Chapter 9 – Gravitation -

Topics

1. Introduction
2. Electric Current
3. Free Fall
4. Motion of objects under Gravity
5. Mass and Weight
6. Thrust and Pressure
7. Buoyancy
8. Archimedes Principle
9. Relative Density

Introduction

If earth can attract an apple why not moon or other celestial bodies?If moon is attracted by earth why it does not fall towards it?
Why earth is not moving towards apple?

These are some questions which came to Newton when he saw an apple falling from a tree.

He conjectured that the nature of the force is same whether it is moon or earth, and earth attracts all bodies.

Now as force is there then why there is no acceleration? Well there is acceleration, called CENTRIPETAL acceleration and the force which causes this is termed as CENTRIPETAL FORCE, it acts towards center.

An object moving in a circle experiences centripetal force, it changes the direction of object at every moment.

These two points can explain the movement of planets around sun.

The motion of moon around the earth is due to centripetal force. The centripetal force is provided by the force of attraction of earth.

The earth is also attracted towards the apple by the same amount of force, in accordance with the Newton’s third law, but we cannot see it moving because acceleration is proportional to mass and mass of earth is very large in comparison to apple.

Universal law of Gravitation

Gravitational force is a UNIVERSAL FORCE; it applies to all bodies.

UNIVERSAL LAW OF GRAVITATION:

All objects attract all other objects.
The force of attraction is proportional to the sum of their masses, and inversely proportional to the square of the distance between them.

The force is along the line joining the centers of two objects.

Importance of universal law of Gravitation

The universal law of gravitation successfully explained several phenomena which were believed to be unconnected:

The force that binds us to the earth;
The motion of the moon around the earth;
The motion of planets around the Sun;
The tides due to the moon and the Sun.

Free Fall

When a body is under the influence of Gravitational force of earth only , then we say that body in under free fall. Practically it is possible under vacuum only as there is always some air resistance present.

The acceleration under free fall is called ‘acceleration due to gravity’ and denoted by “g”.

Earth is not a perfect sphere. As the radius of the earth increases from the poles to the equator, the value of g becomes greater at the poles than at the equator

Motion of objects under Gravity

We take value of g constant near earth. So equations for uniformly accelerated motion are applicable.

We have replaced “a” with “g” here. g = 9.8 m s^-2

The important point here is sign convention.
Value of g is positive if acceleration is in the direction of velocity and vice-versa.

Mass & Weight

Massis the measure of object’s inertia, more the mass more the inertia.

It is a property of material , so it does not change with place.
SI unit is ‘kg’.
It is a scalar quantity.

Weight of an object on earth is the force by which it is attracted towards earth.

As it is force so it has both magnitude and direction (i.e. downwards).
SI unit ‘N’.
W = mass x g.
g changes with location, so does weight.

Similarly weight of an object on moon is the force by which it is attracted towards moon.

Thrust & Pressure

Thrust: Force acting on an object perpendicular to the surface is called thrust.

SI unit is ‘N’.

Pressure: Thrust acting on a unit are is called pressure.

SI unit is ‘N m^-2’ or ‘Pa’ (Pascal)
Pressure = Thrust /Area
In both the cases thrust is same as the weight of your arm is same.
Pressure in first picture is more as the surface area is less than the surface area in second picture.
The same force acting on a smaller area exerts a larger pressure, and a smaller pressure on a larger area.
This is the reason why a nail has a pointed tip, knives have sharp edges and buildings have wide foundations.

Buoyancy

The upward force exerted by fluids (liquid and gas) on objects when they are immersed in them is called buoyant force and the phenomenon is called buoyancy.

Now to keep the object immersed we have to apply external force from upward direction to overcome buoyant force.