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Buoyancy from pressure difference

A fluid exerts a net upward buoyant force on an immersed object because pressure is greater at greater depth. In the IB model,

$F_b=\rho_fV_{disp}g$

where $V_{disp}$ is the displaced fluid volume.

Separate buoyancy from net force

The buoyant force is one force in the free-body diagram. The net force is found after combining it with weight, tension, drag or other forces.

Floating condition

For an object at rest on the fluid, buoyancy balances its weight. This gives a useful density or submerged-volume relationship, but only after the equilibrium assumption is stated.

Common trap

Use the density of the displaced fluid and the displaced volume, not automatically the object’s total volume or density.

[ 1 ]

Show that $F_{\mathrm{b}}$ is about 2 mN .

Build the force model

Choose the system, draw a labelled free-body diagram, classify the interactions and resolve components. Apply Newton’s laws with the correct boundary: contact forces, field forces, friction, tension, buoyancy and restoring forces each have their own direction and conditions.

Track momentum

Use $ec p=m ec v$ , $ec J=\Delta ec p$ and momentum conservation only after checking external impulse. Distinguish elastic and inelastic collisions, explosions and energy transfer.

Track circular motion

The inward resultant provides $a_c=v^2/r=\omega^2r$ . It may come from tension, gravity, normal, friction or a field force. Angular and linear descriptions are linked by $v=\omega r=2\pi r/T$ .

Final checks

Ask: Which body is the system? Which forces are external? Is mass constant? Is acceleration uniform or radial? Is kinetic energy conserved, transferred or increased?

A.2.11—Buoyancy

Calculate Buoyant Force from Displaced Fluid

Retrieve the A.2 Forces and Momentum Model

A.2.11 Exam Analysis