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The Complete Equilibrium

In figure, th...

Question

In figure, the bar is uniform and weighing $500 N$ . How large must $W in N$ be if $T_{1}$ and $T_{2}$ are to be equal?

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Solution

Taking torque about the attachment point for $W$ , we get
$- T_{1} (0.4 L) + T_{2} (0.3 L) + 500 (0.2 L) = 0$
where $T_{1} = T_{2} = T$
$T (0.1) = 100 \Rightarrow T = 1000 N$
By balancing forces
$\sum F_{y} = 0 \Rightarrow 2 T - W - 500 = 0$
$\Rightarrow W = 1500 N$

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