Why do Things Float ?

Recommended Lessons

Not sure where to start? These are the lessons and games we recommend most to students, parents and teachers on Basic-mathematics.com. Each lesson explains the topic in plain language, walks you through worked examples step by step, and ends with practice so you can check your understanding. Pick one below, or use the menu to find lessons on fractions, algebra, geometry, statistics and more.

Why Do Things Float in Water?

In this lesson, you will learn

  • which two forces decide whether an object floats, sinks, or does neither
  • how to compare the density of an object with the density of water
  • the rule for floating, sinking, or doing neither

“Why do things float in water?” is really a great question. In order to understand the concept, you will need to review the lessons about density, Archimedes' principle and buoyancy.

Two Forces: Weight and Buoyant Force

Whether an object floats or sinks or does neither will depend on its weight or the force that pushes the object down and its buoyant force or the force that pushes the object up.

Definition

The buoyant force is the upward push that water (or any fluid) puts on an object in it. The weight is the downward pull on the object.

When an Object Neither Floats nor Sinks

First, let us consider the case where the object neither floats nor sinks.

Common sense tells us that when the object neither sinks nor floats, the force that pushes the object up (buoyant force) is equal to the force that pushes the object down (weight).

This fact will help us deduce something important about the density of the object and the density of water.

Let us suppose that

Buoyant force = weight of object   (1)

We also saw the following in the lesson about Archimedes' principle

Buoyant force = weight of displaced water   (2)

Putting equations (1) and (2) together will give us

weight of object = buoyant force = weight of displaced water

We can then make this conclusion

When the buoyant force is equal to the weight of the object, weight of object = weight of displaced water.

We need two more things in order to make our conclusion.

Remember

First, we saw in the lesson about buoyant force that when an object is completely under water, the volume of the object is equal to the volume of the displaced water.

Second, we need the formula for density.

density = weightvolume

Note: Weight divided by volume is also called weight density. Since weight = mass × gravity, comparing weight densities gives the same result as comparing ordinary densities (mass ÷ volume).

Let us put it all together!

Weight of object = weight of displaced water
volume of object = volume of displaced water

What does this tell us about the density?

Suppose weight of object = weight of displaced water = 5 N

Suppose volume of object = volume of displaced water = 500 cm³

The density of the object will therefore be the same as the density of water and it will be equal to

densityobject = densitywater = 5 N500 cm³ = 0.01 N/cm³
Rule

An object will neither float nor sink when the density of the object is the same as the density of the water or the fluid the object is submerged in.

A ball has a density of 0.01 N/cm³. The water has a density of 0.01 N/cm³ too. What will the ball do?

Show answer

It will neither float nor sink. The two densities are the same, so the buoyant force equals the weight.

Why Do Things Float Then?

Suppose buoyant force > weight of object when the object is completely under water. Then the object will float.

Weight of object < buoyant force

Since buoyant force = weight of displaced water, we get

weight of object < weight of displaced water

And again, when the object is completely under water, we know

volume of object = volume of displaced water
Worked example: Will this object float?
  1. Suppose weight of object = 4 N and weight of displaced water = 5 N.
  2. Suppose volume of object = volume of displaced water = 500 cm³.
  3. density of object = 4 N500 cm³ = 0.008 N/cm³
  4. density of displaced water = 5 N500 cm³ = 0.01 N/cm³

0.008 N/cm³ < 0.01 N/cm³, so the object floats.

Note: Because the upward push is bigger than the weight, the object rises until only part of it is under water. A floating object then displaces just enough water to equal its own weight (4 N in this example).

Why do things float then?

Rule

An object will float when the density of the object is less than the density of water or the fluid the object is submerged in.

On the other hand, when the density of the object is more than the density of water or the fluid the object is submerged in, the object will sink.

Common mistake

“Heavy things sink and light things float.” Not quite! A huge wooden log floats, while a tiny pebble sinks. What matters is density (weight compared with volume), not weight alone.

Object A has a density of 0.012 N/cm³ and object B has a density of 0.007 N/cm³. Water has a density of 0.01 N/cm³. Which object floats?

Show answer

Object B. 0.007 is less than 0.01, so B floats. Object A sinks because 0.012 is more than 0.01.

Summary

The figure below is a summary that will help you determine when an object will float, sink, or do neither. It sums up the explanations above.

Why do things float: an object floats when its density is less than the density of water, stays in place when the densities are equal, and sinks when its density is greater
  • Weight pushes an object down, and the buoyant force pushes it up.
  • Buoyant force = weight of displaced water (Archimedes' principle).
  • Density = weight ÷ volume.
  • Density of object < density of fluid: the object floats.
  • Density of object = density of fluid: the object neither floats nor sinks.
  • Density of object > density of fluid: the object sinks.

Test Yourself: 10-Question Quiz

Now check what you learned. Every answer is explained, and each time you play you get new numbers.

Question 1 of 10Score: 0

Keep learning