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$\sum Fy = 0$ $F_1 + W_F = \gamma_wh_2A_F$ $h_2A_F = \dfrac{108 + m_f*g}{\gamma_w}$ From here, you need to solve this problem by iteration. For the preliminary trials, I would assume $W_F$ is negligible. Once the optimum $h_2$ & $A_F$ is find, re-iterate the result with $W_F = m_f*g = \rho Vg$ ($\rho = mass density of the material, V is the solid volume ...

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