Basics of Gravitation and Flotation

Overview

This lecture covers the basics of gravitation and flotation, including Newton's Universal Law of Gravitation, the concept of gravity versus gravitation, properties of gravitational force, acceleration due to gravity, motion equations under gravity, pressure in liquids, buoyancy, Archimedes’ principle, and relative density.

Universal Law of Gravitation

• Every mass attracts every other mass with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
• Mathematical formula: F = G * (m₁ * m₂) / r², where G is the Universal Gravitational Constant.
• G (Universal Gravitational Constant) = 6.67 × 10⁻¹¹ N·m²/kg², and it is the same everywhere in the universe.
• Gravitational force is always attractive, acts as an action-reaction pair, and does not depend on the medium, size, shape, or mass.

Gravity vs. Gravitation and Acceleration Due to Gravity

• Gravitation is the general force between any two bodies with mass.
• Gravity specifically refers to the attraction between planets/heavenly bodies and objects near them.
• Acceleration due to gravity (g) on Earth: g = G * (mass of Earth) / (radius of Earth)², approximately 9.8 m/s².
• Value of g varies with location: it’s higher at the poles (about 9.83 m/s²) and lower at the equator (about 9.78 m/s²).

Motion Under Gravity

• Equations for vertical motion:
  • v = u + gt
  • s = ut + ½gt²
  • v² = u² + 2gs
• For objects dropped (u = 0), these equations simplify for solving free fall problems.
• The value of g is used in place of general acceleration (a).

Properties and Applications of Gravitation

• Explains phenomena such as apples falling, moon's orbit, tides, satellite motion, and why we are anchored to Earth.
• Gravitational force is the weakest fundamental force but significant due to massive bodies like Earth.

Differences Between Mass and Weight

• Mass: amount of matter in a body, scalar, constant, measured in kilograms (kg), does not change with location.
• Weight: force exerted by gravity on a body, vector, varies with g, measured in Newtons (N), W = mg.

Pressure in Liquids and Buoyancy

• Thrust: force perpendicular to a surface.
• Pressure: thrust per unit area, P = F/A, measured in Pascals (Pa).
• Pressure in liquids acts equally in all directions at a given depth; increases with depth (P = ρgh).

Buoyancy and Archimedes’ Principle

• Buoyant force (upthrust): upward force exerted by fluid, F_b = ρ_fluid * V_submerged * g.
• Archimedes' Principle: a body immersed in a fluid experiences an upward force equal to the weight of the fluid displaced.
• Whether an object floats/sinks depends on the comparison between its density and the fluid’s density.

Relative Density & Floating/Sinking

• Relative Density (RD) = density of substance / density of water.
• If RD < 1, object floats; if RD > 1, object sinks.
• Ships float despite iron’s high density because of their shape and the volume of water they displace.

Key Terms & Definitions

• Gravitation — Force of attraction between any two masses.
• Gravity — Attraction between a planet (or similar body) and objects near it.
• Universal Gravitational Constant (G) — Constant of proportionality in Newton’s law, equal to 6.67 × 10⁻¹¹ N·m²/kg².
• Acceleration due to Gravity (g) — The acceleration experienced by an object due to gravitational pull near a planet’s surface.
• Thrust — Perpendicular force applied to a surface.
• Pressure — Force per unit area, measured in Pascals (Pa).
• Buoyant Force/Upthrust — Upward force exerted by a fluid on an immersed object.
• Archimedes’ Principle — Upward force on an immersed object equals the weight of fluid displaced.
• Relative Density (RD) — Ratio of the density of a substance to the density of water.

Action Items / Next Steps

• Review provided concept bites/video explanations for deeper understanding.
• Solve numerical questions on gravitation, motion, and flotation.
• Homework: Explain why ships made of iron float despite iron being denser than water.
• Watch for full chapter notes in your Telegram group.
• Prepare for the upcoming session focused on problem-solving.