How can I find the mass of a sphere held in a set of wires hanging from two roofs?

Jun 2017
218
6
Lima, Peru
The problem is as follows:

The figure 1. shows a diagram where a sphere is hanging from two roofs and it is an equilibrium. Find the mass of the sphere. You may consider that gravity is $10\frac{m}{s^2}$.​



$\begin{array}{ll}
1.&50\,kg\\
2.&20\,kg\\
3.&30\,kg\\
4.&60\,kg\\
5.&25\,kg\\
\end{array}$

I became tangled with drawing different tensions in this set. Can somebody help me with this?. I don't know if there is a way to simplify this set to find what it is being requested?. :help:
 

skeeter

Math Team
Jul 2011
3,129
1,695
Texas
$T_1\cos(60) = T_2\cos(30)$

$T_1\sin(60)= T_2\sin(30)+50g$

$T_2\cos(30)=T_3\cos(30)$

$T_2\sin(30)+T_3\sin(30) = mg$

solve the system for $m$
 

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