The gravitational force of earth is called gravity.i.e., gravity is force by which earth pulls a body towards its centre. The acceleration produced in a body due to force of gravity is called acceleration due to gravity and its value is 9.8 m/s2. Gravity, also called gravitation, in mechanics, the universal force of attraction acting between all matter. On Earth all bodies have a weight, or downward force of gravity, proportional to their mass, which Earth’s mass exerts on them. Gravity is measured by the acceleration that it gives to freely falling objects.
NEWTON’S LAW OF GRAVITATION
|NEWTON’S LAW OF GRAVITATION|
The force of gravitational attraction between two point bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
i.e.,F = G ✕ m1m2/r2
where G is universal gravitational constant, it’s value is 6.67✕10-11 N-m2 kg-2
VARIATION IN GRAVITY (g)
Value of g decreases with height or depth from earth’s surface.
g is maximum at poles.
g is minimum at equator.
g decreases due to rotation of earth.
g decreases if angular speed of earth increases and increases, if angular speed of earth decreases.
Satellite are natural or artificial bodies revolving around a planet under its gravitational attraction.
Orbital speed of a satellite is independent of its mass and depends upon the radius of orbit.
The orbital speed of a satellite revolving near the surface of earth is 7.9 km/s.
Time period of revolution of satellite revolving near the surface of earth is 1 hr 24 min (84 min).
Period of revolution of a satellite depends upon the height of satellite from the surface of earth.
Every body inside the satellite is in a state of weightlessness.
Period of revolution of a satellite is independent of its mass.
If a satellite revolves in equatorial plane in the direction of earth’s rotation i.e., fro west to east with a period of revolution equal to time period of rotation of earth on its own axis i.e., 24 hours, then the satellite will appear stationary satellite.Such a satellite revolves around the earth at a height of 3600 km.
Polar satellite revolves around the earth in polar orbit at a height of 800 km. Time periods of the satellite is 84 min.
These are used for weather forecasting and mapping etc.
Escape velocity is that minimum velocity with which a body should be projected from the surface of earth, so as it goes out of gravitation field of earth and never return to earth.
Escape velocity at the earth surface is 11.2 km/s.
The escape velocity at moon surface is 2.4 km/s. So,there is no atmosphere.
The value of g on the moon is 1/6th of that on the earth.
MASS AND WEIGHT
The mass of a body is the quantity of matter contained in it.
It is scalar quantity and its SI unit is kg. Mass does not change from place to place and remains constant.
The weight of body is the force with which it is attracted towards the centre of the earth.
Weight of the body w = mg
Weight of a body is not constant it changes from place to place.
WEIGHT OF A BODY IN LIFT
If lift is stationary of moving with uniform speed (either upward or downward), the apparent weight of a body is equal to its true weight.
If lift is going up with acceleration, the apparent weight of a body is more than the true weight.
If lift is going down with acceleration, the apparent weight of a body is less than the true weight.
If the rod of the lift is broken, it fall freely.In this situation, the weight of a body in the lift become zero.This is the situation of weightlessness.
SIMPLE HARMONIC MOTION
If a particle repeats its motion about a fixed point after a regular time interval in such a way that at any moment the acceleration of the particle is directly proportional to its displacement from the fixed point at that moment and is always directed towards the fixed point than the motion of the particle is called simple harmonic motion.
When a particle executing SHM passes through the mean position
- no force acts on the particle.
- acceleration of the particle is zero.
- velocity is maximum.
- kinetic energy is maximum.
- potential energy is maximum.
When a particle executing SHM is at the extreme end,then
- acceleration of the particle is maximum.
- restoring force acting on particle is maximum.
- velocity of particle is zero.
- kinetic energy of particle is zero.
- potential energy is maximum.
A motion which repeats itself after equal intervals of time is called a periodic motion.
A motion in which an object moves back and forth repeatedly about a fixed position is called an oscillatory motion.
A simple pendulum consists of a small metal ball suspended by a long thread from a rigid support, such that the both is free to swing back and forth.
The distance of the pendulum from its mean position is called its displacement.
The maximum displacement of the pendulum on either side of its mean position is called the amplitude of oscillations.
Time period is the time taken by the pendulum to complete one full oscillation.
Frequency is the number of full oscillations completed by the pendulum in one second.
Second pendulum is one whose time period is 2 seconds.
Time period of simple pendulum T=2ℼ√L/g where L is length of thread.The time period of a simple pendulum of infinite length 84.6 min.A pendulum clock goes slow in summer and fast in winter.