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

Jun 2017
399
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 I should 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 whose weight is $m$? :)
 

skeeter

Math Team
Jul 2011
3,360
1,850
Texas
$T_1\sin{\theta} = 2mg$

$T_2 = T_1\cos{\theta}$

$T_1 = T_2+mg$

solve the system for $T_2$
 

Attachments