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Torque about a Point

In Fig. the b...

Question

In Fig. the bar is uniform and weighing $500 N$ . How large must $W$ be in $N$ 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
$- T_{1} (0.4 L) + T_{2} (0.3 L) + 500 (0.2 L) = 0$
$T = 1000 N$ , where $T_{1} = T_{2} = T$
$\sum F_{y} = 0 \Rightarrow 2 T - W - 500 = 0$
$\Rightarrow W = 1500 N$

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