A nonuniform, horizontal bar of mass m is supported by two massless wires agains

Question

A nonuniform, horizontal bar of mass m is supported by two massless wires against gravity. The left wire makes an angle ?1 with the horizontal, and the right wire makes an angle ?2. The bar has length L. (Figure 1)

A nonuniform, horizontal bar of mass m is supported by two massless wires against gravity. The left wire makes an angle ?1 with the horizontal, and the right wire makes an angle ?2. The bar has length L. (Figure 1) Find the position of the center of mass of the bar, x, measured from the bar's left end. Express the center of mass in terms of L, ?1, and ?2.

Explanation / Answer

As always for such a plane system in equilibrium you can balances horizontal forces(x) , vertical forces (y) and the torques about an arbitrary fulcrum.

Set up balance of forces acting on the bar in x-direction
F?x + F?x = 0
<=>
-F?

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