Tension of two strings/picture frame

[P944]

Homework Statement

Hey guys and girls I have tried to solve this one but I got part (b) wrong any help would be awesome :)

A picture hangs on the wall suspended by two strings, as shown in Figure 6-24, with θ = 72°. The tension in string 1 is 2.0 N

there is a picture with two strings attached to a ceiling and a picture frame hanging beneath. The θ angle is on string one to the left and string to the right has an angle of 32 degrees.

a) calculate the force tension of string 2

b) What is the weight of the picture?

Homework Equations

The Attempt at a Solution

Since the forces are at equilibrium, i set net forces = 0.

the sum of Forces (x) = Force (string 2) - (string 1) = 0
Sum of Forces (y) = Force tension string 2 + Force tension string 1 - w*g = 0

I get two equations:
1) Force tension 1 cos 32 - 2.0 N cos 72 = 0
2) Force tension 2 sin 32 - 2.0 N sin 72 -(9.80 * w) = 0

solving for equation 1 i get Force of tension on string 2 = 0.7288 N which comes out as correct

However, I get part b) weight of the picture wrong

I put my Force of tension 2 into equation 2 to get weight

(0.5299)(0.7288) + 1.902 -9.80*w = 0
solving i get weight = 0.2335 N but that comes out as wrong. Help lol

 

[kuruman]

2) Force tension 2 sin 32 - 2.0 N sin 72 -(9.80 * w) = 0

Why the negative sign here? Aren't both vertical components of the tensions positive? Also, why are you multiplying the weight by 9.8?