Presented By:-Name – Akshat Saxena

What is Force? Who discovered Gravitational law? Discovery of Gravitational Force. Calculation used by Newton. Calculating the constant. Gravity- A special Case. Effect of Gravity and its Uses.

Sir Issac newton gave many laws of nature.In his First law of motion, he described the

inherent property of matters,qualitatively.In his second law,he wrote “A force action on a

body gives it an accelaration which is in the direction of force and has a magnitude given by ma.”

So,it describes force quantitatively also.In his third law,he describes how force are exerted.Therefore,we can say he discovered “Force”.

The force is an external effort(cause) in the form of a push or pull which either changes or tends to change the state of rest or the uniform motion of a body along a straight line.

They are classified into two categories:- (i) Contact Force. - Frictional force, normal reaction,tensile force etc.(ii) Non-Contact Force. - electric,magnetic,gravitational force.

Sir Isaac Newton (1642-1727) Perhaps the greatest genius of all time Invented the reflecting telescope Invented calculus Connected gravity and planetary forces Philosophiae naturalis principia mathematica

In 1665, Issac Newton performed brilliant theoretical and experimental tasks in mechanics and optics.

In this year, he focused his attention on the motion of the moon about the earth.

While doing so, he had a question that what is the force that makes moon to revolve.

He had data that moon revolves round the earth in 27.3 days.

Its distance from earth is R = 3.85 105 km. The acceleration of moon is ,therefore, α = ω2R α = 2π 2 × R ( velocity =

disp. ) T

time = 4π2 ×(3.85 ×105 km) (27.3 days)2

Displacement and time were converted into SI units. He had a belief that earth is making the moon

to revolve.But How?

= 0.0027 m/s2

Newton was sitting under an apple tree when an apple fell down from the tree on the earth. This sparked the idea that the earth attracts all bodies towards its centre.He declared that the laws of nature are same for earthly and celestial bodies.

The acceleration of a body falling near the earth’s surface is about 9.8 m/s2 and moon’s acceleration is 0.0027m/s2 .Thus,

aapple amoon

=9.8 m/s2

0.0027 m/s2

Also,

distance of the moon from the earthdistance of the apple from the earth

dmoon

dapple

3.85 105 km

6400 km

= 3600. ....(i)

aapple amoon

= dmoon

dapple

2

= == 60 ….(ii)

By comparing (i)&(ii)

Newton guessed that, acceleration a 1 r2

…..(1) He had, F ma ; (Newton’s second law) …..

(2) . ˙ . F m . ( From (1) ) r2 …..(3)By Newton’s Third law of motion, F M

…..(4)Combining 3 & 4, F Mm r2

F = GMm r2

where,– F = Force of attraction between the two particles.– M = mass of first particle.– m = mass of second particle. – r = distance between the centers of the first and second

particle.– G = Universal gravitational constant. = 6.67 10-11

N·m2/kg

Dimensional formula of F is [MLT-2 ]S.I. Unit = N (Newton)C.G.S. Unit = dyne

m1 m2

ř12 ř21

r

F12 = - Gm2m1

r2

F21 = - Gm1m2 r2

ř21

ř12

Note : -(minus) sign denotes that opposite direction of force and Distance.

Always acts as “Force of Attraction”. Form an action-reaction pair. Central Forces. Independent of the presence of other bodies

and properties of the intervening medium. Weakest Force.

The force of attraction between any two material particles is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. It acts along the line joining the two particles.

i.e, F Mm r2

First measurement was done by Cavendish in 1798,about 71 years after the law was formulated.

The Gravitational constant G is a small quantity and its measurement needs very sensitive arrangement.

Value of G was given through Cavendish Experiment.

Calculating the Gravitational Constant

In 1798 Sir Henry Cavendish suspended a rod with two small masses (red) from a thin wire. Two larger mass (silver) attract the small masses and cause the wire to twist slightly, since each force of attraction produces a torque in the same direction. By varying the masses and measuring the separations and the

amount of twist, Cavendish was the first to calculate G.

G = 6.67 10-11 N·m2/kg2

Cavendish’s Experiment

Earth was treated as a single particle placed at its centre.

Newton spent several years to prove that a spherically symmetric body can be replaced by a point particle as its centre.

In this process he discovered the methods of Calculus.

He did it by use of Calculus. It was then, applicable for the bodies if their entire

mass were concentrated at their centre of mass. Hence, it is applicable to all, whatever the size

may be.

Assumptions

It is a Universal Law. It explains motion of heavenly bodies.

The predictions of eclipses comes true. Tides in oceans because of attraction between

moon and ocean water. The predictions about orbits and time periods

of artificial satellites found to be correct.

Gravity is the force by which earth attracts a body towards its centre.

F e= GMem Re

2

where,– Fe = forces of attraction between Earth and particle of mass

m.– Me = mass of Earth.– m = mass of particle. – Re = distance between the centers of the Earth and particle.– G = Universal gravitational constant. = 6.67 10-11 N·m2/kg

Follows Newton's Law of Universal Gravitation By Newton’s second law , F = mg Compare with F = mg so g = GM/r2

g depends inversely on the square of the distance g depends on the mass of the planet Nominally, g = 9.81 m/s2 or 32.2 ft/s2

• At the equator g = 9.78 m/s2

• -At the North pole g = 9.83 m/s2

• g on the Moon is 1/6 of g on Earth.

Provides necessary centripetal force to moon to revolve.

Provides force to Satellites to revolve round the earth.

To make the bodies fall from height. Formation of Tides in the ocean.

Fg,lead GMEarthM lead

REarth2

Fg,wood GMEarthMwood

REarth2

22, 1•

Earth

earth

leadEarth

leadearth

lead

leadglead R

GMMR

MGMM

Fa

22, 1•

Earth

earth

woodEarth

woodearth

wood

woodgwood R

GMMR

MGMM

Fa

Lead Wood

aawoodwoodaaleadlead

Q. If two bodies one of lead and other of wood of same volumeare fallen from same height from the state of rest. Then which will strike to the ground first?(Neglect air-resistance)Sol.

…..(a)

…..(b)

Let, h be their height above the ground.By second equation of motion, S = ut + 1/2at2

For lead, h = 1/2aleadt1

2; …..(c) For wood, h = 1/2awoodt2

2; ..…(d)Equating (c)&(d), 1/2aleadt1

2 = 1/2awoodt22

t12 = t2

2

Or, t1 = t2

Thus, they will reach earth at same instant.

(From (a) &(b))

www.wikipedia.org/Gravitationwww.physicsclassroom.comwww.google.books.com

BooksProf. H.C.Verma : Concept of Physics Vol. IKumar,Mittal : ISC PHYSICS Class XIModern ABC : Physics Vol.I

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