How Do Forces Distribute in a Block and Tackle System?

[ksle82]

Given a block and tackle system and a known weigt, give the magnitude of the forces at the numbered points. [see attached for figure]
https://www.physicsforums.com/attachment.php?attachmentid=7026&stc=1&d=1149034106
blocktackle.JPG

My answers:
Point 2: 20
Point 3: 20
Point 4: 10
Point 1: 40

I arrived at the answers simply by looking at the figure and do a force balance at each tackle. I think some (if not all) are wrong because the systems doesn't provide any mechanical advantage (according to my answers). Please Help.

 

[Doc Al]

Looks OK to me (assuming all ropes are essentially vertical). Why do you say there's no mechanical advantage? A 10 unit weight (shown) lifts a 20 unit weight (that's point 2).

 

[kyle8921]

Your approach of using force balances at each tackle is a good start. However, in order to accurately determine the magnitude of the forces at each point, we must take into consideration the mechanical advantage of the block and tackle system. The mechanical advantage is the ratio of the output force (in this case, the weight being lifted) to the input force (the force applied at point 1).

In this system, there are 4 ropes supporting the weight, so the mechanical advantage is 4. This means that the force at point 1 (the input force) is 1/4 of the weight being lifted.

Therefore, the correct answers would be:
Point 2: 5 (1/4 of 20)
Point 3: 5 (1/4 of 20)
Point 4: 2.5 (1/4 of 10)
Point 1: 20 (the weight being lifted)

It is important to take into consideration the mechanical advantage when analyzing any block and tackle system, as it greatly affects the forces at each point.