Lecture Notes - Gravity, Buoyancy, and Fluid Mechanics

Announcements

• Homework for Chapter 13 is due soon, possibly by Wednesday.
• Chapter 14 material will be on the final, but no homework turn-in required.
• Focus on understanding materials in Chapters 13 and 14 for final exam preparation.

Chapter 13: Newton’s Law of Universal Gravitation

• Key concept: Two masses attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

F_g = G * (m1 * m2) / r²

• Calculated orbital velocity using centripetal force principles.
• Gravitational potential energy at large distances:

U_g = -G * (m1 * m2) / r

• Potential Energy derivation: Recognizing that the force of gravity changes with position.
• Escape Velocity: Minimum speed required for an object to escape Earth’s gravitational influence.

v_esc = sqrt(2 * G * M / R)

Chapter 14: Fluid Mechanics

• Fluid mechanics: first dealing with fluids, requires differential equations for complexity but basic principles can be demonstrated.
• Properties: Density (ρ) and Pressure (P)

ρ = mass/volume
P = force/area

• Pressure in a fluid increases with depth.

P = P₀ + ρgh

• Archimedes’ Principle: A body submerged in a fluid experiences a buoyant force equal to the weight of the displaced fluid.
  • Buoyant Force (B) calculation:

B = ρ_fluid * V_displaced * g

Demonstrations and Lab Experiment Overview

• Observing buoyant forces with different materials and fluids.
  • Weight measurements in air vs. submerged in fluid to observe changes due to buoyant force.
  • Importance of understanding density differences across materials and fluids.
  • Real-life applications: Understanding why objects float or sink based on density comparison.
  • Examples with wood (floats) and metals (sink) to demonstrate principle.

Ideal Gas and Pressure Examples

• Understanding pressure changes with examples such as air-filled balloons and diving experiences.

Practical Applications Discussed

• Rock and scales demonstration to differentiate actual weight from perceived weight on a scale.
• Discussion on space missions, escape velocities of different planets (Mars vs Earth), and implications for launching and returning from other celestial bodies.
• Historical reference to fluid buoyancy principles such as the behavior of objects in various states of liquids.

Lab Exercises

• Oil cans and soda cans illustrating density differences and buoyancy.
• Explaining why regular soda sinks due to higher density while diet soda floats due to lower density.
• The importance of checking for air-filled cavities in objects for accurate measurements of buoyancy force.