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Question Number 68642 by Maclaurin Stickker last updated on 14/Sep/19

$${\mathrm{Young}}^{\prime }\mathrm{s}\mathrm{modulus}\mathrm{of}\mathrm{a}\mathrm{material}\mathrm{measures}$$$$\mathrm{its}\mathrm{resistance}\mathrm{caused}\mathrm{by}\mathrm{external}\mathrm{stresses}.$$$$\mathrm{On}\mathrm{a}\mathrm{vertical}\mathrm{wall}\mathrm{is}\mathrm{a}\mathrm{solid}\mathrm{mass}\mathrm{of}\mathrm{specific}$$$$\mathrm{mass}\rho \mathrm{and}\mathrm{Young}\epsilon \mathrm{modulus}\mathrm{in}\mathrm{a}\mathrm{straight}$$$$\mathrm{parallelepiped}\mathrm{shape},\mathrm{the}\mathrm{dimensions}$$$$\mathrm{of}\mathrm{a}\mathrm{which}\mathrm{are}\mathrm{shown}\mathrm{in}\mathrm{the}\mathrm{figure}.$$$$\mathrm{Based}\mathrm{on}\mathrm{the}\mathrm{correlations}\mathrm{between}\mathrm{physical}$$$$\mathrm{quantities},\mathrm{determine}\mathrm{the}\mathrm{the}\mathrm{expression}\mathrm{that}$$$$\mathrm{best}\mathrm{represents}\mathrm{the}\mathrm{deflection}\mathrm{suffered}$$$$\mathrm{by}\mathrm{the}\mathrm{solid}\mathrm{by}\mathrm{the}\mathrm{action}\mathrm{of}\mathrm{its}\mathrm{own}\mathrm{weight}.$$

Commented by Maclaurin Stickker last updated on 14/Sep/19

Commented by mr W last updated on 14/Sep/19

Commented by mr W last updated on 14/Sep/19

$$\delta =\frac{{wL}^4}{8EI}$$$$L=a$$$$E=ϵ$$$$I=\frac{{bh}^3}{12}$$$$w=bh\rho g$$$$\Rightarrow deflection\delta =\frac{bh\rho {ga}^4}{8ϵ\frac{{bh}^3}{12}}=\frac{3\rho {ga}^4}{2ϵh^2}$$

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