Learning Objectives
- Understand Newton's Universal Law of Gravitation
- Distinguish between mass and weight
- Learn about free fall and acceleration due to gravity
- Understand thrust, pressure, and buoyancy
- Learn Archimedes' Principle and its applications
Key Concepts
Universal Law of Gravitation
Every object in the universe attracts every other object with a force that is:
- Directly proportional to the product of their masses
- Inversely proportional to the square of the distance between them
F = G × (m₁ × m₂) / d²
Where G = Universal Gravitational Constant = 6.674 × 10⁻¹¹ N·m²/kg²
G was experimentally determined by Henry Cavendish using a sensitive balance.
Acceleration Due to Gravity (g)
When an object falls freely towards the Earth, it accelerates due to gravitational force. This acceleration is called g.
g = GM/R² where M = mass of Earth, R = radius of Earth.
Value of g = 9.8 m/s² (approximately). The value of g decreases as we move away from the surface of the Earth or go deep inside it.
For free fall: u = 0 (if dropped), a = g = 9.8 m/s² (downward).
Mass and Weight
Mass: Amount of matter in an object. Constant everywhere. SI unit: kg. Scalar quantity.
Weight: Force of gravity on an object. W = mg. Varies with location (changes with g). SI unit: Newton (N). Vector quantity.
Weight on Moon = (1/6) × Weight on Earth (because g on Moon ≈ 1.63 m/s²).
Equations of Motion for Free Fall
Replace a with g in the standard equations:
- v = u + gt
- h = ut + (1/2)gt²
- v² = u² + 2gh
For falling objects, g is positive (+9.8 m/s²). For objects thrown upward, g is negative (-9.8 m/s²).
Thrust and Pressure
Thrust: The force acting perpendicular to a surface. SI unit: Newton.
Pressure = Thrust / Area. SI unit: Pascal (Pa) = N/m².
Same force exerts more pressure on a smaller area (e.g., sharp knife cuts better than blunt one).
Pressure in fluids: Fluids (liquids and gases) exert pressure equally in all directions.
Buoyancy and Archimedes' Principle
Buoyant Force (Upthrust): The upward force exerted by a fluid on an object immersed in it. It depends on the volume of the object submerged and the density of the fluid.
Archimedes' Principle: When an object is immersed in a fluid, it experiences an upward force equal to the weight of the fluid displaced by the object.
Floating condition: An object floats if its density is less than the density of the fluid.
Relative density = Density of substance / Density of water. It has no unit.
Summary
Gravitation is the universal force of attraction between all masses. The acceleration due to gravity (g) on Earth is approximately 9.8 m/s². Weight is the gravitational force on an object and varies with g. Pressure depends on force and area. Archimedes' Principle explains buoyancy — objects float when their density is less than the fluid's density.
Important Terms
- Gravitation: The force of attraction between any two masses in the universe
- g (Acceleration due to gravity): 9.8 m/s² on Earth's surface
- Weight: Gravitational force on an object, W = mg
- Pressure: Force per unit area, P = F/A
- Buoyant Force: Upward force on an object immersed in a fluid
- Relative Density: Ratio of density of a substance to density of water
Quick Revision
- F = Gm₁m₂/d²; G = 6.674 × 10⁻¹¹ N·m²/kg²
- g = GM/R² = 9.8 m/s² on Earth
- Weight = mg; weight varies with location, mass does not
- Pressure = Force / Area (Pa)
- Archimedes: buoyant force = weight of displaced fluid
- Object floats if its density < fluid density