Answer to Question #162169 in Molecular Physics | Thermodynamics for Golardha

Question

A 500kg polar bear stands on a round ice floe (diameter 4m), which swims in the Arctic Ocean. a) What is the minimum thickness of the clod so that the paws of the Polar bears stay dry? (ρ ice = 918 kg m3, ρsaltwater = 1025 kg m3) b) Now the polar bear climbs onto another floe with the same diameter and thickness of 0.5m! Because the polar bear is constantly warming up with its paws indicates the ice floe, it will begin to melt (spec Ice qs = 333.5 kJ kg), so that the polar bear and ice floe after a certain time sink as the meltwater drains away. Energy consumption per day of B¨ars: 78MJ. How many days does it take for the polar bear to start getting wet paws? to get.

Answer 1

a)

$m_ig+mg=F_A,$

$\rho_i Shg+mg=\rho _w gSh,$

$(\rho_w-\rho _i)Sh=m,$

$h=\frac{m}{(\rho _w-\rho_ i)S},$

$h=\frac{500}{(1025-918)\cdot 3.14\cdot 4}\approx 37.2~cm.$

b)

$Q=nQ_d=\lambda m,$

$n=\frac{\lambda m}{Q_d}=\frac{\lambda \rho_i S(H-h)}{Q_d},$

$n=\frac{333.5\cdot 10^3\cdot 918\cdot 3.14\cdot 4\cdot(0.5-0.372)}{78\cdot 10^6}\approx 6.3~days.$