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

[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

 

[zuzelle]

 

[BvU]

Hello @zuzelle ,

$\qquad$!​

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 ?

Please read and follow the PF guidelines

And show your work

$\$

 

[BvU]

If tension is the same everywhere

So apparently it is not. Can you see why ?
[edit] hint: a free body diagram for the bottom pulley wheel ? For the top one ?

$\$

 

[Lnewqban]

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.

 

[haruspex]

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.