FYKOS Year 33 Series 2 Problem 3 — Danka's (non-)equilibrium cutting board · FYKOS 33 #33.2.3

Physics · mechanics

Problem

Cutting board with thickness t=1.0 mmt=1.0\,\mathrm{mm} and width d=2.0 cmd =2.0\,\mathrm{cm} is made up of two parts. The first part has density ρ1=0.20⋅103 kg⋅m−3\rho_1 =0.20\cdot 10^{3}\,\mathrm{kg\cdot m^{-3}} and length l1=10 cml_1 = 10\,\mathrm{cm}, the second part has density ρ2=2.2⋅103 kg⋅m−3\rho_2 =2.2\cdot 10^{3}\,\mathrm{kg\cdot m^{-3}} and length l2=5.0 cml_2 = 5.0\,\mathrm{cm}. We place the cutting board on water surface, which density is ρv=1.00⋅103 kg⋅m−3\rho_{\mathrm{v}} = 1.00\cdot 10^{3}\,\mathrm{kg\cdot m^{-3}} and then we wait until it is in equilibrium position. What angle will a plane of the cutting board hold with the water surface? How big the part of the cutting board which will stay above the water level will be?

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