What Is Buoyancy and How Is It Calculated?

Buoyancy is the upward force exerted by a fluid on an immersed or floating object. In IB Physics SL and HL topic A.2, calculate its magnitude using $F_b=\rho Vg$, where $V$ is the volume of fluid displaced.

The Reasoning and Mechanism

Fluid pressure increases with depth because a deeper point supports a greater weight of fluid above it. Consequently, the fluid exerts a larger upward force on the object's lower surface than the downward force on its upper surface. The resultant of these pressure forces is the buoyant force, also called upthrust.

The equation is:

$$F_b=\rho Vg$$

This expression is equivalent to saying that buoyancy equals the weight of the displaced fluid: $F_b=m_{\text{fluid}}g=(\rho V)g$.

For example, a fully submerged object displaces $2.0\times10^{-3}\,\text{m}^3$ of water. With $\rho=1000\,\text{kg m}^{-3}$:

$$F_b=(1000)(2.0\times10^{-3})(9.8)=19.6\,\text{N}$$

The force is $19.6\,\text{N}$ upward. If the object's weight is $25.0\,\text{N}$, the resultant force is $25.0-19.6=5.4\,\text{N}$ downward, so it accelerates downward.

For a floating object in vertical equilibrium, $F_b=mg$. It therefore displaces exactly enough fluid for the buoyant force to balance its weight. If an object is fully submerged and suspended without acceleration, buoyancy also equals its weight.

A common misconception is that $V$ always means the object's total volume. It means the submerged volume; these are equal only when the object is completely submerged. Another mistake is using the object's density instead of the fluid's density.

Exam Technique

Draw a free-body diagram with buoyancy upward and weight downward. For a Calculate question, show the equation, substitution and answer; convert volume to $\text{m}^3$, use the fluid density, and give the resultant force's direction.