# Buoyancy

Students explore the relationship of buoyancy and density in fluids.

## Introduction

In this lesson we will explore buoyancy, how it applies forces, and possible connections between buoyancy and density.

## What is Buoyancy?

Buoyancy is the tendency for materials to float in a fluid. We refer to the force that causes buoyancy as the buoyant force. The buoyant force is the upward force exerted on an object if it is submerged in a fluid. Sometimes the buoyant force is referred to as the “anti-gravity” force because the upward exerted force pushes against the force of gravity (or away from the Earth). The buoyant force is measured in newtons (N). A newton is the amount of force it takes to accelerate a 1kg object to a rate of 1 m/s.

## Average Density

Think of many things that we use to transverse the water, ships can and are built out of steel. They have large, hollow hulls, that cover a very area. The reason these objects float is because, even though steel is far denser than water, it is spread out over a very large area. The design of the hull allows for other less dense materials to enter the hull, like air, and reduce the average density of the object. Remember, when measuring density we must consider the volume of the object, boats take advantage of this by having strong outshells, but generally hollow interiors.

When determining buoyancy, we need to take into account the average density of the object. One interesting example of this in nature is the fish. The fish has an air bladder (also known as the swim bladder) that stores a mixture of air and water. By increasing the amount of air in this sac the fish can rise closer to the surface.

Like the fish, the submarine uses the idea of air bladders to control its depth. Submarines store compressed air in tanks. When they want to sink they open their badder and allow water into it. Likewise, when they want to rise they pump air into their bladders expelling the water and lowering its average density.

## Archimedes’ Principle

The Greek scientist Archimedes made a brilliant discovery around 212 B.C.E. Hiero II, ruler of Syracuse, suspected that the royal goldsmith had not used pure gold to make his crown. The king asked Archimedes to determine whether the crown was made entirely of gold. Archimedes knew that all he had to do was determine whether the density of the crown matched the density of gold. Recall that the formula for density requires only two values: mass and volume. Archimedes could measure the mass of the crown easily with a balance. How could he measure the volume of an object as irregularly shaped as a crown?

Archimedes solved the problem while at the public baths. He stepped into the almost-full bath, and water gushed all over the floor. The solution to the problem came to Archimedes in a flash — a solid object can displace water out of a container.

Archimedes applied his new ideas to another property of fluids. He believed that the displaced fluid held the key to whether the object placed in the fluid would sink or float. He wondered why he would sink if he stepped into a bathtub, but he would float if he stood in a boat on the water. He concluded that the amount of buoyant force that would push up against the object immersed in the fluid would equal the force of gravity (the weight) of the fluid that the object displaced. If the water in a container is still, or at rest, then the water particles are neither rising nor sinking. An object immersed in a fluid such as water does not rise or sink if the amount of force pulling down (gravity) equals the amount of force pushing up (buoyancy). When gravity equals buoyancy, this condition is known as neutral buoyancy. The water particles in the lower part of the container must be exerting a buoyant force equal to the weight, or force of gravity, of the water above it. When Archimedes stepped into the bath, he sank because the amount of water that he displaced weighed less than he did. When he stepped into a boat, however, a larger volume of water was displaced. The weight of this water far exceeded the weight of the boat and Archimedes combined. Therefore, the buoyant force was greater and the boat, with Archimedes in it, floated on the surface. Why would Archimedes and his boat not continue to rise, with such a large buoyant force pushing it upward? At the surface of the water, the fluid supporting the object is air. As mentioned earlier, the buoyancy of air is much less than that of water. Therefore, the upward motion stops at the water’s surface. Archimedes made the following conclusion, now known as Archimedes’ principle: The buoyant force acting on an object equals the weight (force of gravity) of the fluid displaced by the object. Archimedes’ principle is useful in predicting whether objects will sink or float. The buoyant force does not depend on the weight of the submerged object, but rather on the weight of the displaced fluid. A solid cube of aluminum, a solid cube of iron, and a hollow cube of iron, all of the same volume, would experience the same buoyant force!

Science Focus 8

## How Buoyancy and Density Are Related

After reading all of this you may be asking yourself, “How does density affect buoyancy?” Looking back at the last lesson, density is the mass of an object in a specific volume. All objects have a density, even fluids. For example, water has a density of 1 g/mL, while salt water has a density of 1.03 g/mL. Any object with the average density less than 1.0 g/mL and 1.03 g/mL will float in water and salt water respectively. A specific device called a hydrometer can be used to measure density of liquids is often used to check the condition of liquids in many commercial devices like cars. Using a hydrometer denser liquids will extend the indicator further; likewise, less dense liquids will move the indicator a smaller amount.