Topic 8.3 Fluids and Newton's Laws: apply Newton's laws and Archimedes' principle to objects in fluids, including the buoyant force and floating versus sinking.

What this topic is asking

The College Board (Topic 8.3) wants you to apply Newton's laws and Archimedes' principle to objects in fluids: the buoyant force $F_b = \rho V g$, the float-versus-sink condition, and using $F_{net} = ma$ on a submerged object. This ties the pressure of Topic 8.2 to the force analysis of Unit 2.

The buoyant force and Archimedes' principle

The buoyant force is a direct consequence of the pressure-depth relation from Topic 8.2. Because pressure increases with depth, the fluid pushes up on the bottom face of an object with more force than it pushes down on the top face, and the net upward result is the buoyant force. Archimedes' principle packages this neatly: the upward force equals the weight of the displaced fluid, $\rho_{fluid} V g$. Note that it is the fluid's density that appears, not the object's.

Applying Newton's second law in a fluid

This is where the fluids unit meets the dynamics of Unit 2. A fully submerged object experiences two vertical forces, weight and buoyancy, and Newton's second law settles the outcome. Factoring out $Vg$ shows that whether it sinks or rises depends only on which density is larger, which is why a steel cube sinks and a cork rises. The acceleration follows from $F_{net}/m$, with $m = \rho_{object}V$.

Floating, sinking and apparent weight

When an object floats in equilibrium, Newton's first law requires the buoyant force to equal the weight, so it is no longer fully submerged: it sinks only until the displaced fluid's weight matches its own. Setting $\rho_{object} V g = \rho_{fluid} V_{sub} g$ gives the submerged fraction $\dfrac{V_{sub}}{V} = \dfrac{\rho_{object}}{\rho_{fluid}}$. An iceberg ($\rho \approx 920$ kg/m cubed) floating in seawater ($\rho \approx 1025$ kg/m cubed) sits with about $90\%$ of its volume below the surface, the classic illustration. For a fully submerged object held by a string or scale, the apparent weight is the true weight minus the buoyant force, which is why objects feel lighter underwater. The strategic insight running through the topic is that buoyancy is not a new fundamental force but a consequence of pressure increasing with depth, and that every fluids force problem reduces to a familiar free-body diagram with weight and buoyancy, solved by Newton's laws exactly as in Unit 2. Recognizing that density comparison decides floating, and that the displaced-fluid weight gives the buoyant force, connects Topics 8.1, 8.2 and 8.3 into a single coherent method.

Try this

Q1. A block of volume $1.0 \times 10^{-3}$ m cubed is fully submerged in water (density $1000$ kg/m cubed, $g = 9.8$). Calculate the buoyant force. [2 points]

• Cue. $F_b = \rho V g = (1000)(1.0 \times 10^{-3})(9.8) = 9.8$ N.

Q2. An object has density $800$ kg/m cubed and floats in water ($1000$ kg/m cubed). State the fraction submerged. [1 point]

• Cue. $\rho_{object}/\rho_{fluid} = 800/1000 = 0.80$, so $80\%$ is submerged.