Buoyancy & Archimedes' Principle Cheat Sheet

Key Facts

• Archimedes' Principle states that the buoyant force equals the weight of the displaced fluid, so $F_B = \rho_{fluid} g V_{disp}$.
• The weight of an object is $W = mg$, where $m$ is mass and $g \approx 9.8\,\text{m/s}^2$ on Earth.
• Density is mass per volume, given by $\rho = \frac{m}{V}$.
• An object floats when its average density is less than the fluid density, so $\rho_{object} < \rho_{fluid}$.
• An object sinks when its average density is greater than the fluid density, so $\rho_{object} > \rho_{fluid}$.
• For a floating object at rest, the upward buoyant force equals the downward weight, so $F_B = W$.
• Apparent weight in a fluid is the actual weight minus the buoyant force, so $W_{app} = W - F_B$.
• Only the submerged volume displaces fluid, so use $V_{disp} = V_{submerged}$ in $F_B = \rho_{fluid} g V_{disp}$.

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 $\rho = \frac{m}{V}$.

Apparent weight

The reduced weight an object seems to have while in a fluid, calculated with $W_{app} = W - F_B$.

Neutral buoyancy

The condition when an object neither sinks nor rises because its weight equals the buoyant force.