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Halcyon Tutorials (9741733038)
Gravitation
Gravity is the force that makes objects fall towards the Earth, keeps the Moon in orbit around
the Earth, and makes the planets revolve around the Sun. This force is called gravitational
force, and it's one of the most important forces in the universe.
In this chapter, you'll learn about:
1. Gravitation: What it is and how it works everywhere in the universe.
2. Universal Law of Gravitation: Newton’s famous law that tells us how gravity works
between any two objects, no matter how far apart they are.
3. Motion under Gravity: How objects move when they are influenced by gravity, like
when you drop something.
4. Weight Variation: Why your weight can change depending on where you are on
Earth.
5. Floating Objects: What makes something float in water or other liquids.
9.1 Gravitation:
If Earth can pull the apple down, why doesn’t it also pull the Moon down? And in fact, it
does!
The Earth’s gravity pulls on both the apple and the Moon.
When you throw an object like a ball, it goes up, but then gravity pulls it back down
to the ground.
The Moon doesn’t fall straight to the Earth because it’s moving sideways fast enough
that it keeps missing the Earth. This sideways motion makes it move in a circular path
around the Earth. So, it’s constantly "falling" towards the Earth but never actually
hitting it.
This is what Newton figured out! The same force that makes apples fall to the ground also
keeps the Moon in orbit around Earth. The gravitational force between Earth and the
Moon works just like the force between Earth and the apple—it just affects them
differently because of their motions and distances.
So, even though we don’t see the Moon falling straight down like the apple, gravity is still
at work, keeping it in its orbit!
Activity: 9.1
Objective:
To observe the motion of an object moving in a circular path and its behavior after
releasing the centripetal force.
Halcyon Tutorials (9741733038)
, 2
Materials Required:
A piece of thread (about 50 cm long)
A small stone or any similar object (lightweight but sturdy
A stone describing a circular path with a velocity of constant magnitude.
Procedure:
1. Tie the Stone:
o Take one end of the thread and tie it securely to the small stone.
2. Hold the Thread:
o Hold the other end of the thread tightly in your hand. Make sure there’s
enough space around you.
3. Whirl the Stone:
o Start whirling the stone in a circular motion by rotating your hand in a circular
path. Ensure that the stone moves smoothly in the circle.
4. Observe the Motion:
o While the stone is moving in a circular path, observe that the stone stays on
this path because of the tension in the thread. The thread is providing the
necessary centripetal force to keep the stone moving in the circle.
5. Release the Thread:
o After a few rotations, carefully release the thread while the stone is moving.
6. Observe the Motion After Release:
o When the thread is released, observe the direction of the stone's motion. You
will see that the stone no longer moves in a circle but flies off in a straight
line, tangential to the circle (the direction it was moving at the moment of
release).
7. Conclusion:
o Record the observations. This activity demonstrates that when the centripetal
force (the pull from the thread) is removed, the stone moves in a straight line,
showing that objects tend to move in a straight path unless acted upon by a
force (as per Newton's First Law of Motion).
Halcyon Tutorials (9741733038)
, 3
Some very important concepts about gravity, motion, and Newton's laws!
1. Centripetal Force:
o When the stone is moving in a circular path, it’s constantly changing direction.
This change in direction means the stone is accelerating, and the force that
causes this acceleration is called the centripetal force.
o The centripetal force always acts towards the center of the circle. In the
absence of this force (when you release the thread), the stone flies off in a
straight line, which is tangential to the circular path.
2. Motion of the Moon:
o The Moon goes around the Earth due to the centripetal force. This force is
provided by Earth’s gravitational pull. Without this force, the Moon would
move in a straight line, just like the stone would if you release the thread.
3. Newton's Third Law and the Apple:
o When an apple falls, we see it being pulled towards Earth due to gravity.
According to Newton’s Third Law of Motion, the apple also pulls the Earth
towards itself. However, because the Earth is so massive compared to the
apple, we don’t see the Earth moving.
4. Newton's Second Law:
o According to Newton’s Second Law of Motion, acceleration is inversely
proportional to the mass of an object. Since the Earth has an enormous mass
compared to the apple, the Earth's acceleration due to the apple’s pull is so
tiny that it’s unnoticeable.
5. Planets and the Sun:
o In our solar system, the planets orbit the Sun for the same reason: there’s a
gravitational force between the Sun and the planets. This force acts like the
centripetal force that keeps the planets moving in circular or elliptical orbits.
6. Gravitational Force:
o Newton concluded that every object in the universe attracts every other
object. This attraction is called the gravitational force. Whether it's an apple,
the Moon, the Earth, or the planets, gravity is the force that governs their
motions.
In summary:
The gravitational force is universal and acts between all objects.
Objects in circular motion are kept in their paths due to centripetal force, which,
in the case of the Moon and planets, is provided by gravity.
Newton’s laws of motion help explain why objects behave the way they do when
gravity is involved!
9.1.1 Universal Law of Gravitation:
1. What it says:
o Every object in the universe attracts every other object with a force that
depends on their masses and the distance between them.
Halcyon Tutorials (9741733038)
, 4
The gravitational force between two uniform objects is
directed along the line joining their centres.
1. Proportional to the masses:
o The force of attraction between two objects (A and B) is directly
proportional to the product of their masses. That means the bigger the
masses, the stronger the force.
o This is shown as: F∝ M×m Where
M the mass of object A,
m is the mass of object B.
2. Inversely proportional to the square of the distance:
o The force is inversely proportional to the square of the distance between
the two objects. That means if the distance increases, the force decreases
quickly.
This tells us that the gravitational force is stronger when the masses are larger and
weaker when the distance between the objects is larger.
1. Introducing the gravitational constant (G):
o To convert this proportionality into an equation, we introduce a constant of
proportionality called the universal gravitational constant (denoted as G)
Halcyon Tutorials (9741733038)
Halcyon Tutorials (9741733038)
Gravitation
Gravity is the force that makes objects fall towards the Earth, keeps the Moon in orbit around
the Earth, and makes the planets revolve around the Sun. This force is called gravitational
force, and it's one of the most important forces in the universe.
In this chapter, you'll learn about:
1. Gravitation: What it is and how it works everywhere in the universe.
2. Universal Law of Gravitation: Newton’s famous law that tells us how gravity works
between any two objects, no matter how far apart they are.
3. Motion under Gravity: How objects move when they are influenced by gravity, like
when you drop something.
4. Weight Variation: Why your weight can change depending on where you are on
Earth.
5. Floating Objects: What makes something float in water or other liquids.
9.1 Gravitation:
If Earth can pull the apple down, why doesn’t it also pull the Moon down? And in fact, it
does!
The Earth’s gravity pulls on both the apple and the Moon.
When you throw an object like a ball, it goes up, but then gravity pulls it back down
to the ground.
The Moon doesn’t fall straight to the Earth because it’s moving sideways fast enough
that it keeps missing the Earth. This sideways motion makes it move in a circular path
around the Earth. So, it’s constantly "falling" towards the Earth but never actually
hitting it.
This is what Newton figured out! The same force that makes apples fall to the ground also
keeps the Moon in orbit around Earth. The gravitational force between Earth and the
Moon works just like the force between Earth and the apple—it just affects them
differently because of their motions and distances.
So, even though we don’t see the Moon falling straight down like the apple, gravity is still
at work, keeping it in its orbit!
Activity: 9.1
Objective:
To observe the motion of an object moving in a circular path and its behavior after
releasing the centripetal force.
Halcyon Tutorials (9741733038)
, 2
Materials Required:
A piece of thread (about 50 cm long)
A small stone or any similar object (lightweight but sturdy
A stone describing a circular path with a velocity of constant magnitude.
Procedure:
1. Tie the Stone:
o Take one end of the thread and tie it securely to the small stone.
2. Hold the Thread:
o Hold the other end of the thread tightly in your hand. Make sure there’s
enough space around you.
3. Whirl the Stone:
o Start whirling the stone in a circular motion by rotating your hand in a circular
path. Ensure that the stone moves smoothly in the circle.
4. Observe the Motion:
o While the stone is moving in a circular path, observe that the stone stays on
this path because of the tension in the thread. The thread is providing the
necessary centripetal force to keep the stone moving in the circle.
5. Release the Thread:
o After a few rotations, carefully release the thread while the stone is moving.
6. Observe the Motion After Release:
o When the thread is released, observe the direction of the stone's motion. You
will see that the stone no longer moves in a circle but flies off in a straight
line, tangential to the circle (the direction it was moving at the moment of
release).
7. Conclusion:
o Record the observations. This activity demonstrates that when the centripetal
force (the pull from the thread) is removed, the stone moves in a straight line,
showing that objects tend to move in a straight path unless acted upon by a
force (as per Newton's First Law of Motion).
Halcyon Tutorials (9741733038)
, 3
Some very important concepts about gravity, motion, and Newton's laws!
1. Centripetal Force:
o When the stone is moving in a circular path, it’s constantly changing direction.
This change in direction means the stone is accelerating, and the force that
causes this acceleration is called the centripetal force.
o The centripetal force always acts towards the center of the circle. In the
absence of this force (when you release the thread), the stone flies off in a
straight line, which is tangential to the circular path.
2. Motion of the Moon:
o The Moon goes around the Earth due to the centripetal force. This force is
provided by Earth’s gravitational pull. Without this force, the Moon would
move in a straight line, just like the stone would if you release the thread.
3. Newton's Third Law and the Apple:
o When an apple falls, we see it being pulled towards Earth due to gravity.
According to Newton’s Third Law of Motion, the apple also pulls the Earth
towards itself. However, because the Earth is so massive compared to the
apple, we don’t see the Earth moving.
4. Newton's Second Law:
o According to Newton’s Second Law of Motion, acceleration is inversely
proportional to the mass of an object. Since the Earth has an enormous mass
compared to the apple, the Earth's acceleration due to the apple’s pull is so
tiny that it’s unnoticeable.
5. Planets and the Sun:
o In our solar system, the planets orbit the Sun for the same reason: there’s a
gravitational force between the Sun and the planets. This force acts like the
centripetal force that keeps the planets moving in circular or elliptical orbits.
6. Gravitational Force:
o Newton concluded that every object in the universe attracts every other
object. This attraction is called the gravitational force. Whether it's an apple,
the Moon, the Earth, or the planets, gravity is the force that governs their
motions.
In summary:
The gravitational force is universal and acts between all objects.
Objects in circular motion are kept in their paths due to centripetal force, which,
in the case of the Moon and planets, is provided by gravity.
Newton’s laws of motion help explain why objects behave the way they do when
gravity is involved!
9.1.1 Universal Law of Gravitation:
1. What it says:
o Every object in the universe attracts every other object with a force that
depends on their masses and the distance between them.
Halcyon Tutorials (9741733038)
, 4
The gravitational force between two uniform objects is
directed along the line joining their centres.
1. Proportional to the masses:
o The force of attraction between two objects (A and B) is directly
proportional to the product of their masses. That means the bigger the
masses, the stronger the force.
o This is shown as: F∝ M×m Where
M the mass of object A,
m is the mass of object B.
2. Inversely proportional to the square of the distance:
o The force is inversely proportional to the square of the distance between
the two objects. That means if the distance increases, the force decreases
quickly.
This tells us that the gravitational force is stronger when the masses are larger and
weaker when the distance between the objects is larger.
1. Introducing the gravitational constant (G):
o To convert this proportionality into an equation, we introduce a constant of
proportionality called the universal gravitational constant (denoted as G)
Halcyon Tutorials (9741733038)
