Gravitation

Gravitation describes the fundamental force that causes objects to attract each other. Sir Isaac Newton introduced the Law of Universal Gravitation to explain this phenomenon. Gravitation is a key force that pulls two bodies toward one another, influencing the movement of celestial objects and objects on Earth.

Gravitation And Gravity

Gravitation-It is the force of attraction that exists between any two objects in the universe.

Gravity specifically refers to the force of attraction between Earth and other material objects. While gravitation is a universal concept, gravity is the localized effect of Earth's gravitational pull.

1.0Newton’s Universal Law of Gravitation

Newton’s Universal Law of Gravitation states that:

• Gravitational force(F) is directly equitable to the product of the masses of two objects (m1 and m2).
• It is inversely equitable to the square of the distance r between their centers.
• The formula for this law is $F=\frac{G{m}_1{m}_2}{r^2}$  where G is the Universal Gravitational Constant, approximately $6.673\times 10^{-11}N{m}^{2}K{g}^{-2}$
• This constant represents the force between two 1 kg masses separated by 1 meter.

2.0Characteristics of Gravitational Force

1. Universal Attraction: It acts between all objects with mass.
2. Line of Action: It acts along the line joining the centers of the masses.
3. Newton’s Third Law: The force is equal and opposite on both objects.
4. Inverse Square Law: The force decreases as the distance between objects increases.
5. Dependence on Mass: The force increases with greater mass.
6. Long Range: It has an effect over long distances.

3.0Importance of The Universal Law of Gravitation

• Anchors to Earth: It keeps us grounded on Earth.
• Planetary Orbits: Explains why planets orbit the Sun.
• Tides: Accounts for tides caused by the Moon and Sun.

4.0Free Fall(Motion Under Gravity) 

Free fall alludes to the motion of an object subjected only to the force of gravity. This occurs when an object drops from rest, or is thrown downward or upward. The equations of motion under gravity are:

• $v=u+at$
• $s=ut+\frac{1}{2}a{t}^2$
• $v^2=u^2+2as$

Where u is the initial velocity, v is the final velocity, aaa is acceleration (equal to g for free fall), s is displacement, and t is time.

5.0Acceleration Due To Gravity(g)

• It is the rate at which an object accelerates when in free fall due to Earth's gravitational pull. On Earth’s surface, this acceleration g is approximately $9.8\frac{m}{s^2}$
• $g=\frac{GM}{R^2}$
• Where G is the Universal Gravitational Constant, M is the mass of Earth, R is the radius of Earth.
• For Earth g=9.8m/s2

6.0Acceleration Due To Gravity On Earth’s Surface

$F_g=\frac{GMm}{r^2}$..............(1)

$F_g=ma$.................(2)

From equation (1) and (2)

$ma=\frac{GMm}{r^2}$

$a=\frac{GM}{r^2}$             (a=g)

$g=\frac{GM}{r^2}$

$g=\frac{(6.67\times 10^{-11})(6\times 10^{24})}{(6.4✕10^6{)}^2}=9.8m/s2$

7.0Mass And Weight

Mass-Mass: The amount of matter in an object. It is constant regardless of location and is measured in kilograms (kg) in the SI system. Mass is a scalar quantity and always positive.

Weight: The gravitational force exerted by Earth on an object. It varies with the local gravitational field and is measured in newtons (N). Weight is calculated using:

• W=mg (m-mass of an object, g=acceleration due to gravity)
• On the Moon, an object weighs about $\frac{1}{6}$ of its weight on Earth due to the Moon’s weaker gravity.

Thrust: Thrust is the force acting perpendicular to a surface. 

Pressure: Pressure is the thrust per unit area.

$Pressure=\frac{Force}{Area}=\frac{N}{m^2}=\text{Pascal(Pa)}$

For example, a 1 N force on 1 m² yields 1 Pa.

Fluids: Substances that flow and lack a fixed shape—exert pressure in all directions and this pressure depends on the height of the fluid column above.

Buoyancy: It is the upward force employed by a fluid, which makes objects appear lighter when submerged. According to Archimedes' Principle, the buoyant force equals the weight of the displaced fluid.

• $\text{Buoyant Force}=\text{Weight of fluid displaced}=m_{l}g$     ($m_l$=mass of liquid displaced, $v_l$=volume of liquid displaced)
• $m_l={\rho }_l\times v_l$
• $F_B={\rho }_l\times v_l\times g$

Apparent Weight: It is the weight of an object in air minus the buoyant force.

Apparent weight-Because an upward force acting on a body is engulfed in a fluid, either wholly or partially, there occurs an apparent loss in weight of the body. The net weight of an object engulfed in a fluid is called apparent weight.

$\text{Apparent Weight W’}=\text{Weight of body in air}-\text{Buoyant Force}$

• Density is mass per volume$\frac{Kg}{m^3}$
• Relative Density compares a substance’s density to water’s density at 4°C.