The density of ice is 917 kg/m3, and the density of sea water is 1025 kg/m3. A swimming polar bear climbs onto a piece of floating ice that has a volume of 3.25 m3. What is the weight of the heaviest bear that the ice can support without sinking completely beneath the water?
When the ice flow is fully submerged,
M*g + V*rho2*g = V*rho1*g
Solve for bear mass, M.
rho2 = ice density = 917 kg/m^3
rho1 = seawater density = 1025 kg/m^3
g cancels out
V = 3.25 m^3
M = 3.25 m^3* 108 kg/m^3 = 351 kg
That mass will sink the ice floe, but not the bear. You need to know the bear's density if you want to include the effect of its own flotation.
To determine the weight of the heaviest bear that the ice can support without sinking completely, we need to consider the buoyant force acting on the ice. The buoyant force is equal to the weight of the water displaced by the ice.
First, let's calculate the weight of the water displaced by the ice:
Weight of water = Volume of ice * Density of sea water
Weight of water = 3.25 m^3 * 1025 kg/m^3
Next, we need to calculate the weight of the bear. The bear's weight must be less than or equal to the weight of the water displaced by the ice in order for the ice not to sink completely.
Therefore, the maximum weight of the bear is given by:
Weight of bear ≤ Weight of water
Now, we can substitute the known values into the equation and solve for the weight of the bear:
Weight of bear ≤ 3.25 m^3 * 1025 kg/m^3
Weight of bear ≤ 3331.25 kg
Hence, the weight of the heaviest bear that the ice can support without sinking completely beneath the water is 3331.25 kg.