nEWTON & GRAVITY

Grade 12 General Physics 1

At the end of the module, you

are expected to:

a. use Newton’s law of gravitation to infer gravitational

force, weight, and acceleration due to gravity
b. discuss the physical significance of gravitational field
c. apply the concept of gravitational potential energy
in physics problems
What really Happened with the apple?

Are you familiar with the popular story of Newton, who was
sitting under an apple tree, an apple fell on his head? At that
moment, he saw an apple fell from a tree and made him wonder
why the fruit always fell straight to the ground; why did it not swing
off to the left or right?

By Newton’s 2nd law, there must be a force that acts on the

apple to cause this acceleration, and let’s call this force as
“gravity”. The apple started in the tree and landed on the earth,
which means there must be a force of attraction between the
apple and the earth, this is where the concept of the Law of
Universal gravitation originated.
newton's law of motion

THE LAW OF INERTIA

An object at rest remains at rest, and an object in
1st motion remains in motion at constant speed and in a
straight line unless acted on by an unbalanced force.

THE LAW OF FORCE

The acceleration of an object depends on the mass of the
2nd object and the amount of force applied. It states that the
time rate of change of the momentum of a body is equal in
both magnitude and direction to the force imposed on it.

THE LAW OF ACTION AND REACTION

Whenever one object exerts a force on a second
3rd object, the second object exerts an equal and opposite
force on the first.
 NEWTON’S LAW OF

UNIVERSAL GRAVITATION

Weight is name given to the force acting on the object due to

gravity. The force of attraction between two objects must be
proportion to the objects’ masses, this is known as the gravitational
force. To explain this, we use Newton’s Law of Universal
Gravitation.
Gravitation

is a natural occurrence by which physical objects attract each

other due to their masses.
There is a force that appears whenever masses are present, and
this is a non-contact force.
In relation to this, Newton concluded that this non-contact
gravitational force must be responsible for the falling of an
apple from a tree, as it is also the cause for the rotation of the
moon about the earth.
Newton’s Law of universal Gravitation

Every object in the Universe attracts every other object with a force directed
along the line of centers for the two objects that is proportional to the product of
their masses and inversely proportional to the square of the separation between
the two objects.
Newton’s Law of universal Gravitation

This means that for two point masses M and m, separated by

distance r, the magnitude of the gravitational force attracting
them towards each other is:
EXAMPLE 1

GIVEN solution:

required
EXAMPLE 2

GIVEN solution:

required
 What is the gravitational force between two
practice 15 kg packages that are 0.35 m apart?

given required answer

 What is the gravitational force between two
practice
15 kg packages that are 0.35 m apart?

given required answer

M = 15 kg
m = 15 kg
d = 0.35 m
 What is the gravitational force between two
practice
15 kg packages that are 0.35 m apart?

given required answer

M = 15 kg
m = 15 kg 1.23 x 10^-7 N
d = 0.35 m
 Applications and relevance to daily life

It also plays a very important role in many

Gravitational force is very processes on earth. The gravitational attraction
evident in our everyday life. of both the Moon and Sun on the earth’s
Like for example, when you oceans cause ocean tide.
throw a ball into the air, the
ball will fall back to the The Moon’s gravitational pull generates tidal force.
ground, as Isaac Newton The tidal force causes Earth and its water to
says; “What Goes Up, Must bulge out on the side closest to the moon and the
side farthest from the moon. These bulges of
Come Down”.
water are high tides.
GRAVITATIONAL FIELD

The concept of gravitational field started when Newton

wondered how the sun could exert a force on planet earth,
which was hundreds of millions of kilometers away.
How can two objects exert attractive force on each other
when they are not in contact with each other?
GravitationAL FIELD

It is because gravitational fields affect anything that has mass.

Newton realized that all objects with mass attract each other.

Gravitational attractive forces between two objects only affect

their motion when at least one of the objects is very massive.

This explains why we are aware of the force that attracts us

and other objects towards the Earth – the Earth is very massive.
The mass of the Earth is about 6 × 10^24 kg.
GravitationAL FIELD

When you pick up an object such as a coin, there is a direct

contact between you and the coin. This direct contact exerts a
force on the coin, causing it to move in the way that it does.

However, the coin also has a weight due to its presence in the
Earth’s gravitational field. How is this force exerted, even when there
is no direct contact between the Earth and the coin?

A force is exerted on the coin from the Earth because the coin
is in the Earth’s gravitational field . We can define the field due
to a body as the region of space surrounding it where other bodies
will feel a force due to it.
 GRAVITATIONAL FIELD

The concept of magnetism, which developed by Michael Faraday, was also applied to
gravity. This is the concept of the field to explain how a magnet attract objects.

Gravitational field (vector) is the force field that exists in the space around every mass or
group of masses. This field cannot be touched or seen, but we can try to model it using field
lines or lines of force .

In a field line diagram below, the direction of the field line at a point gives the direction
of the force of attraction that would be felt by a small mass placed there. The
relative density of field lines on the diagram is an indication of the strength of the field.
 How would the earth’s

gravitational field look like?

Photos or screenshots of relevant articles are

also effective in reinforcing a class lesson.

Figure 1: : Close to Figure 2: : Earth’s gravitational Figure 3: : Illustration of

the earth, the field fields represented by lines of the magnetic field in a
forces. looks like. magnet similar to earth’s
gravitational field
GRAVITATIONAL FIELD strength

The gravitational field strength tells us how strong a gravitational

field is. The gravitational field strength of the Earth near surface is
9.8 m/s^2, this means an object that is near the surface of the earth
will accelerate towards it at 9.8 m/s^2.
We could then define the gravitational field strength as the
acceleration of an object that will experience within the
gravitational field.
gravitational field strength

The gravitational field strength at a point is the

gravitational force exerted per unit mass placed
at that point
EXAMPLE 1
Treating the Earth as a perfect sphere, Find the field
strength at the Earth’s surface. Use the given data to
solve the problem.

GIVEN solution:

required
EXAMPLE 2

GIVEN solution:

required
 Compute g for the surface of the moon. Its
radius is 1.7 x10^6 m and its mass is 7.4 x 10^22
practice kg.

given required answer

r=1.7 x10^6 m and its

m= 7.4 x 10^22 kg.

 Compute g for the surface of the moon. Its

radius is 1.7 x10^6 m and its mass is 7.4 x 10^22
practice kg.

given required answer

r=1.7 x10^6 m and its 0.42697 m/s^2

M= 7.4 x 10^22 kg. or .43 m/s^2

Applications and relevance to daily life

Example is the interaction of the

earth and a satellite in orbit
around it. This is very important as a
platforms in the transmission of the
communication.
GRAVITATIONAL potential energy

Gravity is a force which tries to pull two objects toward each other.
The Earth’s gravity is what keeps you standing on the ground, and
what makes objects to fall. Everything on this planet is held by
gravity.

Consider an object that is present at some height, earth’s

gravitational force acts on that object to attract it towards the
earth’s surface, therefore, it is called gravitational potential
energy.
GravitationAL POTENTIAL ENERGY

It is a potential energy associated with a body’s weight and its height

above the ground.

There is a direct relation between gravitational potential energy and the mass
and height of an object.

More massive = greater gravitational potential energy

Higher elevation of an object = greater gravitational potential energy

Example of this is a swimmer on the diving board,they have some amount of

gravitational potential energy. Since the swimmer is massive at a greater height,
the potential energy is greater.
gravitational POTENTIAL ENERGY

1 kg-m/s^2 = 1 Newton [N]

1 newton [N] = 1 joule/meter [J/m]

Unit of Energy = Joules

Formula of Energy = Force x distance
J= Newton x meter
 A cart is loaded with a brick and pulled at constant speed along an
EXAMPLE 1
inclined plane to the height of a seat-top. If the mass of the loaded
cart is 5.0 kg and the height of the seat top is 0.55 meters, then what is the
potential energy of the loaded cart at the height of the seat-top?

GIVEN solution:

required
 A larger block of stone is held at a height of 15m having gained
EXAMPLE 2
4500Jof GPE. How much does its weight?

GIVEN solution:

required
 An object whose mass is 43kg is hanging on a thin wire. The object has
EXAMPLE 2 a gravitational potential energy of 3160.5J. How high is the object above
the ground?

GIVEN solution:

required

h?
 An object has a gravitational potential energy
that is 833 J? Its height above ground is 4.25 m.
practice What is its mass?

given required answer

GPE = 833 J
h= 4.25 m
 An object has a gravitational potential energy
that is 833 J? Its height above ground is 4.25 m.
practice What is its mass?

given required answer

GPE = 833 J 20 kg
h= 4.25 m
 What is the gravitational potential energy of a
150kg object suspended 5m above the earth’s
practice surface?

given required answer

m = 150 kg
h = 5m
 What is the gravitational potential energy of a
150kg object suspended 5m above the earth’s
practice surface?

given required answer

m = 150 kg 7350 J
h = 5m
 An object has a gravitational potential energy
of 41772.5J and has mass of 1550kg. How high is
practice it above the ground?

given required answer

GPRE = 41772.5 J
m= 1550 kg
 An object has a gravitational potential energy
of 41772.5J and has mass of 1550kg. How high is
practice it above the ground?

given required answer

GPRE = 41772.5 J 2.75 m

m= 1550 kg
Applications and relevance to daily life

Example is water that is held in

a dam reservoirs for irrigation,
and generating electricity in
hydropower plants. Since the water
held in reservoirs is at rest and
massive at greater height the
gravitational potential energy is
greater.
Any questions?

Activity 5: deadline Oct 18

Performance Task 5: deadline Oct 18