Equilibrium of a Pulley System

[joej24]

Homework Statement

The picture is located in the attachment

Homework Equations

$$\sum$$ t = 0

$$\sum$$ Fx = 0 Although there are no horiz. forces in this problem

$$\sum$$ Fy = 0

The Attempt at a Solution

I'm not sure how to start. On the top most pulley, I believe that there is a Tension T and a force Mg that is from the hanging block. The second pulley has a Tension pulling it up and Mg pulling it down. The last pulley has a Tension pulling it up and Mg as well as F pulling it down. First, did I analyze the forces correctly?

Or Does the entire system have a Tension pulling it up, a Force F pulling it down, and 3Mg pulling it down as well?
I'm quite confused.

 

[rl.bhat]

If T is the tension in the upper cable, the tension in the each segment of the cable passing through the top pulley will be T/2.
Tension in the each segment of the cable passing through the middle pulley will be T/4.
Tension in the each segment of the cable passing through the bottom pulley will be ...
Total tension in the three segments of the three cables passing through the pulleys balances the weight.
Equate them and find the tension T.

 

[joej24]

So the three tensions acting on the block is T/2, T/4, T/8.

7 T/8 = Mg

T = 44.8

How did you figure out that those tensions in the cable (the one passing the middle pulley being T/4 and the one passing the bottom pulley T/8)?

 

[rl.bhat]

In a single string, each segment has the same tension if the string is in equilibrium.
So T in the top cable is due to T/2 in each segment of the cable passing through the pulley.

 

[joej24]

Okay. Thanks