Simplest Atwood machine question.

[life is maths]

Homework Statement

Hi, the question is like in the picture. How hard should she pull the string to raise with constant speed? She weighs 70 kg together with the bucket.

The Attempt at a Solution

The system must have 0 acceleration, but does this mean she should pull the string with an acceleration equal to g, to balance with it? Or is it enough that she pulls equal to her weight? But in this case, she would not raise.
This is a simple question, I guess, but I'm confused. Thanks for any help :)

 

[ndifabio]

I had this same question a few days ago. You just have to realize that the force she puts on the rope will lift her through the pulley, but also lift her directly. This lead me to believe that she would only need exert half her weight in force. I tried F=(1/2)mg, and it was correct.

 

[ehild]

The person exerts some force F, and this force evolves tension T in the rope: T=F. The tension is the same all along the rope, so the resultant force from the rope on the system (bucket+person) is equal to 2T. If 2T = mg, (weight of the person), that is F=mg/2, the bucket is balanced, but just a bit larger force is enough to move the person upward.

In real life, there is friction, so the person needs to exert some more force to overcome friction.

ehild

 

[life is maths]

Thanks a lot, ndifabio and ehild, I cannot believe that it was that simple. Your help is greatly appreciated :)

 

[ndifabio]

Any time, I'm always happy to help a fellow Physics student :)