Archimedes Principle
Buoyant force equals the weight of displaced fluid.
Formula
Variables
Example
Why ships float
How it works
A fluid pushes upward on an immersed object because pressure increases with depth, so the lower parts of the object are squeezed harder than the upper parts. The net upward force equals the weight of the fluid the object displaces, which is why the formula depends on fluid density, displaced volume, and gravity. This is the reason objects can float, sink, or appear lighter in water: the buoyant force partially or fully offsets their weight.
When to use it
Use this formula whenever you need the upward force exerted by a fluid on an object, especially for floating bodies, submerged objects, or apparent weight in liquids. It is common in problems involving density, volume submerged, ship design, hydrometers, and determining whether an object will sink or float.
Worked example, step by step
A metal block displaces 0.015 m^3 of fresh water. Find the buoyant force on it. Step 1: Write the formula F_b = ρVg Step 2: Substitute values ρ = 1000 kg/m^3 V = 0.015 m^3 g = 9.8 m/s^2 F_b = (1000)(0.015)(9.8) Step 3: Calculate F_b = 147 N Final answer: The buoyant force is 147 N upward.
Common mistakes to avoid
- Using the object's total volume instead of only the displaced fluid volume
- Forgetting to use the fluid density, not the object's density
- Mixing units, such as using cm^3 without converting to m^3
Did You Know?
Archimedes supposedly leapt from his bath shouting "Eureka!" upon realising buoyancy could test a crown's gold.
Share this formula
More in Physics Laws & Theorems
View allNewton's First Law (Inertia)
BasicAn object stays at rest or in uniform motion unless acted on by a net force.
Newton's Second Law
BasicNet force equals mass times acceleration (rate of change of momentum).
Newton's Third Law
BasicFor every action there is an equal and opposite reaction.
Conservation of Momentum
IntermediateTotal momentum of an isolated system stays constant.
Conservation of Energy
BasicEnergy cannot be created or destroyed, only transformed.
Archimedes' Principle
IntermediateBuoyant force equals the weight of fluid displaced.