Static Equilibrium of a tree sapling

In summary, to stabilize the tree sapling, three forces are applied, with vector F_A = 380 N and vector F_B = 260 N. To find the magnitude and direction of vector F_C, it is important to note that the sum of the three forces must be 0 N. Using trigonometry, the magnitude of vector F_C is calculated to be 401 N, with a direction of 141.23 degrees.
  • #1
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Homework Statement



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


Homework Equations





The Attempt at a Solution


I am not sure where to begin...Help!
 
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  • #2
Hint : To stabilize the tree, the sum of the three forces must be [tex]0N[/tex].
 
  • #3
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??
 

1. What is static equilibrium?

Static equilibrium is a state in which the forces acting on an object are balanced, resulting in no net movement or acceleration of the object. In other words, the object is at rest.

2. How does a tree sapling achieve static equilibrium?

A tree sapling achieves static equilibrium through a balance of forces acting on it. The force of gravity pulling the sapling downward is balanced by the tension in the roots and the upward force of the soil and surrounding plants pushing against the sapling.

3. What factors can disrupt the static equilibrium of a tree sapling?

Factors that can disrupt the static equilibrium of a tree sapling include strong winds, uneven soil, and the weight distribution of the sapling itself. These factors can create an imbalance of forces, causing the sapling to tilt or fall over.

4. How does a tree sapling adapt to maintain its static equilibrium?

A tree sapling can adapt to maintain its static equilibrium by adjusting its growth pattern. If the sapling is being pulled in one direction by a strong wind, it may grow thicker or bend in the opposite direction to counteract the force and maintain its balance.

5. Why is static equilibrium important for the growth of a tree sapling?

Static equilibrium is important for the growth of a tree sapling because it ensures that the sapling is stable and able to withstand external forces. Without static equilibrium, the sapling may be more susceptible to damage or even death, hindering its growth and survival.

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