INTRO- GRAVITATION –Gravitation is a natural phenomenon by which every object in the universe attracts every other object with a force that acts along the line joining their centres. -This force of mutual attraction between two masses is called the gravitational force. -Everybody that has mass exerts an attractive force on every other body in the universe. -The magnitude of this force depends on: #The greater the masses, the stronger the attraction; the larger the distance, the weaker the force. -The idea of gravitation was explained by Sir Isaac Newton in 1687. (He discovered that the same force that causes an apple to fall to the ground also holds the Moon in orbit around the Earth and the planets in orbit around the Sun. This inspired him to create the Universal Law of Gravitation, which mathematically defines the force.) *Nature of the Gravitational Force Property Description Type of Force Non-contact (acts without physical contact) Direction Always acts along the line joining the centres of two bodies Nature Always attractive, never repulsive Range Infinite (though becomes very weak with distance) Strength Weak compared to other fundamental forces (e.g., electromagnetic) *Difference Between Gravitation and Gravity Basis Gravitation Gravity Definition The universal force of attraction between any two bodies in the universe. The gravitational force specifically exerted by the Earth on objects near its surface. Scope Universal – acts between any two masses. Local – acts only near the Earth. Example Attraction between the Sun and Earth. Attraction between Earth and an apple. Newton’s Universal Law of Gravitation Newton’s Universal law of gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. Let two objects of masses m1 and m2 be separated by a distance . Then, according to Newton’s law, To remove proportionality, a constant G (the universal gravitational constant) is introduced: Where, G = 6.67×10-11 Nm2/kg2 *Relation between Newton’s third law of motion and Newton’s law of gravitation -Newton’s third law of motion: According to Newton’s third law of motion, “Every object exerts equal and opposite force on other object but in opposite direction.” –Newton’s law of gravitation: According to Newton’s law of gravitation, “Every mass in the universe attracts every other mass.” In case of freely falling stone and earth, stone is attracted towards earth means earth attracts the stone. But according to Newton’s third law of motion, the stone should also attract the earth.It is true that stone also attracts the earth with the same force F = m × a but due to very less mass of the stone, the acceleration (a) in its velocity is 9.8 m/s2 and acceleration (a) of earth towards stone is 1.65×10-24 m/s2 which is negligible and we cannot feel it. *Importance of Universal Law of Gravitation FREE FALL OF AN OBJECT AND ACCELERATION DUE TO GRAVITY Free fall is the motion of a body when it falls towards the Earth under the influence of gravitational force only, with no other force (like air resistance) acting on it. When an object is thrown upward, it reaches certain height, then it starts falling down towards earth. It is because the earth’s gravitational force exerts on it. This fall under the influence of earth is called ‘free fall of an object’. During this free fall direction do not change but velocity continuously changes which is called acceleration due to gravity. It is denoted by ‘g’. Its unit is same as acceleration m/s2. *Derivation for Acceleration Due to Gravity From Newton’s law of gravitation: According to Newton’s second law of motion: For a freely falling body: Equating both forces: Cancelling m from both sides: Formula: *The Value of acceleration due to gravity (g) where, *Difference Between Gravitational constant (G) and Acceleration due to gravity (g) Basis of Difference Universal Gravitational Constant (G) Acceleration Due to Gravity (g) 1. Definition It is a constant that measures the strength of the gravitational force between any two bodies in the universe. It is the acceleration produced in a body when it falls freely under the influence of Earth’s gravity. 2. Formula 3. Nature It is a universal constant, same everywhere in the universe. It varies from place to place (depends on height, depth, and latitude). 4. Value G= 6.67×10-11 5. Depends On It does not depend on mass, distance, or location. It depends on the mass and radius of the Earth. 6. Type of Quantity Scalar quantity (has only magnitude). Vector quantity (has magnitude and direction — toward Earth’s center). 7. Symbol G g 8. Unit N·m²/kg² m/s² 9. Discovery Discovered by Sir Isaac Newton. Measured experimentally on Earth. 10. Variation Remains constant throughout the universe. Decreases with altitude and depth; increases at poles. *Equations of Motion for a Freely Falling Body The same kinematic equations apply, replacing a by g: #For Object Falling Downward #For Object Thrown Upward *Factors Affecting the Value of g MASS AND WEIGHT *MASS *WEIGHT *Difference Between Mass and Weight Basis Mass Weight Definition Amount of matter contained in a body. Force with which Earth attracts a body towards its center. Formula m=w/g W = mg Nature Scalar quantity. Vector quantity (acts downward). Unit (SI) Kilogram (kg). Newton (N). Value Constant everywhere. Varies from place to place (depends on (g)). Measuring Instrument Beam balance. Spring balance. Zero Condition Never zero (matter cannot vanish). Becomes zero where (g = 0) (e.g., space). On Moon Same as on Earth. 1/6 of weight on Earth. THRUST AND PRESSURE When a force acts perpendicularly on a surface, it creates an effect known as thrust.The effect of thrust per unit area on a surface is called pressure. *Thrust *Pressure *Examples of Pressure BUYONCY The upward force exerted by a liquid (or fluid) on an object when it is partially or completely immersed in it is called buoyant force, and the property of a fluid to exert this upward force is called buoyancy. It…
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