# Help finding minimum Tension that a rope can withstand without breaking

## Homework Statement

A person of mass M stands in the middle of a tightrope which is fixed at the ends of two buildings separated by a horizontal distance L. The rope sags in the middle, stretching and lengthening the rope slightly.

a)If the tightrope walker wants the rope to sag vertically by no more than a height h, find the minimum tension T, that the rope must be able to withstand without breaking, in terms of h, g, M, and L.

f=ma?

## The Attempt at a Solution

Honestly, I have no idea how to approach this. I do not know a single thing to do. Please be thorough and explain to me what has to be done and what to consider. My teachers homework problems are so much different from the reading and what we discuss in class, it is unbelievably harder without guidance.

You need a value for the mass of the person, also need a value for the young module of the rope, or the material of what is made. Then, look for Hooke's law, that will give you an idea of what you need to find.

I may have posted this in the wrong section.

There are no values, you solve solely on variable.

ehild
Homework Helper
a)If the tightrope walker wants the rope to sag vertically by no more than a height h, find the minimum tension T, that the rope must be able to withstand without breaking, in terms of h, g, M, and L.

You need to know addition of forces. The man stands at the middle of the rope which is sagged a bit. His weight is balanced by the forces both pieces of the rope exert on him. Those forces act along the rope. Draw it.

ehild

I have the diagram.
I also know the forces, but I don't really know what to do with them.
force of gravity on the string
force of gravity on the person
force of person on the string
force of tension(this is the one I kind of don't understand)

How would I do this on paper and solve for those variables?

ehild
Homework Helper
You do not show the diagram, so I show it to you. The person is standing on the string, he is in equilibrium, the resultant force on it is zero.

Gravity pulls the man downwards, and the rope keeps him up. Both strands of rope exert T force on the man (T for "tension": the rope exerts the same force along its length everywhere.) The direction of the tension is the same as that of the rope. It makes the same angle θ with the horizontal direction as the rope does.

So you have three forces exerted on the man: gravity and the two tensions. The forces are vectors, and their sum must be zero.

Do you know how to add vectors?

ehild

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