# Static Equilibrium of a tree sapling

1. Dec 2, 2008

### Bones

1. The problem statement, all variables and given/known data

Three forces are applied to a tree sapling, as shown in the figure, to stabilize it. If vector F A = 380 N and vector F B = 260 N, find vector F C in magnitude and direction.
http://www.webassign.net/gianpse4/12-45.gif

2. Relevant equations

3. The attempt at a solution
I am not sure where to begin...Help!!

2. Dec 2, 2008

### fluidistic

Hint : To stabilize the tree, the sum of the three forces must be $$0N$$.

3. Dec 2, 2008

### Bones

Fa=380N
Fbsin(15)=67.29

380N-67.29=fcsinθ
312.71N=Fcsinθ

Fbcos(15)=Fccosθ

Fbcos(15)= 251.14

so Fccosθ=251.14

we now know Fcsinθ and Fccosθ

tanθ=opp/adj

θ=arctan(312.71/251.14)= 51.23 degrees

so the angle Fa to Fc equals 51.23 degrees+ 90 degrees=141.23 degrees

the magnitude of Fc= √Fcx2+Fcy2

magnitude of Fc= 401N which doesn't seem to be correct...any help??

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook