Is Static Equilibrium Really That Simple?

[urk.nono]

Hello! I'm a student from Norway, and I've been struggling with a static equilibrium for a few hours now. The terms I use might not be "right", but I'll try to explain the problem to the best of my ability.

Homework Statement

Find the forces Fa and Fb on this figure:

http://img44.imageshack.us/img44/4505/321k.jpg

Homework Equations

[tex]\Sigma F_X = 0[/tex]
[tex]\Sigma F_Y = 0[/tex]
[tex]\Sigma \tau = 0[/tex] (sum torque = 0)

The Attempt at a Solution

I solved it by drawing the forces on the figure:
http://img41.imageshack.us/img41/7513/321graph.jpg

After much fiddling with the "relevant equations" I came across the following:

20kN *3,5m - Fb * sin(30) * 5,5m = 0
=> Fb = 37,21kN

OR

20kN * 3,5m - Fb * cos(70) * 5,5m = 0
=> Fb = 37,21kN

Fa * cos(11,75) * 2m - 20m * 3,5m = 0
=> Fa = 35,74kN

I know from my measurements and by checking the solution in the book, it's pretty damn close. By which formula, or by what method I got no clue whatsoever.

I'd appreciate if someone could help me out by pointing me in the right direction

Thanks in advance

Urk

 

[kuruman]

Hi urk.nono, welcome to PF. I am not sure what the second drawing you posted shows. I am used to force vectors represented as arrows, not line segments. Anyway, if you write the x and y components of the force at A as [FSUB]x[/SUB] (to the right) and F_y (up), can you find three equations saying

ΣF_i,x = 0
ΣF_i,y = 0
Σtorques = 0
?

Note: Your work will be much easier if you calculate torques about point A.

 

[tomcue]

han


Hello Urkhan,

First of all, congratulations on attempting to solve the problem on your own and seeking help when needed. That is the mindset of a true scientist.

Static equilibrium is a very important concept in physics and engineering. It refers to a state where all forces acting on an object are balanced, resulting in a net force of zero. This means that the object is not moving or rotating. In your problem, the figure is in static equilibrium, meaning that the sum of all the forces acting on it must be zero.

Your approach to solving the problem is correct. You have correctly identified the relevant equations for static equilibrium, which are the sum of forces in the x-direction, sum of forces in the y-direction, and the sum of torques. These equations are based on Newton's laws of motion, specifically the first and second laws.

To solve the problem, you need to consider all the forces acting on the figure and set up the equations accordingly. From your diagram, it looks like there are three forces acting on the figure: the 20kN force, Fa, and Fb. As you correctly stated, the sum of forces in the x-direction and y-direction must be zero, which means that the forces must be balanced. This will allow you to solve for Fa and Fb.

In addition, you also correctly identified the need to consider the torque, or rotational force, in your equations. This is because the figure is not only experiencing forces in the x and y directions, but also a rotational force due to the 20kN force acting at a distance from the pivot point.

To solve for Fa and Fb, you can use your equations and plug in the given values for the distances and angles. It looks like you may have made a small error in your calculations, which is why your answers are slightly off from the solutions in the book. I would recommend double-checking your calculations to make sure they are correct.

Overall, you have a good understanding of the concept of static equilibrium and have correctly applied the relevant equations. Keep practicing and seeking help when needed, and you will continue to improve your skills as a scientist. Good luck with your studies!