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 5.34 m3. What is the weight of the heaviest bear that the ice can support without sinking completely beneath the water?
F up = weight of water displaced = 917
= density of water * g * volume
= 1025*5.34 g = 5474 g
F down = weight of ice + weight of bear
= 917*5.34 g + w = 4897 g + w`
so
(5474-4897) g = w
w = 577 g = 577*9.81 = 5662 Newtons
To find the weight of the heaviest bear that the ice can support without sinking completely beneath the water, we can use Archimedes' principle.
Archimedes' principle states that the buoyant force exerted on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.
Given:
Density of ice = 917 kg/m^3
Density of sea water = 1025 kg/m^3
Volume of ice = 5.34 m^3
Step 1: Calculate the weight of the water displaced by the ice.
The volume of water displaced by the ice is equal to the volume of the ice itself. Therefore, the volume of water displaced is also 5.34 m^3.
The weight of the water displaced is calculated by multiplying the density of the sea water by the volume of water displaced:
Weight of water displaced = density of sea water * volume of water displaced
Weight of water displaced = 1025 kg/m^3 * 5.34 m^3
Step 2: Calculate the weight of the bear.
Since the ice is floating, the buoyant force is equal to the weight of the bear.
The weight of the bear can be calculated using the formula:
Weight of bear = weight of water displaced - weight of ice
The weight of the ice can be calculated by multiplying the density of ice by the volume of the ice:
Weight of ice = density of ice * volume of ice
Weight of ice = 917 kg/m^3 * 5.34 m^3
Step 3: Subtract the weight of the ice from the weight of the water displaced to find the weight of the bear:
Weight of bear = weight of water displaced - weight of ice
Weight of bear = (1025 kg/m^3 * 5.34 m^3) - (917 kg/m^3 * 5.34 m^3)
Step 4: Calculate the numerical value:
Weight of bear = (5,481.5 kg) - (4,895.38 kg)
Weight of bear ≈ 586.12 kg
Therefore, the weight of the heaviest bear that the ice can support without sinking completely beneath the water is approximately 586.12 kg.
To find the weight of the heaviest bear that the ice can support without sinking completely beneath the water, we need to determine the buoyant force acting on the ice.
The buoyant force is equal to the weight of the water displaced by the submerged part of the ice. Here's how you can calculate it:
1. Calculate the weight of the water displaced:
- The volume of the ice is given as 5.34 m^3. Therefore, the volume of water displaced is also 5.34 m^3.
- Since the density of seawater is 1025 kg/m^3, the weight of the water displaced is (5.34 m^3) * (1025 kg/m^3) = 5458.5 kg.
2. Calculate the weight of the ice:
- The density of ice is 917 kg/m^3, and the volume of the ice is 5.34 m^3. Therefore, the weight of the ice is (5.34 m^3) * (917 kg/m^3) = 4893.78 kg.
3. Calculate the buoyant force acting on the ice:
- The buoyant force acting on the ice is equal to the weight of the water displaced, which is 5458.5 kg.
4. Calculate the maximum weight of the bear that the ice can support:
- Since the buoyant force acts in the upward direction and must balance the downward force (weight) of the bear, the maximum weight that the ice can support is equal to the buoyant force, which is 5458.5 kg.
Therefore, the weight of the heaviest bear that the ice can support without sinking completely beneath the water is 5458.5 kg.