Question

when a 300 kg polar bear climbs onto a sheet of ice, the ice becomes -- just barely -- fully submerged in water. if the ice sheet is uniformly 0.300 m thick, what is the area of the sheet? Density of sea ice = 945 kg/m^3 and density of sea water = 1030 kg/m^3

Answer 1

There are three forces acting on the ice sheet: F_B is the buoyant force of the sea water, W_PB is the normal force applied by the polar bear which is equal to the weight of the polar bear, W_ice is the gravitational force of the Earth on the ice sheet. The free-body diagram of the sheet is shown below:

In equilibrium, the net force on the ice sheet is equal to zero

Let m_ice be the mass of the ice, m_PB=300kg is the mass of polar bear, V be the volume of the ice sheet. be the density of the sea water

where g is the gravitational acceleration

We know that mass=volume x density

Using volume = area x thickness

Substituting m_PB=300kg, , ,