Confusion over the reduction of force for pulleys

In summary, the window washer needs to pull with a force equal to half of her weight (mg/2) in order to raise herself slowly at a constant speed using the bucket-pulley apparatus shown in the figure. This is because the pulley reduces the force required by half, and the window washer is lifting herself using the tension (T) in the rope, which is equal to the upward force the rope applies to her. This is different from cases where an external force lifts the load, as the window washer is lifting herself.
  • #1
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Homework Statement


A window washer pulls herself upward using the bucket-pulley apparatus shown in the figure. How hard must she pull downward to raise herself slowly at constant speed? The mass of the person plus the bucket is 71kg .
GIANCOLI.ch04.p32.jpg

Homework Equations


F of gravity = mg
F effort = mg/2

The Attempt at a Solution


I found out later that using a pulley reduces the force to half, so I did Force = mg/2 which is the correct answer. I am confused because according to this website http://www.explainthatstuff.com/pulleys.html and http://www.ehow.com/how-does_5231254_much-weight-pulley-off_.html , two wheels are needed for a reduction of force by one half. There is only a single wheel on the pulley for the window washer.
howpulleyswork1.gif
howpulleyswork2.gif


In other words, the force to pull the window washer up should be equal to to her weight (mg) and not half of that. Did I misread something or is one of the websites wrong?
 
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  • #2
The window washer set-up is different from the cases when the load is lifted by an external force. The window-washer lifts himself. Draw the free-body diagram: the force he pulls the rope is equal to the upward force the rope pulls him. This is the tension T in the rope, and it is applied also to the bucket. So the bucket and window-washer experience 2T force from the rope, and mg downward force from gravity.

ehild
 

What is a pulley and how does it work?

A pulley is a simple machine that consists of a wheel with a groove around its circumference and a rope or belt that runs along the groove. It is used to change the direction of a force, making it easier to lift heavy objects by distributing the weight over multiple ropes or belts.

What is the reduction of force for pulleys?

The reduction of force for pulleys refers to the decrease in the amount of force needed to lift an object using a pulley system. This is achieved by spreading the weight of the object over multiple ropes or belts, reducing the amount of force needed to lift it.

How is the reduction of force calculated for pulleys?

The reduction of force for pulleys can be calculated by counting the number of ropes or belts supporting the object. Each additional rope or belt will reduce the force needed by that amount. For example, if a pulley system has 3 ropes supporting an object, the force needed to lift it will be reduced by 3 times.

Does the reduction of force apply to all types of pulleys?

Yes, the reduction of force applies to both fixed and movable pulleys. However, the amount of reduction may vary depending on the type of pulley and the arrangement of ropes or belts.

What are some common misconceptions about the reduction of force for pulleys?

One common misconception is that the reduction of force is equal to the number of ropes or belts used in the pulley system. In reality, the reduction may be less due to friction and other factors. Additionally, the reduction of force only applies to the lifting force needed, not the total weight of the object.

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