# Buoyancy and Archimedes' Principle of steel

• The_Fritz
In summary: What you've done is fine. But what you need to remember is that the total volume of the drum is the sum of the volumes of gas and steel.In summary, the volume of steel used in the drum must be equal to the difference between the volume of water displaced by the full gasoline drum and the volume of gasoline itself. This can be calculated using the densities of water, gasoline, and steel, and Archimedes' principle.
The_Fritz

## Homework Statement

Because gasoline is less dense than water, drums containing gasoline will float in water. Suppose a 260 L steel drum is completely full of gasoline.
What total volume of steel can be used in making the drum if the gasoline-filled drum is to float in fresh water?

## Homework Equations

P=$$\rho$$*V*g
Archimedes' principle - the buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by that object.

## The Attempt at a Solution

$$\rho$$_steel*V_steel*g+$$\rho$$_gas*V*g=$$\rho$$_water*V*g

Solve for V_steel: *gravity cancels*
V_steel= ($$\rho$$_water*V)-($$\rho$$_gas*V)/($$\rho$$_steel)

plug in values:
density water = 1000 kg/m^3
density gas = 680 kg/m^3
density steel = 7800 kg/m^3
Volume of drum= 260 L = .26 m^3

The_Fritz said:
$$\rho$$_steel*V_steel*g+$$\rho$$_gas*V*g=$$\rho$$_water*V*g

Steel displaces water as well.

Last edited:
One assumption that you make which may be throwing you off is that the volume of steel is negligible. In other words there are two volumes, one of gas and one of steel which displace a total volume of water. See if that helps. Otherwise me answer of 10.66L agrees with yours.
EDIT: Simultaneous post there.

## 1. What is Buoyancy?

Buoyancy is the upward force exerted by a fluid on an object immersed in it. It is a result of the difference in pressure between the top and bottom of the object.

## 2. How does Archimedes' Principle relate to buoyancy?

Archimedes' Principle states that the buoyant force on an object is equal to the weight of the fluid it displaces. This means that the more fluid an object displaces, the greater the buoyant force on it.

## 3. Why does steel sink in water?

Steel sinks in water because it is denser than water, meaning it has a greater mass per unit volume. According to Archimedes' Principle, the buoyant force on an object is equal to the weight of the fluid it displaces. Since steel is denser than water, it displaces less water and therefore experiences a smaller buoyant force compared to its weight, causing it to sink.

## 4. Can an object float in a liquid with the same density?

Yes, an object can float in a liquid with the same density. This is known as neutral buoyancy. In this case, the weight of the object is equal to the buoyant force acting on it, causing it to remain suspended in the liquid.

## 5. How does the shape of an object affect its buoyancy?

The shape of an object does not affect its buoyancy. The buoyant force is determined by the volume of fluid displaced by the object, not its shape. However, the shape can affect the distribution of the buoyant force and therefore impact how the object floats or sinks in the fluid.

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