Statics Equilibrium Problem - 3 Force body in equilibrium

[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?

Thanks in advance! :)

 

[pongo38]

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

 

[yoohoo]

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.

 

[pongo38]

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.

 

[jhae2.718]

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

 

[yoohoo]

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.