Gravitation and Properties of Gravitation

Introduction

     We have learnt that a force changes or tends to change the state of rest, speed or direction of motion of an object, i.e., the force produces an acceleration. In this chapter, we are going to identify one of the forces which produces acceleration in all objects on the surface of the Earth irrespective of their mass.

Force of Gravitation

     What do you observe when you drop a stone from a height? The stone which was initially at rest starts moving towards the ground and attains a maximum speed just before it touches the ground.

The Universal Law of Gravitation or Newton's Law of Gravitation

     Sir Issac Newton gave a mathematical relation to calculate the force of gravitation and this relation is known as the universal law of gravitation.

Dependence of Gravitational Force on Mass

     According to Newton's law of gravitation, the force of attraction is directly proportional to the mass of the body.

Gravitational Force between Two Light Objects

     Let us now calculate the force of gravitation existing between two unit masses separated by a unit distance.

Newton's Third Law of Motion and Force of Gravitation

     Is Newton's third law of motion applicable to gravitational force? Yes it is. Let us now see how Newton's third law of motion is applicable to the gravitational force existing between the various objects in the universe.

Falling Objects and Acceleration due to Gravity

     We know that whenever an object is dropped from a height, it falls towards the Earth. Similarly, when an object is projected vertically upwards, it goes up but after attaining a certain height, it starts falling down. It is the force of gravitation which pulls the object towards the Earth. The object, which is projected vertically upwards, is moving against the force of gravitation.

Expression for Acceleration due to Gravity

     Consider an object of mass m lying on or near the surface of the Earth. Let M_e be the mass of the Earth and R_e be its radius i.e., R_e is the distance between the object and the centre of the Earth.

Equations of Motion for a Body Moving under Gravity

     The motion of a body under gravity is a uniformly accelerated motion and hence all the equations of motion for uniformly accelerated motion in a straight line is applicable to the motion of bodies under gravity.

Acceleration due to Gravity on Moon

     The Earth's gravitational force causes an acceleration of 5 m/s2 in a 1kg mass somewhere in space.

Mass and Weight

     Mass and weight are commonly mistaken as the same, but they are two different quantities. Now let us try to find out the differences between them.

Weightlessness

     We often hear that an astronaut experiences weightlessness in space. What does this mean? Let us perform a simple experiment to demonstrate weightlessness.

Projectiles

     So far we have studied only the motion of an object under only one force. In this section we are going to study the motion of an object acted upon by two forces acting at right angles to each other. When an object is thrown horizontally from a certain height from the ground, then the object follows a curved path. An object thrown into space horizontally under the action of Earth's gravity is called a "Projectile".

An experiment to show that the vertical and horizontal motions of a body are independent of each other

     Place two coins A and B near the edge of a table as shown in the figure. Simultaneously drop the coin A vertically and flick the coin B horizontally. After a while we will hear just one clink, showing that both the coins reach the ground at the same time.