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 5.70 m3. What is the weight of the heaviest bear that the ice can support without sinking completely beneath the water?
5.7 * 1025 = 5842.5 kg of water displaced by ice submerged
mass of ice = 5.7 * 917 = 5226.9 kg
mass additional to submerge = 5842.5-5226.0
= 615.6 kg mass of maximum bear
then weight in Newtons = 615.6 *9.81 N
To find the weight of the heaviest bear that the ice can support without sinking completely beneath the water, we need to compare the weight of the bear to the buoyant force exerted on the ice.
The buoyant force is equal to the weight of the water displaced by the submerged part of the ice. Since a portion of the ice is submerged, we need to calculate the volume of ice submerged.
Given:
Density of ice (ρ_ice) = 917 kg/m^3
Density of sea water (ρ_water) = 1025 kg/m^3
Volume of ice (V_ice) = 5.70 m^3
First, we can calculate the submerged volume of the ice using Archimedes' principle:
Submerged volume (V_submerged) = V_ice * (ρ_ice / ρ_water)
Next, we can calculate the buoyant force (F_buoyant) exerted on the ice:
F_buoyant = ρ_water * g * V_submerged
Where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Now, we can set up an equation to find the weight of the heaviest bear:
Weight of the bear (W_bear) = F_buoyant
Let's calculate it step by step.
Step 1: Calculate the submerged volume of the ice:
V_submerged = 5.70 m^3 * (917 kg/m^3 / 1025 kg/m^3)
V_submerged = 5.70 m^3 * 0.8951
V_submerged ≈ 5.10 m^3
Step 2: Calculate the buoyant force exerted on the ice:
F_buoyant = 1025 kg/m^3 * 9.8 m/s^2 * 5.10 m^3
F_buoyant ≈ 50319 N
Step 3: Calculate the weight of the heaviest bear the ice can support:
W_bear = 50319 N
Therefore, the ice can support a bear weighing up to 50319 N without sinking completely beneath the water.