How can I find the maximum value of a mass supported by one end of a suspended bar?

Jun 2017
352
6
Lima, Peru
The problem is as follows:

A homogeneous bar of $1\,kg$ in mass is at equilibrium and supported by two wires labeled $A$ and $B$ as shown in the graph. Find the maximum value of the mass in kilograms of the block such that the system remains at equilibrium.



The alternatives given in my book are as follows:

$\begin{array}{ll}
1.&3\,kg\\
2.&4\,kg\\
3.&6\,kg\\
4.&30\,kg\\
\end{array}$

What I've attempted to do was to establish the torque about the end on B. But I end up with two unknowns for the mass and for the tension. How can I get the mass?.
 

skeeter

Math Team
Jul 2011
3,292
1,776
Texas
torques about the far left end ...

$F_A \cdot L + F_B \cdot 8L = g \cdot 4L $

$\color{red}F_A + 8F_B = 4g$

equilibrium in the vertical ...

$\color{red}F_A + F_B = (m+1)g$

subtraction yields ...

$7F_B = (3-m)g$
 
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