How Do Counterweights Affect the Sag of a Rope Bridge?

[maroonandgold]

Homework Statement

Alright, here we go. In the problem, there is a bridge. Basically it's a bridge in the amazon over the trees to make it easier for the explorers to walk and also to protect the forest floor. The bridge is rope bridge, and it's also a pulley system. There are are three masses involved in keeping the bridge horizontal. Each end of the rope supporting the walkway goes over a branch and then is attached to a large weight hanging down. When the team member is at the center of the walkway between two trees, you need to determine how the sag of the walkway is related to the mass of the counterweights and the total mass of the team member with the equipment. Alright, that's the situation, and what I actually have to do is find an equation for the vertical displacement of the large object in the middle in terms of the mass of the large object, the mass of the weights on the other sides of the branches, and the horizontal distance between the two pulleys. And the final equation shouldn't depend on pulleys.

Homework Equations

Hm, I don't know. We just started force this week so I'm not familiar with forces yet. How about f=ma?

The Attempt at a Solution

I have been staring blankly at the problem for an hour. And the book has no problem similar to it. I know it involves trigonometry, but that's about all I know.

TIA!

 

[tiny-tim]

Welcome to PF!

Hi maroonandgold! Welcome to PF!

Hm, I don't know. We just started force this week so I'm not familiar with forces yet. How about f=ma?

a, the acceleration, is zero, so this is just the vector equation F_total = 0.

Concentrate on the bit of rope at the centre …

it has three forces acting on it, the two tension forces and the weight of the man …

so call the tension T, and the angle θ, and put that into F_total = 0 …

what do you get? ​