Mechanical advantage of a crane

In summary, the scenario where the man has the pulley has a mechanical advantage over the crane. He only needs to supply half the force over twice the length to lift the platform. This can be realized by considering the length of the rope and the distance the platform needs to be lifted. It is similar to a bosun's chair, where the person hoisting themselves requires less force than someone hoisting them from the ground. The force on the man contributes to lifting the platform in this scenario, unlike the crane where it doesn't. This principle can be formulated with energy conservation, as it requires a certain amount of work to raise the platform a certain height regardless of the setup.
  • #1
aaaa202
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2
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
aaaa202 said:
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?
 
  • #3
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.
 
  • #4
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
aaaa202 said:
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.
 

What is the definition of mechanical advantage?

Mechanical advantage refers to the ratio of the output force produced by a machine to the input force applied to it. In other words, it measures how much a machine amplifies the force applied to it.

How is the mechanical advantage of a crane calculated?

The mechanical advantage of a crane is calculated by dividing the load weight by the effort or input force required to lift the load. This ratio is also known as the ideal mechanical advantage.

What factors affect the mechanical advantage of a crane?

The mechanical advantage of a crane can be affected by various factors such as the length of the crane arm, the weight of the load, the angle of the crane arm, and the type of pulleys used in the crane system.

Why is the mechanical advantage important in cranes?

The mechanical advantage is important in cranes because it determines the amount of force required to lift heavy loads. A higher mechanical advantage means less effort or force is needed to lift the load, making the crane more efficient and effective.

How can the mechanical advantage of a crane be increased?

The mechanical advantage of a crane can be increased by using longer crane arms, heavier counterweights, and multiple pulleys in the crane system. However, it is important to consider the balance between mechanical advantage and the safety of the crane when making these adjustments.

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