A ship has an area of cross sections as the water line of 2000m,by what depth does the ship sink in fresh water when it load a cargo of 4000 tonnes
Please help me
A ship has an area of cross section at the water line 2000m
To determine the depth to which the ship sinks in fresh water when loaded with a cargo of 4000 tonnes, we need to apply Archimedes' principle.
Archimedes' principle states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. In this case, the fluid is fresh water, and the object is the ship.
Step 1: Calculate the volume of the ship
The volume of the ship can be calculated by dividing the weight of the cargo by the density of fresh water. The density of fresh water is approximately 1000 kg/m³.
Volume of ship = weight of cargo / density of water
Weight of cargo = 4000 tonnes = 4000000 kg
Volume of ship = 4000000 kg / 1000 kg/m³ = 4000 m³
Step 2: Calculate the displaced water
The volume of water displaced by the ship is equal to the total volume of the ship, as the ship sinks completely into the water.
Displaced water = Volume of ship = 4000 m³
Step 3: Calculate the depth to which the ship sinks
The depth to which the ship sinks can be calculated by dividing the volume of water displaced by the area of the water line (cross section) of the ship.
Depth = Displaced water / Area of water line
Depth = 4000 m³ / 2000m = 2m
Therefore, when the ship is loaded with a cargo of 4000 tonnes, it will sink to a depth of 2 meters in fresh water.
To calculate the depth at which a ship sinks in fresh water when loaded with a cargo, we need to consider the concepts of buoyancy and Archimedes' principle.
Archimedes' principle states that when a body is submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid it displaces. In this case, the ship displaces a volume of water equal to its cross-sectional area multiplied by the depth it sinks.
To find the depth at which the ship sinks, we can use the formula:
Buoyant force = Weight of the ship and cargo
The weight of the ship and cargo can be calculated as:
Weight = Mass × gravitational acceleration
In this case, the mass of the ship and cargo is given as 4000 tonnes. To convert it to kilograms, we multiply by 1000:
Mass = 4000 tonnes × 1000 kg/tonne = 4,000,000 kg
The gravitational acceleration can be taken as approximately 9.8 m/s^2.
Weight = 4,000,000 kg × 9.8 m/s^2 = 39,200,000 N (Newtons)
Now, let's determine the cross-sectional area of the ship. You mentioned that the area of the cross-sections at the water line is 2000 m^2.
So, the buoyant force is equal to the weight of the water displaced by the ship:
Buoyant force = weight of water displaced
To find the depth the ship sinks, we can rearrange the equation as follows:
Buoyant force = weight of water displaced
Weight of water displaced = Buoyant force
The buoyant force is given by:
Buoyant force = density of water × volume of water displaced × gravitational acceleration
The density of fresh water is approximately 1000 kg/m^3.
Now, we can calculate the volume of water displaced:
Volume of water displaced = Cross-sectional area × depth
By substituting the values, we can solve for the depth the ship sinks:
density of water × Cross-sectional area × depth × gravitational acceleration = weight of water displaced
Substituting the values:
1000 kg/m^3 × 2000 m^2 × depth × 9.8 m/s^2 = 39,200,000 N
Simplifying the equation:
2,000,000 × depth = 39,200,000
Now, we can solve for the depth:
depth = 39,200,000 / 2,000,000
depth ≈ 19.6 meters
Therefore, the ship would sink to a depth of approximately 19.6 meters in fresh water when loaded with a cargo of 4000 tonnes.