Pulley with Chair Question

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In summary, the conversation discusses the concept of tension in a rope with two points of contact. The man pulling the rope exerts an upward force on both the chair and his hand, allowing for the possibility of the chair rising. The rope behaves like a spring and the man can control the movement of the chair by pulling the rope from different points. The resulting force on the chair and man is equal to twice the tension in the rope minus their combined weight.
  • #1
trogdor5
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Homework Statement



http://i.imgur.com/rjxR2.jpg

Homework Equations



F = ma

The Attempt at a Solution



I know that the rope is pulling the man up twice as much because there are two points of contact between him and the rope. I'm really just looking for somebody to explain why that is?

It seems to me that when he pulls down on the rope, the chair will move with a force upwards, but the other side will move with a force downwards and he will basically be in the same position unless he let's go of the rope with his hands.

What I'm trying to say is, the tension on each side of the rope is going in opposite directions. Why would it count as if the man is being pulled up twice when, the way I see it, the two forces should cancel each other out?
 
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  • #2
The rope is like a spring, it stretches a bit when pulled from both sides and a tension evolves all along its length to withstand that stretching external force. According to Newton's Third Law, the rope also exerts force on the objects pulling it, at both ends. These forces are of equal magnitude (the tension T) and point inward, to the bulk of the rope. So the rope exerts an upward force T on the chair, and also an upward force T on the hand of the man. When the man is in rest, the sum of these upward forces balance the weight of the chair/man.
The man can rise by moving his hand down, pulling the rope, and then grabbing the rope with the other hand higher. So the rope gets shorter and shorter between the chair and his hand. That can be if the chair rises.

The chair/man moves upward either with uniform velocity or with a given acceleration under the resultant force F= 2T-mg.

ehild
 

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What is a pulley with chair question?

A pulley with chair question is an inquiry about the principles and mechanics of using a pulley system with a chair to lift objects or people. It is a common physics demonstration used to illustrate the concept of mechanical advantage.

How does a pulley with chair work?

A pulley with chair works by using a combination of a fixed and a movable pulley to reduce the amount of force needed to lift an object. The fixed pulley is attached to a solid support while the movable pulley is attached to a chair. When the chair is pulled down, the fixed pulley allows the force to be distributed between the chair and the object being lifted, making it easier to lift the object.

What are the advantages of using a pulley with chair?

The main advantage of using a pulley with chair is that it reduces the amount of force needed to lift an object. This can be especially helpful when lifting heavy objects or when a person is unable to lift the object on their own. Additionally, using a pulley with chair can also help to distribute the force more evenly, making the lifting process smoother and more efficient.

What are some real-life applications of a pulley with chair?

A pulley with chair is commonly used in construction, particularly in situations where heavy materials need to be lifted to higher levels. It is also used in rescue operations, such as in a fire department's ladder truck, to lift people and equipment to higher floors. In homes, a pulley with chair can be used to lift heavy furniture or other objects to upper levels.

Are there any limitations to using a pulley with chair?

While a pulley with chair can be helpful in reducing the amount of force needed to lift an object, it does have some limitations. The pulley system must be properly set up and maintained, and the weight of the object being lifted cannot exceed the weight capacity of the pulley or chair. Additionally, the angle of the pulley and the direction of the force applied can affect the efficiency of the system.

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