Overview
This lecture covers the key principles of gravitation, including Newton's law of gravitation, acceleration due to gravity, differences between mass and weight, pressure, buoyant force, law of flotation, and Archimedes' principle, with example problems.
Universal Law of Gravitation
- Every two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance.
- The formula: ( F = G \frac{M_1 M_2}{R^2} ), where ( G ) is the universal gravitational constant.
- The value of ( G ) is ( 6.67 \times 10^{-11} ) Nm²/kg².
Acceleration Due to Gravity (g)
- ( g ) is found using the formula: ( g = \frac{GM}{R^2} ), where ( M ) is Earth's mass and ( R ) is Earth's radius.
- The standard value of ( g ) on Earth's surface is ( 9.8, \text{m/s}^2 ) (or 10 m/s² as an approximation).
- ( g ) decreases with increase in height or depth and varies with latitude (higher at poles, lower at equator).
Mass and Weight
- Mass is constant and a scalar (measured in kg), while weight is ( \text{mass} \times g ) and a vector (measured in Newtons).
- Mass does not change on the Moon, but weight does because the Moon's gravity is ( \frac{1}{6} ) of Earth's.
Thrust and Pressure
- Thrust is a force applied perpendicularly to a surface; its unit is Newton.
- Pressure is thrust per unit area (( P = \frac{F}{A} )), with the unit Pascal (Pa).
- Smaller area means higher pressure (e.g., sharp knife), and larger area means lower pressure (e.g., camel's feet).
Buoyant Force and Law of Flotation
- Buoyant force is the upward force a fluid exerts on an immersed object.
- Law of flotation: An object floats if its density is less than the fluid; it sinks if more; it is suspended if densities are equal.
Archimedes' Principle
- When an object is fully or partially immersed in a fluid, it experiences an upward force equal to the weight of the fluid displaced.
Key Example Problems
- When an object is dropped, use ( s = ut + \frac{1}{2}gt^2 ) (for gravity) with initial velocity ( u = 0 ).
- For a 2 kg ball dropped from 20 m: time to ground is 2 s; final velocity is 20 m/s; force on ball is 20 N.
- Weight on Moon: ( \text{Weight} = \text{mass} \times (\frac{g}{6}) ); for 60 kg mass, weight = 100 N.
Key Terms & Definitions
- Universal Gravitational Constant (G) — Constant of proportionality in universal gravitation, ( 6.67 \times 10^{-11} ) Nm²/kg².
- Acceleration due to Gravity (g) — Acceleration objects experience due to Earth's gravity, ( 9.8, \text{m/s}^2 ).
- Thrust — Perpendicular force applied to a surface.
- Pressure — Force per unit area, measured in Pascals (Pa).
- Buoyant Force — Upward force exerted by a fluid on an immersed object.
- Law of Flotation — Floating depends on density comparison between object and fluid.
- Archimedes' Principle — Upward buoyant force equals the weight of fluid displaced.
Action Items / Next Steps
- Review and memorize formulas for universal gravitation, gravity, pressure, and buoyancy.
- Practice solving gravitation and buoyancy problems using example methods provided.
- Prepare answers for conceptual questions on mass vs. weight, pressure, and flotation.
- Read next chapters: Work, Energy, and Sound.