Buoyancy and Archimedes' Principle
1. Buoyant Force
Learning outcomes
- I can define buoyant force and describe its direction.
- I can explain why fluids exert an upward force on objects.
- I can identify factors that affect buoyant force.
- I can compare buoyant forces acting on different objects.
- I can relate buoyant force to pressure differences in fluids.
Why can a huge ship float while a small metal coin sinks? Why does your body feel lighter when you are standing in a swimming pool? Why does a helium balloon rise through the air?
All of these situations involve buoyant force.
Buoyant force is produced because fluids exert pressure on objects. Since fluid pressure usually increases with depth, the bottom of a submerged object experiences greater pressure than the top. This pressure difference produces a net upward force.
What Is Buoyant Force?
Buoyant force is the upward force exerted by a fluid on an object that is partly or completely immersed in the fluid.
Buoyant force is sometimes called upthrust.
Its direction is:
upward
This is opposite to the direction of the object's weight, which acts downward.
For an object in water:
↑
Buoyant force
│
[object]
│
Weight
↓The motion of the object depends partly on the relationship between these two forces.
Fluids Produce Buoyant Force
Remember that a fluid is any substance that can flow.
This includes:
- liquids
- gases
Therefore, buoyant force occurs in both liquids and gases.
Water produces buoyant force on:
- swimmers
- boats
- submarines
- fish
- floating objects
Air produces buoyant force on:
- balloons
- airships
- objects in the atmosphere
Buoyancy is therefore not only a property of water.
All fluids can produce buoyant forces.
Where Does Buoyant Force Come From?
To understand buoyant force, we need to connect it to our previous topic: fluid pressure.
Recall that liquid pressure increases with depth:
greater depth → greater pressure
Imagine a rectangular block completely underwater.
Water pushes against every surface of the block.
The water pushes:
- downward on the top
- upward on the bottom
- sideways on the sides
The sideways forces largely balance each other.
But the bottom of the object is deeper than the top.
Therefore:
Pressure at bottom > Pressure at top
This means the upward force on the bottom is greater than the downward force on the top.
The result is a net upward force.
That net upward force is the buoyant force.
Connecting Pressure to Force
Remember:
Pressure = Force ÷ Area
Therefore:
Force = Pressure × Area
Suppose the top and bottom of an underwater block have the same area.
Because the bottom is deeper:
Pbottom > Ptop
Therefore:
Fbottom > Ftop
So:
larger upward force − smaller downward force = buoyant force
This gives us an important connection:
Buoyant force exists because fluid pressure changes with depth.
A Numerical Example
Imagine a rectangular object underwater.
The water produces:
Upward force on bottom = 80 N
and:
Downward force on top = 50 N
The sideways forces balance.
The net upward force caused by the pressure difference is:
Buoyant force = 80 N − 50 N
Buoyant force = 30 N upward
So the fluid produces a buoyant force of 30 N.
What Determines the Size of the Buoyant Force?
The buoyant force depends mainly on:
1. Volume of Fluid Displaced
An object that displaces more fluid experiences a greater buoyant force.
More fluid displaced → greater buoyant force
2. Density of the Fluid
A denser fluid produces a greater buoyant force for the same displaced volume.
Greater fluid density → greater buoyant force
3. Gravitational Field Strength
Stronger gravity increases the weight of the displaced fluid.
Greater gravitational field strength → greater buoyant force
These ideas can be summarized by Archimedes' Principle, which we will explore in more detail in the next topic.
Displacement
When an object enters water, it pushes some of the water out of the space it occupies.
This is called displacement.
A completely submerged object displaces a volume of water equal to its own volume.
For example:
An object with a volume of 500 cm³ that is completely underwater displaces:
500 cm³ of water
A partially submerged object displaces only the volume of the part below the water.
Exploring Buoyancy
The relationship between object density, fluid density and displaced fluid determines whether an object floats, sinks or remains suspended.
Notice that buoyancy depends on the interaction between the object and the fluid. It is not simply a property of the object itself.
Buoyant Force and Displaced Fluid
A very useful rule is:
The buoyant force on an object is equal to the weight of the fluid displaced by the object.
This is known as Archimedes' Principle.
So if an object displaces water weighing 20 N, the water produces a buoyant force of:
20 N upward
If it displaces water weighing 75 N, the buoyant force is:
75 N upward
This explains why increasing the volume of displaced water increases buoyant force.
Example: Comparing Two Submerged Objects
Object A and Object B are completely submerged in the same water.
Object A has a volume of:
200 cm³
Object B has a volume of:
600 cm³
Object B displaces three times as much water.
Therefore, Object B experiences approximately three times the buoyant force.
Notice something important:
We did not need to know the masses of the objects to compare their buoyant forces.
For completely submerged objects in the same fluid:
larger volume → more fluid displaced → greater buoyant force
Does an Object's Mass Determine Buoyant Force?
Not directly.
This is a common source of confusion.
Suppose two objects have exactly the same size and shape and are completely submerged in water.
One is made from aluminium.
The other is made from steel.
If both have the same volume, they displace the same volume of water.
Therefore, they experience the same buoyant force when completely submerged in the same fluid.
However, the steel object may have a greater weight.
So even though their buoyant forces are equal, their motions may be different.
Buoyant Force vs Weight
Whether an object rises, sinks, or remains at the same level depends on the net force.
Consider an object completely surrounded by water.
Two major vertical forces act on it:
Weight downward
and
Buoyant force upward
There are three important possibilities.
Situation 1: Buoyant Force Greater Than Weight
If:
Buoyant force > Weight
there is a net upward force.
The object accelerates upward.
↑↑↑
Buoyant force
[●]
Weight
↓This can happen when an object is released underwater and is less dense overall than the surrounding fluid.
Situation 2: Weight Greater Than Buoyant Force
If:
Weight > Buoyant force
there is a net downward force.
The object accelerates downward.
↑
Buoyant force
[●]
Weight
↓↓↓The object sinks.
Situation 3: Buoyant Force Equals Weight
If:
Buoyant force = Weight
the forces are balanced.
There is no net vertical force.
The object does not accelerate vertically.
↑↑
Buoyant force
[●]
Weight
↓↓Depending on the situation, the object may float at the surface or remain suspended within the fluid.
Floating Objects
A floating object settles until it displaces enough fluid for the buoyant force to balance its weight.
Therefore, for an object floating at rest:
Buoyant force = Weight
This is why a floating boat does not continue rising out of the water.
As it rises, less of the boat remains underwater.
Less water is displaced.
The buoyant force decreases.
Eventually:
Buoyant force = Weight
and the boat reaches equilibrium.
Why Does a Heavier Boat Sit Lower in the Water?
Imagine people getting into a small boat.
The mass and weight of the boat increase.
To remain floating:
Buoyant force must equal the new, greater weight.
How can the boat obtain a greater buoyant force?
It sinks slightly deeper.
This causes it to displace more water.
More displacement → greater buoyant force
Eventually the new buoyant force balances the greater weight.
This explains why heavily loaded ships sit lower in the water.
Why Do Ships Float?
Steel is denser than water, so a solid block of steel normally sinks.
Yet enormous steel ships float.
Why?
A ship is not a solid block of steel.
Its hull contains a large volume of air.
This gives the entire ship a large volume compared with its mass.
As the ship enters the water, it displaces a large amount of water.
Eventually, it displaces enough water that:
weight of displaced water = weight of ship
Therefore:
buoyant force = ship's weight
and the ship floats.
Buoyant Force and Fluid Density
The density of the fluid also affects buoyancy.
Consider the same object placed in:
- freshwater
- saltwater
Saltwater is denser than freshwater.
For the same displaced volume:
denser fluid → heavier displaced fluid → greater buoyant force
This is why people generally float slightly more easily in saltwater than in freshwater.
Example: Freshwater vs Saltwater
Imagine the same completely submerged object displaces 1 litre of fluid.
If the saltwater is denser than the freshwater, then 1 litre of saltwater has greater mass.
Therefore:
Weight of displaced saltwater > Weight of displaced freshwater
Since buoyant force equals the weight of displaced fluid:
Buoyant force in saltwater > Buoyant force in freshwater
Why Objects Float Higher in Denser Fluids
Suppose a boat moves from freshwater into denser saltwater.
The boat's weight does not change.
To float:
Buoyant force = Weight
Because saltwater is denser, a smaller volume of saltwater needs to be displaced to produce the required buoyant force.
Therefore, the boat floats slightly higher in saltwater.
This is one reason ships have different safe-loading markings for different water conditions.
Submarines and Buoyant Force
Submarines control their movement partly by changing their overall density and buoyancy using ballast tanks.
To Dive
Water enters the ballast tanks.
The submarine's mass increases.
Its weight can become greater than the buoyant force.
The submarine descends.
To Rise
Compressed air forces water out of the ballast tanks.
The submarine's mass decreases.
The balance of forces changes, allowing it to rise.
To Remain at a Constant Depth
The submarine can adjust its buoyancy so that approximately:
Buoyant force = Weight
This condition is called neutral buoyancy.
Buoyancy in Gases
Buoyant force also acts in gases.
A helium balloon experiences an upward buoyant force because it displaces surrounding air.
The surrounding air has weight.
The balloon experiences a buoyant force equal to the weight of the air it displaces.
If the total weight of:
- balloon
- helium
- string or basket
- passengers or equipment
is less than the buoyant force, the balloon can accelerate upward.
Hot-Air Balloons
Hot-air balloons use the same principle.
Heating the air inside the balloon causes it to expand and become less dense than the cooler surrounding air.
The balloon displaces denser surrounding air.
If the upward buoyant force becomes greater than the total weight of the balloon system, the balloon rises.
So buoyancy connects several ideas we have already studied:
temperature → density → buoyant force → motion
Apparent Weight in Water
You may have noticed that objects seem lighter underwater.
Their actual gravitational weight has not changed significantly.
Instead, the water provides an upward buoyant force.
For example, suppose an object has:
Weight = 100 N
and experiences:
Buoyant force = 30 N
The downward force that would be measured by a supporting scale or tension system is reduced.
Its apparent weight is:
100 N − 30 N = 70 N
So:
Apparent weight = Actual weight − Buoyant force
Worked Example: Finding Buoyant Force from Apparent Weight
An object weighs 80 N in air.
When completely submerged in water, its apparent weight is 55 N.
Calculate the buoyant force.
Use:
Buoyant force = Actual weight − Apparent weight
Substitute:
Buoyant force = 80 − 55
Buoyant force = 25 N
Answer:
The water exerts a buoyant force of:
25 N upward
Comparing Buoyant Forces
When comparing buoyant forces, ask these questions:
Are the objects in the same fluid?
If yes, fluid density is the same.
Are they completely submerged?
If yes, compare their volumes.
Larger submerged volume → greater displacement → greater buoyant force
Are they the same size but in different fluids?
Compare fluid densities.
Denser fluid → greater buoyant force
Are the objects floating?
If they are floating at rest:
Buoyant force = object's weight
Therefore, a heavier floating object must experience a greater buoyant force.
Example: Three Objects
Consider three objects completely submerged in the same water:
- Object A: volume = 100 cm³
- Object B: volume = 300 cm³
- Object C: volume = 500 cm³
Which experiences the greatest buoyant force?
Object C displaces the most water.
Therefore:
Object C experiences the greatest buoyant force.
Object A experiences the smallest.
Their masses are not needed to answer this question.
Does Greater Depth Mean Greater Buoyant Force?
This question can be tricky.
We know:
Pressure increases with depth.
So it may seem that an object moved deeper underwater must experience a greater buoyant force.
However, for a completely submerged rigid object in a liquid of approximately constant density, both the pressure on the top and the pressure on the bottom increase as the object moves deeper.
The pressure difference between the top and bottom remains approximately the same.
Therefore, the buoyant force remains approximately the same.
So:
Greater absolute pressure does not automatically mean greater buoyant force.
For the same fully submerged rigid object in the same approximately incompressible fluid, buoyant force is approximately independent of depth.
Common Mistakes
Mistake 1: Saying buoyant force always makes objects float
Every immersed object experiences buoyant force, including objects that sink.
An object sinks when:
Weight > Buoyant force
Mistake 2: Thinking buoyant force is caused simply by "water pushing upward"
Water does push upward, but it also pushes downward and sideways.
Buoyant force results from the difference in fluid pressure between different parts of the object.
Mistake 3: Thinking a heavier submerged object always has greater buoyant force
Not necessarily.
Two completely submerged objects with the same volume in the same fluid experience the same buoyant force even if their masses are different.
Mistake 4: Thinking greater depth always means greater buoyant force
Pressure increases with depth, but the pressure on both the top and bottom increases.
For the same completely submerged rigid object in a liquid of nearly constant density, the buoyant force remains approximately constant with depth.
Mistake 5: Thinking floating means there is no gravity
Gravity still acts on a floating object.
The object floats because:
Buoyant force = Weight
The forces are balanced.
Mistake 6: Saying a floating object experiences a larger buoyant force than its weight
If an object is floating at rest:
Buoyant force = Weight
If the buoyant force remained greater than its weight, the object would accelerate upward.
Mistake 7: Thinking buoyancy only occurs in liquids
Gases are fluids too.
Air produces buoyant forces on balloons, airships, and every other object in the atmosphere.
Check Your Understanding
1. Recall
Define buoyant force and state its direction.
2. Explain
Why does a completely submerged object experience a net upward force from the surrounding water?
3. Apply
An underwater object experiences:
- 90 N upward force from pressure on its bottom
- 65 N downward force from pressure on its top
Calculate the buoyant force.
4. Compare
Two objects of equal volume are completely submerged in the same water.
Object A has a mass of 2 kg.
Object B has a mass of 5 kg.
Which object experiences the greater buoyant force? Explain.
5. Fluid Density
The same object is completely submerged first in freshwater and then in denser saltwater.
In which liquid does it experience the greater buoyant force? Explain.
6. Forces
An object has a weight of 40 N and experiences a buoyant force of 25 N.
Calculate the net vertical force and predict what will happen.
7. Floating
A boat weighing 12 000 N is floating at rest.
What is the buoyant force acting on the boat?
Explain how you know.
8. Challenge
A solid block is completely submerged 2 m below the surface of a swimming pool. It is then moved to 5 m below the surface without changing its volume.
The water pressure is much greater at 5 m.
Does the block necessarily experience a greater buoyant force?
Explain your answer using pressure differences.
Key Terms
- Buoyant force – upward force exerted by a fluid on an immersed object
- Upthrust – another name for buoyant force
- Fluid – substance that can flow, including liquids and gases
- Displacement – movement of fluid caused when an object occupies space within it
- Fluid pressure – force per unit area exerted by a fluid
- Archimedes' Principle – buoyant force equals the weight of displaced fluid
- Apparent weight – measured weight of an object when buoyant force acts on it
- Neutral buoyancy – condition in which buoyant force balances weight while an object is within a fluid
- Net force – overall force after all forces are combined
- Equilibrium – condition in which the net force is zero
Key Takeaways
- Buoyant force is the upward force exerted by a fluid on an immersed object.
- Buoyant force occurs in both liquids and gases.
- Fluid pressure increases with depth, so the bottom of an immersed object usually experiences greater pressure than the top.
- This pressure difference produces the net upward buoyant force.
- Buoyant force increases when more fluid is displaced.
- A denser fluid produces a greater buoyant force for the same displaced volume.
- According to Archimedes' Principle, buoyant force equals the weight of the displaced fluid.
- If weight > buoyant force, an object accelerates downward.
- If buoyant force > weight, an object accelerates upward.
- A floating object at rest has buoyant force = weight.
- Two equally sized objects completely submerged in the same fluid can experience the same buoyant force even if their masses are different.
- For the same rigid, completely submerged object in a nearly incompressible fluid, moving deeper does not necessarily increase buoyant force even though the surrounding pressure increases.