\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

Buoyancy

The force of buoyancy on an object is $$\vec B=\rho_fgV_{sub}\uparrow$$

• $\rho_f$ 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.