A crane lifts the 22000kg steel hull of a ship out of the water. Determine the tension in the crane's cable when the hull is submerged in the water.
Determine the tension when the hull is completely out of the water.
To determine the tension in the crane's cable when the hull is submerged in the water, we need to consider two forces: the weight of the hull and the buoyant force acting on it.
First, let's calculate the weight of the hull. The weight of an object is given by the formula:
Weight = Mass * Acceleration due to gravity
Given that the mass of the hull is 22000 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:
Weight = 22000 kg * 9.8 m/s^2 = 215600 N
Next, let's determine the buoyant force acting on the hull when it is submerged in water. The buoyant force is equal to the weight of the fluid displaced by the submerged object. For a fully submerged object, this is equal to the weight of the object itself.
Therefore, the buoyant force acting on the hull when it is submerged in water is equal to the weight of the hull, which is 215600 N.
The tension in the crane's cable, when the hull is submerged in water, is equal to the sum of the weight of the hull and the buoyant force:
Tension = Weight of the hull + Buoyant force
= 215600 N + 215600 N
= 431200 N
So, when the hull is submerged in water, the tension in the crane's cable is 431200 N.
Now, let's determine the tension in the crane's cable when the hull is completely out of the water.
When the hull is completely out of the water, there is no buoyant force acting on it, as it is not displacing any water. Therefore, the tension in the crane's cable is equal to the weight of the hull.
The weight of the hull is still 215600 N, so the tension in the crane's cable when the hull is completely out of the water remains 215600 N.
To determine the tension in the crane's cable when the hull is submerged in the water, we need to calculate the buoyant force acting on the hull.
Step 1: Calculate the weight of the steel hull in the air.
The weight of an object is given by the equation: weight = mass × gravity.
Given that the mass of the steel hull is 22000 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight of the steel hull in the air as follows:
Weight = 22000 kg × 9.8 m/s^2 = 215600 N
Step 2: Calculate the buoyant force acting on the hull when submerged in water.
The buoyant force is equal to the weight of the displaced water, and it counteracts the weight of the hull. Therefore, the buoyant force acting on the hull is equal to its weight when submerged.
Since water has a density of approximately 1000 kg/m^3, the volume of water displaced by the hull can be calculated as follows:
Volume = Mass of water displaced / Density of water
The mass of water displaced is equal to the mass of the hull, which is 22000 kg.
Volume = 22000 kg / 1000 kg/m^3 = 22 m^3
The buoyant force can be calculated using the equation: Buoyant force = Volume × Density of water × gravity
Buoyant force = 22 m^3 × 1000 kg/m^3 × 9.8 m/s^2 = 215600 N
Step 3: Determine the tension in the crane's cable when the hull is submerged in water.
When the hull is submerged, the crane cable needs to support the weight of the hull minus the buoyant force acting on it.
Tension = Weight of the hull - Buoyant force
Tension = 215600 N - 215600 N = 0 N
Therefore, the tension in the crane's cable when the hull is submerged in the water is 0 N.
To determine the tension in the crane's cable when the hull is completely out of the water, we need to calculate the weight of the hull.
Since the hull is out of the water, there is no buoyant force acting on it.
Step 1: Calculate the weight of the steel hull in the air.
We have already calculated this in the previous step. The weight of the steel hull is 215600 N.
Therefore, the tension in the crane's cable when the hull is completely out of the water is 215600 N.