Solving a Static Problem with Conflicting Results

[subho123]

Static Problem...i am confused

Homework Statement

The Problem says " A rod is 5 ft long and its weight is 60 lb. one end of the rod is fastened to a vertical wall by a clip. other end is bound by a rop which is attached to point on the vertical wall situated at a 12 ft height from the clip. Now i have to calculate the tension of the rope & the reaction on the clip. "

Homework Equations

http://img822.imageshack.us/img822/660/63432505.png

If i use the first figure then taking the moment of all the forces w.r.t the point A we get T x 60/13 = 60 X 2.5

T = 32.5 lb wt

again using lami's theorem on the 2nd figure

T/sin90 = 60/sinθ = R/sin(90 -θ)

T = 60/12/13 = R/5/13

using T = 32.5 lb wt we have R =(5/13)* 32.5 = 12.5 lb wt...

but if i use the lami's theorem directly then i get T = 60/12/13 = 65 lb wt...why i am getting two value of T ?

eventually the answer is that the value of T and R are 32.5 lb wt.

The Attempt at a Solution

 

[graphene]

Start with drawing a free-body diagram showing all the forces on the rod.

 

[subho123]

i have drawn the diagram...can u pleasez help me out...

 

[graphene]

Balancing the moments about A, you should get
$$T\sin\theta l = mg\frac{l}{2}$$

And I don't quite know these units, so i couldn't proceed. :P

 

[subho123]

that's why i have done above...but i am confused that when i am using lami's theorem..i am getting different result...

 

[PhanthomJay]

Don't use Lami's theorem unless 3 non-co-linear loads are applied at the same joint. Your 60 pound weight is not applied at the joint. Incidentally, while the tension is 32.5 pounds in the cable, the horizontal force in the rod is 12.5 pounds. The magnitude of the resultant reaction force at the clip (A) is 32.5 pounds (resultant of its A_x and A_y components). Don't confuse the two.

 

[subho123]

now i understand ..thanks very much...