A 1.47 x 10^6 kg steel hull has a base that is 2.5 x 10^3 m^2 in area. If it is placed in sea water (density= 1025 kg/m^3), how deep does the hull sink?
if the hull sinks x meters, it displaces 2500x m^3 of water.
1m^3 of water weighs 1000kg so
2500*x*1025 = 1.47*10^6
x = 0.573m
Thanx!!!!
To determine how deep the steel hull sinks when placed in sea water, we need to calculate the buoyant force acting on the hull.
The buoyant force is equal to the weight of the water displaced by the object. It can be calculated using the formula:
Buoyant Force = Volume of the displaced water * Density of the fluid * Acceleration due to gravity
The volume of the displaced water can be calculated using the formula:
Volume of the displaced water = Area of the base * Height of the submerged part
Now, let's calculate the submerged part of the hull:
The total weight of the steel hull is equal to the mass of the hull multiplied by the acceleration due to gravity:
Weight of the hull = Mass of the hull * Acceleration due to gravity
Weight of the hull = 1.47 x 10^6 kg * 9.8 m/s^2
Weight of the hull = 1.4416 x 10^7 N
Since the buoyant force is equal to the weight of the hull when the hull is submerged, we can calculate the volume of the displaced water using:
Buoyant Force = Volume of the displaced water * Density of the fluid * Acceleration due to gravity
Volume of the displaced water = Buoyant Force / (Density of the fluid * Acceleration due to gravity)
The density of the fluid (sea water) is given as 1025 kg/m^3, and the acceleration due to gravity is 9.8 m/s^2.
Volume of the displaced water = 1.4416 x 10^7 N / (1025 kg/m^3 * 9.8 m/s^2)
Volume of the displaced water = 1.4416 x 10^7 N / 10045 kg/m^3
Volume of the displaced water = 1435.316 m^3
Now, let's calculate the height of the submerged part of the hull using the formula:
Volume of the displaced water = Area of the base * Height of the submerged part
1435.316 m^3 = 2.5 x 10^3 m^2 * Height of the submerged part
Height of the submerged part = 1435.316 m^3 / (2.5 x 10^3 m^2)
Height of the submerged part = 0.574 m
Therefore, the hull sinks to a depth of 0.574 meters when placed in sea water.
To calculate how deep the steel hull sinks in sea water, we need to consider the concept of buoyancy.
Buoyancy is the upward force exerted on an object immersed in a fluid, counteracting the force of gravity. It depends on the density of the fluid and the volume of the object. The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.
Here are the steps to calculate the depth to which the hull sinks:
Step 1: Determine the volume of the hull.
The volume of the hull can be calculated by dividing its mass by its density:
Volume = Mass / Density = 1.47 x 10^6 kg / 1025 kg/m^3.
Step 2: Determine the weight of the fluid displaced.
The weight of the fluid displaced by the hull is equal to its volume multiplied by the density of the fluid:
Weight of Fluid Displaced = Volume * Density.
Step 3: Calculate the buoyant force.
The buoyant force is equal to the weight of the fluid displaced by the hull:
Buoyant Force = Weight of Fluid Displaced.
Step 4: Calculate the depth of the hull sink.
The depth to which the hull sinks can be calculated by dividing the buoyant force by the area of the base of the hull. This is because the pressure increases with depth, and the force exerted on an object is equal to the pressure multiplied by the area on which the force is applied:
Depth = Buoyant Force / (Area of Base).
Now let's plug in the values and calculate:
Volume = (1.47 x 10^6 kg) / (1025 kg/m^3)
Weight of Fluid Displaced = Volume * Density = (Volume) * (1025 kg/m^3)
Buoyant Force = Weight of Fluid Displaced
Depth = Buoyant Force / (Area of Base)
By using these calculations, we can determine how deep the hull sinks in sea water.