# How does this system work? (Four pulleys and a rope lifting a mass)

• zuzelle
In summary, the conversation discussed the use of pulleys to reduce the force needed to lift a weight. The tension in the rope is the same throughout and the teacher summed up the tension forces of the vertical strings to find the value of force needed to balance the weight.

#### zuzelle

Homework Statement
The masses of pulleys are negligible. What is the value of force F that keeps the block of weight 40 N in balance?
Relevant Equations
This system confuses me a lot. Our teacher just summed up all the tension forces of vertical strings, got 5F = 40, but can we really do that? If tension is the same everywhere, why isn't F = 40? Because all these strings aren't attached to the block itself I think. Could someone please explain how do systems like this actually work?
I used the regular way of solving problems with pulleys. I tried to find the tension forces, which must be the same in the rope, but I get it wrong

Hello @zuzelle ,

zuzelle said:
Homework Statement:: The masses of pulleys are negligible. What is the value of force F that keeps the block of weight 40 N in balance?
Relevant Equations:: This system ...

WHAT system ? Are we suposed to be telepathic ? Do you want us to guess ?

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If tension is the same everywhere
So apparently it is not. Can you see why ?
 hint: a free body diagram for the bottom pulley wheel ? For the top one ?

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Welcome @zuzelle !

The whole reason for using so many pulleys is to reduce the force needed to be applied at the end of the rope, which happens to be the value of the tension for any section of the going-around rope.

Just like it happens for a typical lever, that reduction of applied force is achieved by increasing the distance that the hand has to move respect to the distance the load moves upwards.

What you see in that diagram is basically a group of (rotating) levers simultaneously working.

zuzelle
zuzelle said:
Our teacher just summed up all the tension forces of vertical strings, got 5F = 40,
Not exactly. Your teacher summed the five forces that the string wrapped around the pulleys exert on the lower pulley assembly. That excludes the string attached to the ceiling and the string attached to the weight.
Since it is all the same massless string, and can freely rotate the pulleys, the tension must be the same in each section.

zuzelle