How can I find the tension in a wire when an equilibrium system makes a closed loop?

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

Find the tension on wire labeled (1) as shown in the figure. (You may use $g=10\frac{m}{s^2}$)



The alternatives given in my book are as follows:

$\begin{array}{ll}
1.&\frac{1}{2}mg\\
2.&mg\\
3.&\frac{3}{2}mg\\
4.&2mg\\
4.&\frac{5}{2}mg\\
\end{array}$

In this particular problem I'm lost at how should I proceed with the vectors. Can somebody help me on how is the interaction between the weight on the sphere which is labeled as 2m and the block which weight is $m$?. :)
 

skeeter

Math Team
Jul 2011
3,129
1,695
Texas
$T_1\sin{\theta} = 2mg$

$T_2 = T_1\cos{\theta}$

$T_1 = T_2+mg$

solve the system for $T_2$
 

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