# Statics Equilibrium Problem - 3 Force body in equilibrium

• yoohoo
In summary, the conversation is about a static equilibrium problem involving a T-shaped bracket supporting a 150-N load. The reactions at points A and C are being determined when alpha is equal to 90 degrees and 45 degrees. The textbook answer for A and C is 150 N [down] for A and 167.7 N [W 63.4 N] for C, but the person solving the problem is getting double the values using the force triangle and the sine law. Other sources have also confirmed the textbook answer may be incorrect.
yoohoo
Statics Equilibrium Problem -- 3 Force body in equilibrium

## Homework Statement

Q: A T-shaped bracket supports a 150-N load as shown. Determine the reactions at A and C when (a) alpha=90o, (b) alpha =45o

A: (a)A=150N going down, C=167.7N,63.4degrees (b)A= 194.5N going down; C=253N, 77.9 degrees

Here's the diagram from the book:

http://www.glowfoto.com/viewimage.php?img=23-165339L&rand=2124&t=jpg&m=07&y=2010&srv=img6

## Homework Equations

sum of forces (it is in equilibrium) and force triangle

## The Attempt at a Solution

I made a force triangle where I found the angle 23.565 degrees (which makes sense since they give 63.4 degrees in the textbook). However, using the sine law I expected to come out with the right answer using:

150N/sin(23.565) = A/sin(63.4)

and

150N/sin(23.565) = C/sin(90)​

... instead I keep coming out with A and C values that are double what they should be. Ie. A = 300 N and C = 335.4 N

What am I doing wrong? Am I approaching it the wrong way?

Last edited by a moderator:

Taking moments about C, it is clear that A = 300 and C=sqr(300^2+150^2)

Hmmm... that's what I got... however, the answer in the textbook and according to other sources is 150 N [down] for A and 167.7 N [W 63.4 N] for C.

Engineers in practice don't have 'answers in the back' for their real problems, and have to find other ways of checking their solutions. That's what you have to do here. I looked at it algebraically and graphically as a check. It wouldn't be the first time that a book was wrong, although I do accept one should have regard to the answer given with a view to discovering whether you have made an awful error. But in this case, I think you are right. Maybe someone else could confirm.

I get the same answers you two do. I think the book is probably wrong, based on the problem statement given here.

Thanks both of you for your help... I guess I should have more faith!

Whenever I think a textbooks wrong, I think back to one of my first year profs telling the class that usually when a student gets a different answer than the textbook, it's the student who's wrong --not the textbook haha.

## 1. What is a static equilibrium problem?

A static equilibrium problem involves analyzing a system of forces acting on an object that is not in motion. The goal is to determine whether the object is in equilibrium, meaning that the forces acting on it are balanced and there is no net force causing it to move.

## 2. What is the significance of a 3 force body in equilibrium?

A 3 force body in equilibrium is a special case of static equilibrium where there are only three forces acting on the object. This is significant because it simplifies the analysis and makes it easier to determine whether the object is in equilibrium or not.

## 3. How do you solve a static equilibrium problem with 3 forces?

To solve a static equilibrium problem with 3 forces, you need to apply the principles of vector addition and sum the forces acting on the object. Then, using the equations of equilibrium, you can determine the unknown forces or angles that will result in a balanced system.

## 4. What are the equations of equilibrium?

The equations of equilibrium are three mathematical equations that describe the conditions for static equilibrium. They are sum of forces in the x-direction equals 0, sum of forces in the y-direction equals 0, and sum of moments (torques) equals 0. These equations can be used to solve for unknown forces or angles in a static equilibrium problem.

## 5. How do you know if an object is in static equilibrium?

An object is in static equilibrium if the sum of all forces acting on it is equal to 0 and the sum of all moments (torques) acting on it is also equal to 0. This means that the object is not moving or rotating, and all the forces acting on it are balanced.

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