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The Universal Law of Gravitation
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Let's Start:
Good day, everyone. Today, we are going to discuss the concept of gravitation and their applications. Gravitation is the force of attraction between two bodies due to their masses. It is one of the fundamental forces of nature that governs the motion of celestial bodies as well as objects on Earth. In this chapter, we will explore the concept of gravitation, its effects, and various laws and formulas associated with it. This knowledge will help us understand the motion of planets, satellites, and objects falling under the influence of gravity.
The Universal Law of Gravitation
What's Gravitation:
The Universal Law Of Gravitation given by Sir Isaac Newton and formulated the law of gravitation in 1687.
According to this law, Every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Mathematical Formulation:
F = G m1 ×m2 / r²
Where:
- F = Gravitational force between two bodies (N),
- G = Universal gravitational constant 6.6743×10−11 N⋅m2/kg2,
- m1 and m2 = Masses of the two bodies (kg),
- r = Distance between the centers of the two masses (m).
Importance of the Universal Law of Gravitation:
The universal law of gravitation explains several phenomena in nature, such as:
- The force that binds us to the Earth.
- The motion of planets around the Sun.
- The motion of the Moon around the Earth.
- The formation of tides due to the gravitational pull of the Moon and Sun on Earth's water bodies.
Free Fall:
When an object falls towards the Earth due to the gravitational force only, it is said to be in free fall.
- During free fall, the only gravity force acting on the object, and (object) its motion is influenced by Earth's gravitational acceleration, denoted by g.
- Acceleration due to Gravity:
The acceleration experienced by a body during free fall due to Earth's gravity is called the acceleration due to gravity, denoted by g .
- The average value of g on Earth is 9.8 m/s².
Formula for g :
g = G M /R²
Where:
- M = Mass of Earth,
- R = Radius of Earth,
- G = Gravitational constant.
Motion of Objects under Gravity:
When objects are dropped or thrown, they move under the influence of gravity. The equations of motion can be applied to study their movement. For an object falling freely under gravity, the following equations of motion are used, replacing acceleration a with g .
1. v = u + gt
2. s = ut + 1/2gt²
3. v² = u² + 2gs
Where:
- ( v ) = Final velocity,
- ( u ) = Initial velocity,
- ( g ) = Acceleration due to gravity,
- ( t ) = Time,
- ( s ) = Displacement.
Mass and Weight:
Mass:
The mass of an object is the amount of matter contained in it.
It is a scalar quantity and remains constant everywhere in the universe.
The SI unit of mass is the kilogram (kg).
Weight:
The weight of an object is the force with which it is attracted towards the center of the Earth due to gravity.
weight is a vector quantity and changes depending on the location (e.g., on Earth, on the Moon, etc.).
Formula for Weight:
W = mg
Where:
- W = Weight (N),
- m = Mass (kg),
- g = Acceleration due to gravity 9.8m/s².
Note: Weight is dependent on the value of ( g ), which changes with altitude, depth, or location (e.g., it is lower on the Moon than on Earth).
Weight of an Object on the Moon:
- The value of g on the Moon is about 1/6th of its value on Earth.
- Hence, the weight of an object on the Moon is 1/6th of its weight on Earth.
- Formula:
W{Moon} = 1/6 W{Earth}
For example, if an object weighs 60 N on Earth, it will weighs 10 N on the Moon.
Thrust and Pressure:
Thrust:
- The force acting normally on a surface is called thrust.
- SI unit: Newton (N).
Pressure:
Pressure is defined as the thrust per unit area.
- Formula:
P = F / A
Where:
- P = Pressure (Pa or N/m²),
- F = Force or Thrust (N),
- A = Area (m²).
Archimedes’ Principle:
Archimedes' principle states that when an object is fully or partially immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by it.
Applications of Archimedes’ Principle:
- Designing ships and submarines.
- Hydrometers to measure the density of liquids.
- Floating of icebergs in the sea.
Relative Density:
Relative density is the ratio of the density of a substance to the density of water. It is a dimensionless quantity.
Formula:
Relative Density = Density of substance / Density of water
°In Shortly Ending:
Summary of Important Formulas
1. Gravitational Force:
F = G m1 × m2 / r²
2. Acceleration due to Gravity:
g = G M / R²
3. Weight of an Object:
W = mg
4. Pressure:
P = F /A
5. Archimedes’ Principle:
Buoyant Force = Weight of the fluid displaced
Thank you for your attention! Now let’s move on to the exercise questions to solidify our understanding.
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