Unit 8: Fluids

Introduction

Fluids obey Newton’s Laws of Motion, just like solid objects. In this section, we analyze how forces cause fluids to accelerate, how buoyancy works, and how forces in fluids affect motion.

Key Concepts

• Newton's Second Law in Fluids: \[ F_{\text{net}} = m a \] This applies to objects moving through fluids, such as sinking or floating objects.
• Buoyant Force: The upward force exerted by a fluid on a submerged object: \[ F_B = \rho_{\text{fluid}} g V_{\text{submerged}} \] where:
  • ρ = fluid density (kg/m³)
  • g = acceleration due to gravity (9.81 m/s²)
  • V_submerged = volume of fluid displaced (m³)
• Archimedes' Principle: The buoyant force on an object is equal to the weight of the fluid displaced: \[ F_B = W_{\text{fluid displaced}} \]
• Equilibrium Conditions:
  • If F_B = mg, the object floats.
  • If F_B < mg, the object sinks.
  • If F_B > mg, the object rises.
• Drag Force: A resistive force acting against the motion of an object in a fluid: \[ F_D = \frac{1}{2} C_D \rho A v^2 \] where C_D is the drag coefficient, A is the cross-sectional area, and v is velocity.

Mathematical Routines

• Use F_B = ρ g V to calculate buoyant force.
• Apply ΣF = ma to analyze forces on floating and sinking objects.
• Use the drag force equation to determine resistive forces in moving fluids.

Creating Representations

• Diagrams: Draw force diagrams for floating and sinking objects.
• Graphs: Plot buoyant force vs. depth to understand equilibrium.

Scientific Questioning & Argumentation

• Why does an object weigh less in water than in air?
• How does drag force affect the terminal velocity of a falling object?

Use Newton’s Laws and force diagrams to support your answers.

Practice Activities

Summary & Exam Preparation Tips

• Newton’s Laws apply to fluids, affecting buoyancy, drag, and fluid motion.
• Archimedes’ Principle explains floating and sinking.
• Buoyant force is equal to the weight of displaced fluid.
• Drag force increases with velocity and surface area.