Class 9 Science Chapter 10 Gravitation

 📝Class 9 Science Chapter 10 Gravitation

Introduction 

A force is needed to change the speed or the direction of motion of an object. We always observe that an object dropped from a height falls towards the earth. We know that all the planets go around the Sun. The moon goes around the earth. In all these cases, there must be some force acting on the objects, the planets, and on the moon. Isaac Newton could grasp that the same force is responsible for all these. This force is called the gravitational force

Gravitation

Issac Newton 

Source: https://en.wikipedia.org/wiki/Isaac_Newton

We know that the moon goes around the earth. An object when thrown upwards, reaches a certain height and then falls downwards. Newton thought that: if the earth can attract an apple, can it not attract the moon?  Isaac Newton conjectured that the same type of force is responsible in both cases. He argued that at each point of its orbit, the moon falls towards the earth, instead of going off in a straight line.

Activity

●Take a piece of thread.

● Tie a small stone at one end. Hold the other end of the thread and whirl it round, as shown in Fig. 

● Note the motion of the stone.

● Release the thread.

● Again, note the direction of motion of the stone

Before the thread is released, the stone moves in a circular path with a certain speed and changes direction at every point. The change in direction involves a change in velocity or acceleration. The force that causes this acceleration and keeps the body moving along the circular path is acting towards the centre. This force is called the centripetal (meaning ‘center seeking) force. In the absence of this force, the stone flies off along a straight line. This straight line will be a tangent to the circular path.

The motion of the moon around the earth is due to the centripetal force. The centripetal force is provided by the force of attraction of the earth. If there were no such force, the moon would pursue a uniform straight-line motion.

👉 Centripetal force is a force that acts on an object moving in a circular path, always directed towards the center of the circle. It is responsible for keeping the object moving in a curved path and preventing it from moving in a straight line tangent to the circle.

Every Object in the Universe Attracts Every Other Object

According to Newton every object in this universe attracts every other object with a certain force. The force with which two objects attract each other is called gravitational force. 

➤ If the masses of the object are small, then the gravitational force between them is very small ( which cannot be detected easily). 

➤ If however one of the objects is very big (having a large mass), then the gravitational force becomes very large (its effect can be detected easily). 

UNIVERSAL LAW OF GRAVITATION

Every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centres of two objects.

The gravitational force between two objects is directed along the line joining their centres.

Let two objects A and B of masses M and m lie at a distance d from each other as shown in Fig. Let the force of attraction between two objects be F. According to the universal law of gravitation, the force between two objects is directly proportional to the product of their masses. That is,

`F propto M× m`.........(i)

And the force between two objects is inversely proportional to the square of the distance between them, that is,

`F  propto 1/d^2`..........(ii)

Combining Eqs. (i) & (ii), we get

`F  propto  frac{M× m}{d^2}`

`F  = Gfrac{M× m}{d^2}`

where G is the constant of proportionality and is called the universal gravitation constant. By multiplying crosswise,  gives 

`F × d ^2 = G  M × m`

or, `G = frac{Fd^2}{M×m}` 

The SI unit of G can be obtained by substituting the units of force, distance, and mass, as `N m^2 kg^{–2}`. The value of G was found out by Henry Cavendish (1731 – 1810) by using a sensitive balance. The accepted value of G is `6.673 × 10^{–11} N m^2 kg^{–2}`.

Inverse-square

Saying that `F` is inversely proportional to the square of d means, for example, that if `d` gets bigger by a factor of 6, `F` becomes `1/36` times smaller.

Importance of the universal law of gravity 

The universal law of gravitation successfully explained several phenomena 

(i) the force that binds us to the earth

(ii) the motion of the moon around the earth

(iii) the motion of planets around the Sun

(iv) the tides due to the moon and the Sun.

Acceleration due to Gravity

If you drop a ball from a height, it falls. As time passes its speed increases. The velocity of the ball changes, i.e, the ball is accelerated. 

Let an object of mass `m` moving freely near the earth's surface. Neglecting air resistance, the only force on it is due to gravity.

`F = frac{GM_em}{R_e^2}`

Where `M_e` = mass of the earth = `6× 10^24` kg

`m` = mass of the object

`R_e` = radius of the earth = 6400 km

Its acceleration is 

`a = F/m = frac{GM_e}{R_e^2}`

Note, that this acceleration does not depend on the mass of the object. 

If gravity is the only force (meaning that air resistance is neglected), all objects move with the same acceleration near the earth's surface. This acceleration is called the acceleration due to gravity, whose magnitude `'g'` is given by 

                                                       `g = frac{GM_e}{R_e^2}`

`approx  9.8 ms^{-2}`

Thrust & Pressure 

The force acting on an object perpendicular to the surface is called thrust.

The thrust on unit area is called pressure. Thus, 

Pressure = Thrust/Area 

Substituting the SI unit of thrust and area in Eq., we get the SI unit of pressure as `N/m^2` or `N m^-2`.

In honour of scientist Blaise Pascal, the SI unit of pressure is called pascal, denoted as Pa.

👉  The same force acting on a smaller area exerts a larger pressure, and a smaller pressure on a larger area. 

 Archimedes’ Principle

When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.

Density 

The density of a substance is defined as mass of a unit volume.

The unit of density is `kg m^-1`

Density = mass/volume 

Relative Density

The relative density of a substance is the ratio of its density to that of water:

Since the relative density is a ratio of similar quantities, it has no unit. 

References:

1. https://en.wikipedia.org/wiki/Isaac_Newton