Equilibrium and Tension: Finding a Tightrope Walker's Mass

[fatmanx]

Homework Statement

A tightrope walker stands at position shown below. The Tension in the cable on the right is 1800 N, find the walker's mass.
The angle on the right is 70º and the one on the left is 80º.

The Attempt at a Solution

So I presume you have to draw a vector diagram, but I am totally unsure of how to do that for this situation. Once the vector diagram is drawn I assume that you use the sin law to figure out the other angle. And then from the force of gravity derive the weight. I just need some help getting started, and then I should be able to do it on my own.

 

[cryptoguy]

Alright well, for the free-body diagram, you know the system is in equilibrium (Fnet = 0). Vertically, that means the guy's weight must be equal to what? How about horizontally, what must be equal so the system is in equilibrium?

 

[fatmanx]

I know that it all has to add up to 0, therefore the tension in the cable or the force on the poles has to balance out the force of gravity on the guys mass. I understand that, but I just don't know where to start

 

[cryptoguy]

i'd start with writing out the equations for what you just said, one equation for horizontal forces and one for vertical. you can then solve the equations simultaneously by substitution

 

[tiny-tim]

vector diagram

So I presume you have to draw a vector diagram, but I am totally unsure of how to do that for this situation. Once the vector diagram is drawn I assume that you use the sin law to figure out the other angle. And then from the force of gravity derive the weight. I just need some help getting started, and then I should be able to do it on my own.

Hi fatmanx!

Before you draw any vector diagram:

i] decide which body the forces are acting on (it must always be the same body)

ii] then draw lines with arrows on the original diagram to show the forces, before you draw the actual force diagram.

So there'll be lines with arrows on the two parts of the cable, and a line with an arrow for the weight of the walker.
​

Now slide the lines across the page until they all meet and form a triangle, with the arrows going the same way round!

 

[fatmanx]

There is a force down...the force of gravity, there are two forces up. What next?

 

[tiny-tim]

There is a force down...the force of gravity, there are two forces up. What next?

Two options:

i] draw a vector triangle:

Now slide the lines across the page until they all meet and form a triangle, with the arrows going the same way round!

or ii] leave all the vectors where they are (sticking out of the guy's feet), and take components in the horizontal and vertical directions.

Do whichever one you've been taught.