Archimedes’ Principle, Buoyancy, and
Density
Equipment
• Chemical splash goggles (Students bring their own)
• Distilled/Deionized Water, Isopropyl alcohol
• Computer with a spreadsheet software
• Set of Digital Calipers
• Force Sensor
• Plastic bins to catch overflow.
• Graduated cylinder
• Aluminum Container with and without spout
• Vertical stand, perpendicular clamp, horizontal rod (between 20 cm and 50 cm)
• Metal Ball with a string attached to it
• Wooden cylinder with pencil lines marking off equal lengths
Objectives
• Verify Archimedes’ principle and use it to determine the density of a given liquid.
Introduction
The famous legend tells us that Archimedes was the person who discovered that the volume of
displaced water equals the volume of a submerged object. He came up with that idea as he was
trying to measure the volume of a crown of unusual shape. Puzzled he had filled his bathtub flush
with water and water overflowed when he got inside of the tub. The idea that the amount of water
splashed out of the tub is exactly the volume of his own body struck him and he ran outside of his
house crying “Eureka!” This means, “I have found it”.
Archimedes’ Principle itself isn’t directly about volume, it’s about buoyancy. It states that the
buoyant upward force acting on an object entirely or partially submerged in a fluid is equal to the
weight of the fluid displaced by the object.
For a given object, the weight can be directly calculated from the mass or from the density and
volume:
𝐹
𝑔=𝑚𝑔 = 𝜌𝑉𝑔
The buoyant force is found by applying the same idea to the fluid instead of the object:
𝐹
𝐵= 𝑚fluid𝑔 = 𝜌flu id𝑉displaced𝑔 (1)
Here, 𝑚fluid is the mass of the displaced fluid, which is broken down as the density of the fluid 𝜌fluid
multiplied by the submerged volume of the object 𝑉displaced.
