How Do You Calculate Tension in a Wire at a 45 Degree Angle?

[rAz:DD]

Homework Statement

A body of mass m = 10kg is suspended by a fixed support through a perfect wire. The body is resting on the vertical support to another disk, so that the thread
formed with a vertical angle α = 45 °, as shown. The tension from the wire has the value:
a. T = 41N
b. T = 100N
c. T = 141N
d. T = 241N

Homework Equations

The Attempt at a Solution

 

[AEM]

Draw a diagram of the forces acting on the mass. Since there is no motion, the forces must be in equilibrium. That means the vector sum of the forces in the x direction mus be equal to zero and similarly for the vector sum the forces in the y direction. You'll have to write the tension T in component form to do this. After you get the unknown components of T, you'll have to find its magnitude to answer the question.

By the way, you're supposed to show us your attempt at a solution.

 

[rAz:DD]

I've written Gx = G / cos a = T and got a strange result, but i realize now it was a math fail; the correct answer should be c) 141N right ?

 

[AEM]

I've written Gx = G / cos a = T and got a strange result, but i realize now it was a math fail; the correct answer should be c) 141N right ?

Well, I get T = 139N. Summing the forces in the y direction, I get

$$T = \frac{Mg}{cos(45)} = \frac{98.1}{\frac{1}{\sqrt{2}}} = 138.7$$

which I'd round off to 139N. I don't see a reason for the discrepancy right now.

Is the picture you gave the whole picture?