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2.8 Gravity

Gravitational Force

Sir Isaac Newton said that every mass in universe attracts every other mass with a gravitational force. The magnitude of the force is big if one of the object is massive  and the distance between them is small. Both objects pulls on each other with the same gravitational force even one of the objects is tiny and the other massive, like and apple and the earth.

According to Newton , all objects are pulled by this force which causes them to fall to the surface of earth.

This force which originates from the centre of the Earth pulls all objects towards the ground.

 

Gravitational Field

 

Gravitational field is a region in which an on objects experiences a force due to gravity.

The earth’s gravitational field extends out into space , in all directions. This field gets weaker the further you go out from the centre of the Earth.

 

Gravitational field  strength , g

 

The gravitational field  strength , g  is defined as force per unit m.

                                    g  =  F

                                            m

The unit of the gravitational field  strength , g is N kg-1

The gravitational field strength , g of the Earth is 9.8 N kg-1 .

The gravitational field  strength , g of the Moon is only 1.6 N kg-1  because the mass of the Moon is about one-eightieth that of the Earth’s.

 

Acceleration due to gravity, g

 

From the definition of the gravitational field  strength,

g  =  F    …………………(1)

                                              m

According to Newton’s second law of motion,

                                                                F = ma   ………………….(2)

 Substituting for F ,

                                a = g = 9.8 ms-2

 

So, the acceleration due to gravity , g , is equal to 9.8 ms-2 for Earth.

All objects on the Earth fall with the same acceleration due to gravity regardless of their size or mass.

Free fall

An object falls with an acceleration due to gravity, g is said to be free falling.

This happen when the object falls without encountering any resistance.

The following graph shows he graph velocity against time of any free-falling object  :

clip_image002

The gradient of the graph is 9.8 ms-2

 

From the equation  s = ut + ½ at2  ,

 

                 Thus we know that   u = o  ,  a = g

                           

From   s  = ½ gt2   so the t will be

clip_image002

 

These means that the time for free fall will depend upon

(i)            height from where the object is let go off

(ii)           the value of the acceleration due gravity

 

The free fall time does not depend on

(i)            the mass of the object

(ii)           the shape of the path (straight line or parabola)

 

 

Example 1

 

A man release a stone into a well. If the distance between the top of the well and the water surface is 30 m , what is the time taken for the stone to reach the surface of the water.

 

 Solution

 

 

                               

 

Example  2

 

clip_image007

A trolley moving with a uniform velocity of  5 ms-1 on a table . The height  of the table is 1.25 m.

Calculate

(a)           time taken to reach the floor

 

(b)           the value of  x

 

Solution

 

 

Weight,(W)

The weight , W of an object is the gravitational force exerted on it .

From F = ma       ,  a = g                

Hence  W = mg

The S.I. units of weight is Newton (N)

Example 3

 

An astronaut who landed on the moon brought back a stone. On the Moon’s surface, the stone had a weight of 8.0 N . On weighing the stone on Earth , a weight of 50 N is recorded.

( acceleration due to gravity for Earth is 9.81 ms-2)

Calculate ,

(a)           the mass of the stone on Earth

(b)           acceleration due to gravity for  Moon

 

Solution:

 

 

 

 

The difference between mass and weigh

Mass

Weight

Is the quantity of matter in an object

Is the gravitational force

The S.I units is Kilogram

The S.I. units is  Newton

A base quantity

A derived quantity

A scalar quantity

A vector quantity

Measured with an inertial balance or  a chemical balance

Measured with a spring balance

Is fixed at all places

Varies from place to place

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