Buoyancy explains why objects feel lighter in water and why some objects float while others sink. This cheat sheet covers Archimedes' Principle, density, displaced fluid, and apparent weight. Students need these ideas to solve force problems involving objects in liquids or gases.
The same principles apply to boats, balloons, submarines, and hydrometers.
The central rule is that the buoyant force equals the weight of the fluid displaced by the object. Density helps predict floating, sinking, or neutral buoyancy by comparing the object's density to the fluid's density. Free-body diagrams often include weight downward and buoyant force upward.
For floating objects, the buoyant force balances the object's weight, so .
Key Facts
- Archimedes' Principle states that the buoyant force equals the weight of the displaced fluid, so .
- The weight of an object is , where is mass and on Earth.
- Density is mass per volume, given by .
- An object floats when its average density is less than the fluid density, so .
- An object sinks when its average density is greater than the fluid density, so .
- For a floating object at rest, the upward buoyant force equals the downward weight, so .
- Apparent weight in a fluid is the actual weight minus the buoyant force, so .
- Only the submerged volume displaces fluid, so use in .
Vocabulary
- Buoyant force
- The upward force a fluid exerts on an object placed in it.
- Archimedes' Principle
- The rule that the buoyant force on an object equals the weight of the fluid displaced by the object.
- Displaced fluid
- The volume of fluid pushed aside by the submerged part of an object.
- Density
- A measure of mass per unit volume, calculated with .
- Apparent weight
- The reduced weight an object seems to have while in a fluid, calculated with .
- Neutral buoyancy
- The condition when an object neither sinks nor rises because its weight equals the buoyant force.
Common Mistakes to Avoid
- Using the object's total volume instead of the submerged volume is wrong because buoyant force depends on the displaced fluid volume, .
- Forgetting that buoyant force points upward is wrong because pressure increases with depth and creates a net upward force.
- Comparing mass instead of density is wrong because floating and sinking depend on compared with , not mass alone.
- Setting for every object is wrong because that equality applies only when the object is floating or neutrally buoyant at rest.
- Using the object's density in is wrong because the buoyant force depends on the density of the fluid being displaced.
Practice Questions
- 1 A rock displaces of water. If , what is the buoyant force on the rock?
- 2 An object has mass and volume . Find its density and determine whether it sinks or floats in water.
- 3 A metal block weighs in air and experiences a buoyant force of in water. What is its apparent weight in water?
- 4 A huge steel ship floats even though a small solid steel ball sinks. Explain how average density and displaced water make this possible.
Understanding Buoyancy & Archimedes' Principle
Buoyancy begins with pressure, not with a mysterious upward push. A fluid presses on every surface it touches. Pressure is greater deeper down because more fluid is above that location.
The bottom of a submerged object therefore receives a stronger upward push than the downward push on its top. Pushes on the sides mostly cancel in pairs. The remaining difference produces a net upward force.
This pressure difference exists in water, oil, air, and every other fluid. It is why a helium balloon rises through air even though air seems almost weightless.
The amount of an object below the surface can change until the forces balance. A wooden block placed in water first moves downward. As more of it goes under, it pushes aside more water, so the upward effect grows.
It stops when the required amount of water has been displaced. This explains why a large steel ship can float even though solid steel sinks. The ship has a hollow shape containing much air, so its total mass is spread across a very large volume.
Its average density is low enough for part of the hull to remain above water. Adding cargo makes the ship sit lower because it must displace more water.
Apparent weight is what a spring scale measures when it supports an object in a fluid. The scale pulls upward while gravity pulls downward. The fluid supplies part of the upward support, so the scale reading decreases.
This is useful for finding volume or density in laboratory work. Students should separate mass from weight carefully. Mass does not change when an object enters water.
Its gravitational pull is essentially unchanged too. What changes is the extra force from the surrounding fluid.
If an object is released and is denser than the fluid, it can still have an upward buoyant force while moving downward. The downward force is simply larger, so the object accelerates downward.
Good problem solving starts by identifying the fluid and the submerged part of the object. Use the density of the fluid, not the density of the object, when calculating the force caused by displaced fluid. A fully underwater object has its whole outside volume submerged, provided it has no water-filled spaces that need separate treatment.
A floating object uses only the portion below the surface. Draw all forces before choosing an equation. Include tension if a string holds the object, or a normal force if it rests on the bottom.
Pay attention to units. Density, volume, and gravity must combine into a force measured in newtons.
In real life, water becomes slightly less dense when it is warmer, while salt water is denser than fresh water. These changes affect how high swimmers, boats, and floating instruments sit in the water.