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

To determine the tension in the crane's cable when the hull is submerged in the water, we need to consider the forces acting on the system.

When the hull is submerged in water, it experiences two main forces: the weight of the hull and the buoyant force acting on it.

The weight of the hull can be calculated using the formula:

Weight = mass × acceleration due to gravity

Given that the mass of the hull is 23000 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight:

Weight = 23000 kg × 9.8 m/s²

Now, we need to consider the buoyant force acting on the submerged hull. The buoyant force is equal to the weight of the water displaced by the hull.

To calculate the buoyant force, we need to know the density of water (ρ) and the volume of the hull (V). Assuming the density of water is 1000 kg/m³, we can calculate the volume:

Volume = Mass / Density

Given that the mass of the hull is 23000 kg, and the density of water is 1000 kg/m³:

Volume = 23000 kg / 1000 kg/m³

Now, we can calculate the buoyant force using the formula:

Buoyant Force = Volume × Density × acceleration due to gravity

Given that the density of water is 1000 kg/m³, and the acceleration due to gravity is 9.8 m/s²:

Buoyant Force = Volume × 1000 kg/m³ × 9.8 m/s²

Finally, to determine the tension in the crane's cable, we need to calculate the difference between the weight of the hull and the buoyant force:

Tension = Weight - Buoyant Force

By substituting the calculated values for weight and buoyant force, we can find the tension in the crane's cable when the hull is submerged in the water.

To determine the tension in the crane's cable when the hull is submerged in the water, we need to consider the forces acting on the hull.

1. Weight of the hull (acting downward):
The weight of the hull is given as 23,000 kg. We can calculate the weight using the formula: weight = mass × acceleration due to gravity.
The standard value of the acceleration due to gravity is approximately 9.8 m/s².
So, the weight of the hull can be calculated as follows:
Weight = 23,000 kg × 9.8 m/s²

2. Buoyant force (acting upward):
When the hull is submerged in water, it experiences a buoyant force opposing the weight. The buoyant force is equal to the weight of the water displaced by the hull. Since water density is approximately 1,000 kg/m³, we can calculate the buoyant force using the formula:
Buoyant force = Volume of water displaced × density of water × acceleration due to gravity

To find the volume of the water displaced, we need to know the dimensions of the hull. Let's assume the hull displaces a volume of 30 m³.
So, the buoyant force can be calculated as follows:
Buoyant force = 30 m³ × 1000 kg/m³ × 9.8 m/s²

3. Tension in the cable (acting upward):
The tension in the cable is the net force acting on the hull, which is the difference between the weight and buoyant force. So,
Tension = Weight - Buoyant force

Now, let's calculate these values.

Weight = 23,000 kg × 9.8 m/s²
Buoyant force = 30 m³ × 1000 kg/m³ × 9.8 m/s²
Tension = Weight - Buoyant force

Calculate Weight, Buoyant force, and Tension using the given equations, and you should have the answer for the tension in the crane's cable when the hull is submerged in the water.

When submerged, the buoyancy force equals the weight of water being lifted with the ship. Therefore the cable tension force is the hull Weight, M g = 2.25*10^5 Newtons