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Kepler’s
second law
states that an
imaginary line
from the Sun to a
planet sweeps
out equal areas
in equal time
intervals.
GRADE 9
ADVANCED –
EOT
presentation
• Kepler found that orbits
might change due to
gravitational effects from, or
collisions with, other objects
in the solar system.
• He also found that the
planets move faster when
they are closer to the Sun
and slower when they are
farther away from the Sun.
Term 3 - 2023-2024
GRAVITATIONAL FORCE
• It is said that Isaac Newton watched
an apple fall and this led to his
theory of gravity.
• He suggested that there was a force
acting on the apple to make it fall.
• He extended that idea to all objects,
including our planet, the Moon and
the Sun.
He called it the gravitational force.
Factors that affect
gravity
The effect of mass on gravity
The effect of distance on gravity
1. Mass
2. Distance
Follows inverse square
law
Law of Universal Gravitation
𝑮 = 𝟔 ⋅ 𝟔𝟕 × 𝟏𝟎 𝟏𝟏 𝑵 𝒎𝟐 ⁄𝒌 𝒈𝟐
CHECKPOINT
Relation between Kepler’s Third Law and
Universal Law of Gravitation
To calculate the orbital period of a satellite
Write the final answer in days.
GUIDED PRACTICE
𝑚 = 5.97 × 10 𝑘𝑔
𝑮 = 𝟔 ⋅ 𝟔𝟕 × 𝟏𝟎 𝟏𝟏 𝑵 𝒎𝟐 ⁄𝒌 𝒈𝟐
𝑚 = 5.97 × 10 𝑘𝑔
𝑟 = 6 ⋅ 38 × 10 𝑚
𝑮 = 𝟔 ⋅ 𝟔𝟕 × 𝟏𝟎 𝟏𝟏 𝑵 𝒎𝟐 ⁄𝒌 𝒈𝟐
𝑟 = 6 ⋅ 38 × 10 𝑚
An ellipse has two foci
Kepler’s first
law
states that the
paths of the
planets are
ellipses, with the
Sun at one focus.
Very
Important
DEFINING WORK
1 joule of work is done when a
force of 1 N acts on a system over
a displacement of 1 m .
1 J = 1 Nm
NOTE :
• Work is a scalar quantity.
• Work is said to be done only if an objects moves
in the same direction as the applied force .
The distance from earth to the
sun changes throughout a year .
Work done by a constant force
Work done = Force x Displacement
W
= F
x
d
Refer to presentations used in class
Module 10 –Lesson 1 – Work and energy – Part 3 to 6
PICTURE 1
FORCE : A force is being applied by the
man on the wall.
DISPLACEMENT : But there is no
displacement happening .
WORK : Since there is no displacement
happening in the direction of applied force ,
no work is being done .
PICTURE 2
FORCE : An upward force is being applied by the
man on the box .
DISPLACEMENT : The box will move in the
upward direction . So, displacement occurred .
WORK :Since there is displacement happening in
the direction of applied force , work is being done .
Types of
work
Positive work
Positive
work
Force and
displacement in
same direction.
Negative
work
Force and
displacement in
opposite
direction.
Zero work
Zero work
1. Force applied , but zero
displacement .
2. Force and displacement
perpendicular to each
other .
Work done by Multiple forces on the box
NOTE:
When there are
multiple forces
acting on an object
Total work done =
Sum of work done
by each force .
RECALL
Do you know how to find out the
area of these shapes?
The force displacement graph
PARTNER
TIME
Find out the work done
Work done on force displacement graphs
CONSTANT FORCE
CHANGING FORCE
Work done by a constant or varying force = Area
under the force displacement graph
Work done by a constant or varying
force = Area under the force
displacement graph
Work is calculated by interpreting the area of the
rectangle in the graph
Work is calculated by interpreting the area of the triangle in
the graph
Practice
Find the total work done
POWER (P)
FORMULAS
• The rate at which energy is transformed is power .
• It is measured in watts (W).
• 1 W = 1 J/s
W = ΔE
1
Δ𝑘𝐸 = 𝑚 𝑣 − 𝑣
2
𝑃=
𝑤
𝑡
𝑃=
𝑃=
𝑃=
𝐹𝑑
𝑡
𝑚𝑔𝑑
𝑡
𝑤
𝑡
Challenge
Practice problem 2
Kinetic
Energy
Energy due to motion
NOTE
Translational
kinetic energy
is proportional
to the square
of the object’s
Speed.
Translational
Kinetic Energy
Energy due to
changing position
𝐾𝐸
=
1
𝑚𝑣
2
m – mass of object
v - velocity of object
Rotational Kinetic
Energy
Energy due to
rotational motion
𝐾𝐸
=
1
𝐼𝜔
2
I – moment of inertia
ω - angular velocity of object
Guided Practice
Gravitational Potential Energy ( GPE )
RECAP
Work done by gravity (Wg)
• Gravitational Potential Energy (GPE) is the stored energy
due to gravity.
GPE = m g h
Where , h is the object’s distance above the reference level
g is the gravitational field strength
• Lifting an object : Wg = - mgh
• Unit - joules (J)
• Lowering an object : Wg = mgh
The negative sign is because displacement is upwards and
gravitational force acts downward .
RECAP
LAW OF CONSERVATION OF ENERGY
The law of conservation of energy states that energy can neither be
created nor destroyed - only converted from one form of energy to another.
𝐾𝐸 + 𝑃𝐸 = 𝐾𝐸 + 𝑃𝐸
Guided Practice 1
EXAMPLE
Kinetic energy
Change in kinetic energy
Change in kinetic energy = Final KE – Initial KE
Analyzing Bernoulli’s Principle
BERNOULLI’S PRINCIPLE
Refer to the textbook – Page 249 and 250
Bernoulli’s principle states that as the velocity of a fluid increases,
the pressure exerted by that fluid decreases.
Velocity
increases
Pressure
decreases
Ideal fluid
Change in
kinetic energy
=Work done
Work is
proportional
to force
Applications of Bernoulli’s principle
Enters
through
wider
mouth of
pipe with
velocity v1
Kinetic energy
increases
Force is
proportional
to pressure
Reaches
narrower
portion of pipe
Velocity
increases
Net work is
positive
CONCLUSION : Relation between
pressure and velocity
Pressure at the input
section , where velocity
is lower, must be larger
than the pressure at
the output end , where
velocity is higher.
Difference between Pascal and Bernoulli’s
Principles
As you learned, both these principles define how fluids behave with
pressure.
Pascal showed that fluid pressure is the same for a given depth and
that pressure change is transmitted equally everywhere.
Paint sprayers
Gasoline engine carburetors
Bernoulli showed that pressure changes in a fluid when it is moving.
Pascal's principle only applies to static fluids, that is, fluids at rest,
whereas Bernoulli's principle only applies to fluids in motion.
Application of Pascal’s Principle – Hydraulic Lift
Force Exerted by a Hydraulic Lift the
force exerted by the second is equal to
the force exerted by the first piston
multiplied by the ratio of the area of the
second piston to the area of the first
piston
WARM-UP QUESTION
Which law states that any change in pressure applied at any point on a
confined fluid is transferred undiminished throughout the fluid?
A
Pascal’s principle
C
buoyancy principle
D
Archimedes’ principle
CORRECT
B
Bernoulli’s principle
WRITING
Guided Practice
CHECKPOINT
Guided Practice
CHALLENGE
Guided Practice
THE WORK – ENERGY THEOREM
Kinetic energy
The work-energy theorem states that the work done
(W) on a system is equal to the change in energy (ΔE)
of the system,
W = ΔE
Change in kinetic energy
Model of work-energy theorem
Change in kinetic energy = Final KE – Initial KE
CHALLENGE
HOMEWORK
Law of Conservation of Energy
• The law of conservation of energy states that in a closed, isolated
system, energy can neither be created nor destroyed.
• So, the total change of energy in any system is always equal to the
total energy transferred into or out of the system
CHALLENGE !
MECHANICAL ENERGY
Imagine a system consisting of a 10 N ball falling to the earth. Find the mechanical energy of
the system in all three cases .
Example 1: Rollercoasters
EXAMPLES OF
CONSERVATION AND OTHER
FORMS OF ENERGY
CHECKPOINT
( LMS > Physics > Week 3 > Period 5> Checkpoint )
Example 2 : Skiing
Example 2 : Skiing
1. At which point is the
PE highest ?
The roller-coaster car is nearly at rest at the
top of the first hill, and the total mechanical
energy in the Earth-roller coaster car system
is the system's gravitational potential energy
at that point.
2 .At which point is the
KE the highest ?
3. At which points are
the ME equal to each
other?
• When you ski down a steep slope, you begin
from rest at the top of the slope and the total
mechanical energy is equal to the gravitational
potential energy.
• Once you start skiing downhill, the gravitational
potential energy is transformed to kinetic energy.
• As you ski down the slope, your speed
increases as more potential energy is
transformed to kinetic energy.
Example 3 : Pendulums
Pendulums
• The simple oscillation of a pendulum also demonstrates
Conservation of mechanical energy.
• The system is the pendulum bob and Earth. The
reference level is chosen to be the height of the bob at
the lowest point. When an external force pulls the bob to
one side, the force does work that adds mechanical
energy to the system.
• At the instant the bob is released, all the energy is in
the form of potential energy, but as the bob swings downward, potential energy is transformed to kinetic energy.
When the bob is at the lowest point, the gravitational
potential energy is zero, and the kinetic energy is equal to
the total mechanical energy.
EXAMPLE
RECAP
Guided Practice 1
LAW OF CONSERVATION OF ENERGY
The law of conservation of energy states that energy can neither be
created nor destroyed - only converted from one form of energy to another.
𝐾𝐸 + 𝑃𝐸 = 𝐾𝐸 + 𝑃𝐸
KEPLER’S LAWS
Kepler’s first
law
Kepler’s
second law
states that the
paths of the
planets are
ellipses, with the
Sun at one focus.
states that an
imaginary line
from the Sun to a
planet sweeps
out equal areas
in equal time
intervals.
The distance from earth to the
sun changes throughout a year .
• Kepler found that orbits
might change due to
gravitational effects from, or
collisions with, other objects
in the solar system.
• He also found that the
planets move faster when
they are closer to the Sun
and slower when they are
farther away from the Sun.
Kepler’s third
law
States that the square of the ratio of the
periods of any two planets revolving
around the Sun is equal to the cube of
the ratio of their average distances from
the Sun.
Thus, if the periods of the planets are TA
and TB, and their average distances from
the Sun are rA and rB, Kepler’s third law
can be expressed as follows:





2
TA   rA 
=
TB   rB 
NOTE
Kepler’s first and second
law applies to each
planet , moon and
satellite individually.
Kepler’s third law relates
motion of two objects
around a single body.
3
Challenge
• It is said that Isaac Newton watched
an apple fall and this led to his
theory of gravity.
• He suggested that there was a force
acting on the apple to make it fall.
• He extended that idea to all objects,
including our planet, the Moon and
the Sun.
He called it the gravitational force.
Factors that affect
gravity
The effect of mass on gravity
The effect of distance on gravity
1. Mass
2. Distance
Follows inverse square
law
CHECKPOINT
Law of Universal Gravitation
𝑮 = 𝟔 ⋅ 𝟔𝟕 × 𝟏𝟎 𝟏𝟏 𝑵 𝒎𝟐 ⁄𝒌 𝒈𝟐
Relation between Kepler’s Third Law and
Universal Law of Gravitation
Write the final answer in days.
To calculate the orbital speed of a satellite
To calculate the orbital period of a satellite
Vocabulary - satellite
A satellite is an object in space that orbits or circles
around a bigger object. There are two kinds of satellites:
natural (such as the moon orbiting the Earth) or artificial
(such as the International Space Station orbiting the
Earth).
GUIDED PRACTICE
What is pressure?
𝑚 = 5.97 × 10 𝑘𝑔
𝑮 = 𝟔 ⋅ 𝟔𝟕 × 𝟏𝟎 𝟏𝟏 𝑵 𝒎𝟐 ⁄𝒌 𝒈𝟐
𝑟 = 6 ⋅ 38 × 10 𝑚
Pressure is the amount of force (F), in newtons applied perpendicular
to the surface of an object per unit area (A) in m2.
𝑚 = 5.97 × 10 𝑘𝑔
𝑮 = 𝟔 ⋅ 𝟔𝟕 × 𝟏𝟎 𝟏𝟏 𝑵 𝒎𝟐 ⁄𝒌 𝒈𝟐
𝑟 = 6 ⋅ 38 × 10 𝑚
SI Unit of Pressure
The SI unit of pressure is the pascal (Pa).
1 pascal is the pressure exerted by a body that applies a force of 1 N over
an area of 1 m2.