# Buoyancy of ship, volume displaced, and tension of crane (in/out) of water

• orbits
In summary, a crane is lifting a 18,000kg steel hull out of the water. The density of steel is 7.8 x 10^3 kg/m3 and water is 1000 kg/m3. The volume of water displaced by the hull can be found by dividing the mass of the steel by its density. The tension in the crane's cable when the hull is fully submerged is 1.8 x 10^7 N, while the tension when the hull is out of the water is 180,000 N. However, the hull may not necessarily fill with water, so it may displace more water than its own volume.
orbits
A crane lifts the 18,000kg steel hull of a ship out of the water.
The density of steel is known to be 7.8 x 103 kg/m3, while that of water is 1000 kg/m3.

A) While the steel hull is fully submerged in the water, what is the volume of water displaced by the hull? I really have no idea how to work this problem out.

Buoyancy = m* density * V displaced * G
m=pv

B) What is the tension in the crane's cable when the hull is fully submerged?
I believe this one is related to A

Density * Volume * G = F m=(density) Volume
1000* 18000/10 *10

f=1.8 x 107

C) What is the tension in the crane's cable when the hull is out of the water?

Ft= mg
Ft = 18,000 * 10 (class standard)
Ft= 180,000N

If you have the mass of the material and its density, can't you find its volume? That volume displace the same volume of water.

Bright Wang said:
If you have the mass of the material and its density, can't you find its volume? That volume displace the same volume of water.

Only if the hull fills with water. If it does not, it displaces far more water than its own volume.

The question seems a bit tricky. It talks about a fully-submerged the hull, which, to me, strongly suggests that the hull has filled with water (unless it's a watertight submarine hull I suppose ).

So, I guess you're right. They're simply talking about the volume of the steel itself, not any kind of bouyant hull-shape.

## 1. What is buoyancy and how does it affect ships?

Buoyancy is the upward force exerted on an object by a fluid, in this case water. It plays a crucial role in the stability and floating of ships, as it helps to counteract the weight of the ship and keep it afloat. If the buoyant force is greater than the weight of the ship, it will float; if the weight is greater, the ship will sink.

## 2. How is the volume of water displaced by a ship calculated?

The volume of water displaced by a ship is equal to the weight of the ship. This can be calculated by measuring the weight of the ship when it is empty and then again when it is fully loaded with cargo. The difference between these two weights is the weight of the cargo, which is also equal to the weight of the water displaced.

## 3. What is the relationship between the tension of a crane and the weight of the object being lifted?

The tension of a crane is directly proportional to the weight of the object being lifted. This means that as the weight of the object increases, so does the tension on the crane. The crane must be able to support this tension in order to safely lift and move the object.

## 4. How does the volume of water displaced affect the buoyancy of a ship?

The volume of water displaced by a ship determines the amount of buoyant force acting on the ship. The greater the volume of water displaced, the greater the buoyant force and the more likely the ship is to float. This is why ships with larger hulls and more cargo are able to float despite their heavy weight.

## 5. How does the tension of a crane change when it is lifting an object out of the water versus lowering it into the water?

The tension of a crane changes when lifting an object out of the water versus lowering it into the water because of the buoyant force acting on the object. When lifting an object out of the water, the buoyant force decreases as the object is removed from the water, resulting in a decrease in the tension on the crane. On the other hand, when lowering an object into the water, the buoyant force increases as the object displaces more water, resulting in an increase in the tension on the crane.

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