What Are the Tensions and Forces in a Multi-Pulley System?

[narfarnst]

Homework Statement

http://i829.photobucket.com/albums/zz220/narfarnst/problem.jpg

Find T1 through T5 and the force on the right side of the diagram above.
(The force balances the weight, so the system is stationary).
EDIT: Oh, and the pulleys and ropes are massless and there is no friction.

Homework Equations

F=ma, various rearrangements of T=m(g+/-a)

The Attempt at a Solution

Based on mostly intuition I've concluded that T1=mg (very sure about that one).
I also think that T2 and T3 equally share the weight, so T2=T3=1/2mg.
T4 has to equal mg+F for it to keep the system up
And I'm not sure about T5 but I'm thinking that it equals mg because the system isn't accelerating.
But I'm not at all 100% sure an these.

Thanks!

 

[rl.bhat]

The single rope has three segments. Each segments must have the same tension. That is the basic constrain in the pulleys.

 

[willem2]

Based on mostly intuition I've concluded that T1=mg (very sure about that one).

Intuition is fine, if you can then find a reason why it is so. Gravity and
the tension of the rope are the only forces on the block, so they
must be equal and opposite.

I also think that T2 and T3 equally share the weight, so T2=T3=1/2mg.

Because the pulleys have no friction and no mass, there must be the
same tension in the ropes on both sides. (if there were not they would
start to accelerate infinitely fast)

T4 has to equal mg+F for it to keep the system up

Ok

And I'm not sure about T5 but I'm thinking that it equals mg because the system isn't accelerating.

but then the forces on the top pulley would be unbalanced