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 4.41 m3. What is the weight of the heaviest bear that the ice can support without sinking completely beneath the water? please help!

Vb = (Do/Df)*Vo,

Vb = (917/1025) * 4.41 = 3.95 m^3.

(917+Db)/1025 = 1,max.
917 + Db = 1025,
Db = 1025 - 917 = 108 kg/m^3 = Density of bear.

Wb = 108kg/m^3 * 4.41m^3 * 9.8N/kg =
4668 N.

NOTE:

Do = Density of object(ice).
Df = Density of fluid.
Db = Density of bear.

To determine the weight that the ice can support without sinking completely, we need to compare the weight of the swimming polar bear with the buoyant force acting on the ice.

Step 1: Calculate the buoyant force
The buoyant force acting on an object submerged or floating in a fluid is equal to the weight of the fluid displaced by the object. In this case, the fluid is sea water.

Buoyant force = Density of fluid * Volume of fluid displaced * Gravitational acceleration

The volume of fluid displaced by the ice is the same as the volume of the ice itself, so we can substitute the volume of the ice into the equation:

Buoyant force = Density of sea water * Volume of ice * Gravitational acceleration

Buoyant force = 1025 kg/m3 * 4.41 m3 * 9.8 m/s2

Step 2: Calculate the weight of the bear
The weight of an object is equal to its mass multiplied by the gravitational acceleration.

Weight of bear = Mass of bear * Gravitational acceleration

To find the maximum weight the ice can support, we need to find the mass of the bear. Rearranging the equation:

Mass of bear = Weight of bear / Gravitational acceleration

Step 3: Substitute values and solve
Substituting the known values:

Buoyant force = 1025 kg/m3 * 4.41 m3 * 9.8 m/s2

Mass of bear = (Buoyant force * Gravitational acceleration) / Gravitational acceleration

Simplifying:

Mass of bear = Buoyant force

Mass of bear = 1025 kg/m3 * 4.41 m3 * 9.8 m/s2

Calculating:

Mass of bear = 45,385.38 kg

As a result, the weight of the heaviest bear the ice can support without sinking completely beneath the water is approximately 45,385.38 kg.