Tension; 2 cables holding weight

[Ramacher]

Homework Statement

A small sphere of weight W is held as shown by two wires AB and CD. If wire AB is cut, determine the tension in the other wire (a) before AB is cut, (b) immediately after AB has been cut. (Ans: (a) TCD = 0.742 W; (b) TCD = 0.940 W).

http://img4.imageshack.us/img4/3763/picture11td.png

Homework Equations

$$\Sigma$$F_y=ma_y
T_y=Tsin$$\theta$$

The Attempt at a Solution

T_CDy+T_ABy-W=ma_y ; a_y=0 (not moving)

T_CDSin(70^$$\circ$$)+T_ABSin(50^$$\circ$$)-W=0 ; solve fot T_AB and plug in

T_ABSin(50^$$\circ$$)=W-T_CDSin(70^$$\circ$$) ; divide Sin(50^$$\circ$$) from both sides

T_AB=[W/Sin(50^$$\circ$$)]-[T_CDSin(70^$$\circ$$)/Sin(50^$$\circ$$)]

T_CDSin(70^$$\circ$$)+[W/Sin(50^$$\circ$$)]-[T_CDSin(70^$$\circ$$)/Sin(50^$$\circ$$)]-W=0 ; Plugging in T_AB from above

T_CD(Sin(70^$$\circ$$)-(Sin(70^$$\circ$$)/(Sin(50^$$\circ$$)=W(1-1/(Sin(50^$$\circ$$)

Solving for T_CD I get 1.066W when its supposed to be 0.742 W

What am i doing wrong?

 

[rl.bhat]

T(CD)*sin70 + T(AB)*sin50 - W = 0.
After this write
T(CD)*cos70 + T(AB)*cos50 = 0
Now solve.

 

[Ramacher]

T(CD)*sin70 + T(AB)*sin50 - W = 0.
After this write
T(CD)*cos70 + T(AB)*cos50 = 0
Now solve.

so do the sum of the forces in the x direction?
Wouldn't it then be T(CD)*cos70 - T(AB)*cos50 = 0 ?

---
Worked out the sum of the forces in x and y direction
solved for T_AB Set them equal to each other and still wrong answer :(

 

[rl.bhat]

In my equation I have given the vector sum. Your equation is correct.
T(CD)*sin70 + T(AB)*sin50 = W ...(1)
After this write
T(CD)*cos70 = T(AB)*cos50
T(AB) = T(CD)*cos70/cos50
Put it in the eq, 1, you get
T(CD)*sin70 + [T(CD)*cos70/cos50]*sin50 = W
Now simplify.
For part (b) T(CD) = component of W along the wire.

 

[Ramacher]

thanks, turned out i just wasn't inputting in the calculator right.

funny how this one of the simplest problems out of the assignment and i was having trouble with it and easily solved the complex ones. Always the easy stuff that gets me, i guess i think about it too hard, make it more complex then it is.

been working on so much homework (thermo, dynamics, eaII, and solids) that my mind is fried!