Mechanical advantage of a pulley system

[EasyPeasy]

Homework Statement

Calculate the mechanical advantage of the system in the picture

Relevant Equations

Ma= output force / input force

I don't know how the bottom two pulleys affect the top one. From what I know, the three ropes should have the same tension, the force of the body, divided between them. So if we take top one, it should have that tension on both sides, but also should support the other two pulleys below it. That is what I am not sure of, how should the bottom two pulleys be accounted for?

 

[jbriggs444]

So if we take top one, it should have that tension on both sides, but also should support the other two pulleys below it

Yes, the two sections of rope extending downward from the top pulley should have the same tension. That is what [ideal massless] pulleys do -- they equalize the tension in the cord that extends to either side.

Let us agree to call the tension in these top two pieces of rope, T. [Short for "top" or "tension" or both]Consider what forces exist on the middle pulley. Can you make a free body diagram for that pulley listing all the forces that act on it? Can you write an equation relating those forces? Does that equation allow you to deduce the tension on the two sections of rope emerging from that pulley?

 

[haruspex]

the three ropes should have the same tension,

@jbriggs444 has given you the benefit of the doubt and assumed you meant that for each rope the tension will be the same on each side of the pulley. But the way I read it you are saying that the three ropes will all have the same tension. That is certainly not true.

The problem as drawn cannot be solved because you would need to know the angles of the ropes, and even then would be rather complicated. I think you have to treat the pulleys as being arbitrarily small so that even though they must all attach to the centre of the block they are all nearly vertical.