A crane lifts the 23000 kg steel hull of a ship out of the water. Determine the following.
(a) the tension in the crane's cable when the hull is submerged in the water
bouyancy=MassSteel/density steel * density water
tension=23000kg-bouyancyabove
To determine the tension in the crane's cable when the hull is submerged in water, we need to consider the forces acting on the hull.
1. Weight of the hull:
The weight of the hull is equal to the mass of the hull (m) multiplied by the acceleration due to gravity (g). In this case, the weight of the hull is calculated as follows:
Weight = mass × gravity
Weight = 23000 kg × 9.8 m/s^2
Weight = 225,400 N
2. Buoyant force:
When the hull is submerged in water, it experiences an upward buoyant force due to the displaced water. This buoyant force is equal to the weight of the water displaced by the hull. The volume of water displaced is equal to the volume of the hull.
Buoyant force = Weight of the water displaced
Buoyant force = Density of water × Volume of water displaced × gravity
To calculate the volume of water displaced, we need to know the density of water. The density of water is approximately 1000 kg/m^3.
3. Calculating the volume of water displaced:
Volume of water displaced = Volume of the hull
Unfortunately, the problem statement does not provide any information about the dimensions of the hull. Without additional information about the shape and size of the hull, we cannot determine the volume of water displaced. Therefore, we cannot calculate the exact buoyant force.
However, we can make some general observations:
- If the hull is fully submerged (completely underwater), the volume of water displaced is equal to the volume of the hull.
- If the hull is partially submerged, we need more information to determine the exact volume of water displaced.
In either case, the tension in the crane's cable when the hull is submerged is the difference between the weight of the hull and the buoyant force.