Tension woes simple mass problem

[veitch]

I thought I had this stuff figured out, but my answer is wrong. Any tips?
Thanks

Homework Statement

A sign hangs precariously from your prof's office door. Calculate the magnitude of the tension in string 1 if theta-1 = 26.10degrees, theta-2 = 54.87degrees, and the mass of the sign is 6.50 kg.

http://img89.imageshack.us/img89/1089/prob05signly6.th.gif http://g.imageshack.us/thpix.php

Homework Equations

$$\sum$$F_x = T_1x - T_2x = 0
$$\sum$$F_y = T_1y + T_2y - F_g = 0
F_g = mg

The Attempt at a Solution

X components:

T_1x = T₁ Cos 26.1
T_2x = T₂ Cos 54.87

Y components:

T_1y = T₁ Sin 26.1
T_2y = T₂ Sin 54.87

$$\sum$$F_x = T₁Cos 26.1 - T₂Cos 54.87 = 0
So...
T₁Cos 26.1 = T₂Cos 54.87
T₁ = T₂(Cos 54.87/Cos 26.1)

and

$$\sum$$F = T₁Sin 26.1 + T₂ Sin 54.87 = (6.5 kg)(9.8 m/s²)

Then I tried plugging that T₁ in there...

T₂(Cos 54.87/Cos 26.1)Sin 26.1 + T₂Sin 54.87 = 24.7 N
T₂(0.6408)Sin 26.1 + T₂Sin 54.87 = 24.7 N
T₂(0.2819) + T₂(0.8178) = 24.7 N
T₂(0.2819 + 0.8178) = 24.7 N
T₂ = 22.5 N

I can't attempt any more solutions as the assignment was due 20 minutes ago (it's online)... but I did poorly on my midterm yesterday so I really need to get a better understand of the material before it's too late... any advice would be greatly appreciated!

 

[Doc Al]

$$\sum$$F = T₁Sin 26.1 + T₂ Sin 54.87 = (6.5 kg)(9.8 m/s²)

Then I tried plugging that T₁ in there...

T₂(Cos 54.87/Cos 26.1)Sin 26.1 + T₂Sin 54.87 = 24.7 N

Your method looks fine, just be careful with the arithmetic: 6.5*9.8 ≠ 24.7.

 

[baba89]

I understand your frustration with getting the wrong answer. It's important to remember that science is all about trial and error, and making mistakes is a natural part of the learning process. My advice would be to go back and review the problem, making sure you understand all the concepts and equations involved. Sometimes, a small mistake in calculation or a misunderstanding of a concept can lead to an incorrect answer. It may also be helpful to work through similar problems to get a better grasp on the material. Don't be afraid to ask for help from your professor or classmates if you're still struggling. With practice and perseverance, I'm sure you'll master this material in no time. Keep up the hard work!