
Плоская льдина толщиной 10 м плавает в воде. Определить толщину подводной части льдины.


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Calculating the Thickness of the Submerged Part of the Iceberg
To calculate the thickness of the submerged part of the iceberg, we can use Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. The formula for the buoyant force is given by:
F = ρ * V * g
Where: - F is the buoyant force - ρ is the density of the fluid - V is the volume of the fluid displaced - g is the acceleration due to gravity
The buoyant force is also equal to the weight of the submerged part of the iceberg, which can be calculated using the formula:
F = m * g
Where: - m is the mass of the submerged part of the iceberg - g is the acceleration due to gravity
Equating the two expressions for the buoyant force, we get:
m * g = ρ * V * g
Calculating the Volume of the Submerged Part of the Iceberg
We can rearrange the equation to solve for the volume V:
V = (m / ρ)
Substituting the Given Values
Given that the density of ice is approximately 917 kg/m^3 and the density of water is 1000 kg/m^3, we can use these values to calculate the volume of the submerged part of the iceberg.
Substituting ρ = 1000 kg/m^3 and m = 10 m * 917 kg/m^3 into the equation, we get:
V = (10 m * 917 kg/m^3) / 1000 kg/m^3
Solving for V: V = 9170 m^3 / 1000 kg/m^3 V = 9.17 m
Conclusion
Therefore, the thickness of the submerged part of the iceberg is approximately 9.17 meters.


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