8.3 Fluids and Newton's Laws

TLDR

In AP Physics 1, fluids follow Newton's laws because each particle accelerates when a net force acts on it, and the bulk motion you see is the sum of those particle interactions plus outside forces like gravity. The buoyant force is the net upward push a fluid exerts on an object, and it equals the weight of the fluid the object displaces: $F_b = \rho V g$.

Why This Matters for the AP Physics 1 Exam

This topic connects everything you learned about forces, free-body diagrams, and Newton's laws to substances that have no fixed shape. When you analyze a floating, sinking, or rising object, you are still doing dynamics: drawing forces, finding the net force, and applying $F_{net} = ma$. That makes this a strong place to show clear reasoning and correct vocabulary on free-response questions, where defending claims with evidence earns points. Buoyancy problems also show up as multiple-choice questions that test whether you can compare densities and predict floating versus sinking without heavy calculation.

Key Takeaways

• Fluid particles obey Newton's laws, so a net force on a particle causes acceleration just like with a solid.
• The large-scale behavior of a fluid (currents, flow, pressure patterns) comes from internal particle interactions combined with external forces like gravity.
• The buoyant force is a net upward force on an object in a fluid, caused by pressure increasing with depth.
• Buoyant force equals the weight of the fluid displaced: $F_b = \rho V g$, where $\rho$ is the fluid density and $V$ is the displaced volume.
• An object floats when its density is less than the fluid's density and sinks when it is greater.
• For a floating object, the buoyant force equals the object's weight, so $V_{submerged} / V = \rho_{object} / \rho_{fluid}$.

Fluid Velocity Changes

Newton's Laws in Fluids

Fluid particles follow the same rules of motion as solid objects. Each particle responds to a net force with an acceleration proportional to that force and inversely proportional to its mass.

• When a net force acts on a fluid particle, it accelerates according to $a = F_{net}/m$, just as with solids.
• The motion of any one particle is shaped by the surrounding particles and the fluid's properties.
• The combined behavior of huge numbers of particles creates the flow patterns you observe at the macroscopic scale.

Macroscopic Fluid Behavior

The bulk movement of a fluid emerges from many individual particle interactions, all following Newton's laws. This produces observable behavior like currents and flow around objects.

• Internal interactions between particles transmit forces through the fluid and affect its pressure and flow.
• External forces such as gravity and pressure differences set the fluid in motion or change its shape.
• Together, these explain why a fluid speeds up, slows down, or changes direction when forces act on it.

Buoyant Force

Upward Fluid Force

The buoyant force comes from the pressure difference between the top and bottom of an object in a fluid. Because pressure increases with depth ($P = P_0 + \rho g h$), the bottom of an object feels more pressure than the top.

• The buoyant force acts straight up on an object immersed in a fluid, opposing the object's weight.
• The greater pressure on the bottom surface produces a net upward force.
• You can feel this when you push a beach ball underwater and the water pushes back up.

Collective Particle Forces

The buoyant force you observe is really the sum of countless small forces from individual fluid particles pressing on the object's surface.

• Each particle exerts a force on the object's surface, and that force is larger where the pressure is larger (deeper down).
• Adding up all those particle forces over the whole surface gives the net buoyant force.
• This is why even oddly shaped objects experience a predictable buoyant force.

Displaced Fluid Weight

The magnitude of the buoyant force equals the weight of the fluid the object displaces.

$F_b = \rho V g$

• $F_b$ is the buoyant force.
• $\rho$ is the fluid density.
• $V$ is the volume of fluid displaced by the object.
• $g$ is the acceleration due to gravity.

When an object's density is less than the fluid's density, the buoyant force is greater than the object's weight and it floats. When the object's density is greater, the buoyant force is less than its weight and it sinks.

How to Use This on the AP Physics 1 Exam

Free Response

Treat a fluid problem like any other dynamics problem. Draw a free-body diagram for the object showing the buoyant force up and the weight down, plus any drag if the object is moving. Then apply $F_{net} = ma$. If the object floats or moves at constant velocity, set the net force to zero. Use precise words: do not say an object floats because it is "lighter," say its density is less than the fluid's density, or its weight is less than the maximum buoyant force available.

Problem Solving

For floating-object questions, the fastest path is the density ratio:

$\frac{V_{submerged}}{V} = \frac{\rho_{object}}{\rho_{fluid}}$

This comes from setting the buoyant force equal to the object's weight, $\rho_{fluid} V_{submerged} g = \rho_{object} V g$. The fraction above the surface is just one minus that ratio.

Common Trap

When something rises or sinks at constant speed, remember the net force is zero, not the buoyant force. A rising air bubble, for example, has buoyant force up balanced by weight and drag down, so $F_b = F_g + F_d$.

Practice Problem 1: Newton's Laws in Fluids

Solution:

The forces acting on the bubble are:

1. Buoyant force ($F_b$) acting upward
2. Weight of the air bubble ($F_g$) acting downward
3. Drag force ($F_d$) acting downward as the bubble rises

Since the bubble moves at constant velocity, the net force must be zero according to Newton's First Law: $F_b - F_g - F_d = 0$

$F_b = F_g + F_d$

The buoyant force equals the weight of the displaced water: $F_b = \rho_{water} V_{bubble} g$

The weight of the air bubble is negligible compared to the buoyant force since $\rho_{air} \ll \rho_{water}$.

Therefore, the buoyant force is primarily balanced by the drag force: $F_b \approx F_d$.

The bubble reaches terminal velocity because as it speeds up, the drag force increases until it balances the buoyant force, giving zero net force and constant velocity.

Practice Problem 2: Buoyant Force

Solution:

Part 1: Block in water

The volume of the block is $V = 10 \text{ cm} \times 8 \text{ cm} \times 6 \text{ cm} = 480 \text{ cm}^3 = 4.8 \times 10^{-4} \text{ m}^3$.

The mass of the block is $m = \rho V = 650 \text{ kg/m}^3 \times 4.8 \times 10^{-4} \text{ m}^3 = 0.312 \text{ kg}$.

For a floating object, the buoyant force equals the weight of the object: $F_b = mg$

The buoyant force also equals the weight of displaced fluid: $F_b = \rho_{water} V_{submerged} g$

Setting these equal and substituting $m = \rho_{block} V$: $\rho_{water} V_{submerged} g = \rho_{block} V g$

Simplifying: $\frac{V_{submerged}}{V} = \frac{\rho_{block}}{\rho_{water}} = \frac{650 \text{ kg/m}^3}{1000 \text{ kg/m}^3} = 0.65$

So 65% of the block is submerged, meaning 35% remains above water.

Part 2: Block in olive oil

Using the same equation: $\frac{V_{submerged}}{V} = \frac{\rho_{block}}{\rho_{oil}} = \frac{650 \text{ kg/m}^3}{920 \text{ kg/m}^3} = 0.707$

So 70.7% of the block is submerged in olive oil, meaning 29.3% remains above the surface.

Practice Problem 3: Fluid Velocity Changes and Newton's Laws

Solution:

The fluid's velocity changes because a net external force acts on the fluid when the container pushes on it. By Newton's second law, fluid particles accelerate when there is a net force. The macroscopic motion of the water results from the motion of many individual particles. Internal interactions between particles transmit forces through the fluid, while the external force from the container causes the fluid as a whole to change velocity.

Common Misconceptions

• "Objects float because they are lighter and sink because they are heavier." What matters is density compared to the fluid, not weight alone. A heavy ship floats because its average density is less than water's.
• "The buoyant force depends on how deep the object is." For a fully submerged object, the buoyant force depends on the displaced volume and the fluid density, not on depth. Pressure increases with depth, but the pressure difference across the object stays the same.
• "Buoyant force equals the object's weight in every case." That is only true when the object floats or is in equilibrium. A sinking object has a buoyant force smaller than its weight.
• "Constant velocity means no buoyant force." Constant velocity means zero net force. The buoyant force is still there, balanced by weight and drag.
• "Buoyant force equals the weight of the whole object's volume of fluid." It equals the weight of the fluid actually displaced. For a floating object, only the submerged part displaces fluid.

Related AP Physics 1 Guides

• 8.1 Internal Structure and Density
• 8.2 Pressure
• 8.4 Fluids and Conservation Laws