes, how can I realize that he must pull twice the amount of rope through the pulley?
In your first diagram, forget the man for a moment. Just imagine both ends of the rope being attached to the platform. If the distance from platform to pulley is L, what's the total rope length? If you want to pull the platform up a distance ΔL closer to the ceiling, how much rope needs to be pulled?
 
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This is just like when i rig a bosun's chair. If I hoist myself it takes less force to pull the rope than if my buddy on the ground pulls me up. While all parts of line in a block system see the same load, my effective weight is reduced by an amount equal to the line load if I'm pulling on the line myself. But my buddy would have to hoist my full weight.
 
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Doc Al. I think you want me to see that I must pull 2x length of rope through the pulley if I want to move the platform up x. But it's just weird for me. Imagine it takes Mg to make the platform move. Are you then suggesting that I can pull the platform up supplying a force of ½Mg over twice distance? That doesn't sound right for me.

Edit: Is it because the force on the man contributes to lifting the platform whilst it doesn't for the crane? That would make sense. But isn't it more or less a "coincidence" that this principle can be formulated with energy conservation?
 
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  • #5
Doc Al
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Doc Al. I think you want me to see that I must pull 2x length of rope through the pulley if I want to move the platform up x. But it's just weird for me. Imagine it takes Mg to make the platform move. Are you then suggesting that I can pull the platform up supplying a force of ½Mg over twice distance? That doesn't sound right for me.
Realize that the man can take advantage of the pulley which is attached to the ceiling. In that arrangement (which is equivalent to a bosun's chair, as Pkruse mentioned) there are two strands of rope attached to the 'man+platform'. So the tension in the rope, which is the force the man must generate, is only half the weight of the platform.
Edit: Is it because the force on the man contributes to lifting the platform whilst it doesn't for the crane? That would make sense.
Yes. The force the man applies, multiplied by the pulley, is what pulls him and the platform up.
But isn't it more or less a "coincidence" that this principle can be formulated with energy conservation?
No coincidence at all. Energy is conserved. If you arrange things so that you only have to pull with half the force, the 'penalty' is that you'll have to pull twice the distance. No matter what you do, it requires a certain amount of work to raise the 'man+platform' a certain height. No getting around that.
 

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