FYKOS Year 32 Series 5 Problem 3 — border · FYKOS 32 #32.5.3

Physics · mechanics

Problem

Imagine an aquarium in the shape of a cube with edge length

a = 1 \mathrm{m}

, which is separated into two parts via a vertical partition perpendicular to sides of the aquarium. Let us assume that the partition can move in the direction perpendicular to the plane of the partition, but it is fixed in other directions. Also, it can't rotate. We pour

V_1 = 200 \mathrm{\ell }

of water (density

\rho \_v = 1 000 \mathrm{kg\cdot m^{-3}}

) into the first part and

V_2 = 230 \mathrm{\ell }

of oil (density

\rho \_o = 900 \mathrm{kg\cdot m^{-3}}

) into the second part. In which position is the partition in mechanical equilibrium? In what height will be the surfaces of the liquids? Bonus: Find frequency of small oscillations of the partition. Assume, that mass of the partition is

m = 10 \mathrm{oz}

and the liquids move without friction or viscosity.

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