Why Do Things Float?

Introduction

• Revisiting Newton's laws and free body diagrams (normal force, friction, tension, etc.)
• Introduction of a new force: buoyant force

Buoyant Force

• The buoyant force is equal to the weight of the displaced fluid
• Weight = mass (m) * gravity (g)
• Density (ρ) = mass/volume, so weight can be expressed as ρ * volume (V) * g*

Example: Boat in Water

• Boat partially submerged in water
• Upward force on the boat = weight of the displaced water

Example: Rock in Water

• Rock above water: no buoyant force
• Rock in water: buoyant force = weight of the water displaced by the rock
• Buoyant force is independent of whether the object floats or sinks

Misconceptions to Avoid

• Buoyant force is based on the weight of the displaced fluid, not the weight of the object
• Common mistake: using the weight of the object instead (especially in late-night homework sessions)

Free Body Diagram Example

• Given: Water, a cube attached to a spring
• Forces: Spring force, gravity, and buoyant force

Calculations

• Volume of the cube: 0.2 m^3
• Density of water: 1000 kg/m^3 (1 g/cm^3)
• Gravity: 9.8 m/s^2
• Buoyant force: 0.2 m^3 * 1000 kg/m^3 * 9.8 m/s^2 = 78.4 N

Solving for Spring Stretch

• Free body equation: -784 N + 78.4 N + k * Δx = 0 (k is the spring constant)
• Solve for Δx (spring stretch)*

Variations of the Problem

• Different scenarios: part of the cube out of water, entire beach ball submerged
• Adjust buoyant force calculation based on the submerged volume

Additional Considerations

• Effect of pressure differences for large objects (not covered in simple problems)
• Negligible mass of beach balls and similar objects

Final Example

• Beach ball tied at the bottom of a lake
• Neglect mass of the beach ball, focus on the buoyant force
• Use volume of a sphere: V = 4/3 * π * r^3

Summary

• Buoyant force is crucial for understanding objects in fluids
• Always base calculations on the weight of the displaced fluid, not the object's weight
• Free body diagrams and proper unit conversions are essential for solving related problems