$$ $$ $$ $$ $$ $$ $$ $$ $$ $\text{Extra close brace or missing open brace}$ $\text{Extra close brace or missing open brace}$ $$

Buoyancy

The force of buoyancy on an object is $$\overrightarrow{B}={\rho }_{f}g{V}_{sub}\uparrow$$

• ${\rho }_f$ is the density of the fluid, not of the object
• $V_{sub}$ (or $V_{uw}$) is the volume of the object that is under the surface of the water. Another way of thinking about it is that $V_{sub}$ is the volume of the water that had to be moved out of the way to put the object there. If the object is completely submerged, then $V_{sub}$ is simply the volume of the object.
• You can use buoyancy as just another force.