Question

An object has a rectangular shape with a surface area of 40m2 and 0.1m thick. What is the maximum mass of a polar bear can sit on the floe before sinking? (density of ice is 900kg/m3 and density of seawater is 1025kg/m3)

Answer 1

$S=40~m^2,~h=0.1~m,~\rho_i=900~\frac{kg}{m^3},~\rho_w=1025~\frac{kg}{m^3}.$

$P=m_ig=\rho_igSh,$

$F_A=\rho_wgV'=\rho_wgSh',$

$P=F_A,$

$\rho_ih=\rho_wh',$

$h'=h\frac{\rho_i}{\rho_w},$

$m_{bear}=m_{upper~ice}=\rho_iS(h-h')=\rho_iSh(1-\frac{\rho_i}{\rho_w}),$

$m_{bear}=900\cdot 40\cdot 0.1\cdot(1-\frac{900}{1025})=439 ~kg.$