3. GROUP
1 II
III IV
1. ABDUL,NADEEM ABUBACAR
2. ARAÑEZ,JAYVINE SUMPIAO
3. TONGAYAN,JAY-AR -
4. ACAPULCO,PRETTY JANE
ABASOLO
5. NAON,ALAICA BACTO
1. KAMLON,ALNA JEAM AGRAVIADOR
2. LAUGANAS,GERALD CASTAÑO
3. DESIO,ALHANNIE DELA PEÑA
4. EMPRIZA,REVICA BAYTA
1. ARCILLA,CHRISTOPHER BORDIOS
2. BEJASA,JHON ALFRED NEMIL
3. AGUA,CHRISTINE JOY BARIENTO
4. SALIOT,RIZZY MAE PASCO
1. MAGHINAY,JOHN ANTHONY FERCOL
2. MATCHON,LORD RUBIO
3. GALOTERA,APRIL KEITH BALBUENA
4. GUALIZA,THREAXEN MARIE ROBLES
5. ARANGCANA,DANICA ERIESO
1. BERBESADA,ALDRIAN MARZAN
2. BRONIDOR,EDITO JR DIGNOS
3. ASMUN,ALMALYN SAYARI
4. ASMUN,ALMALYN SAYARI
5. TACMOY,MARY CRIS SIMAFRANCA
5. TANHAJI,SITTI PAIMA BASARE
5. PUERTO,JUDIE LYN DOLALAS
1. DANLAG,JAMES CARLO BANDIVAS
2. DOMINGO,ANGELO CONDE
3. ASMUN,ALMALYN SAYARI
4. CASERES,VENUS TANOY
5. TOMA,AINA TOMA
1. MAGHINAY,NERIZAMEL OCHEA
2. ABDULLAH,ALIAMEN SANTUA
3. LUMILES,VANESSA ANNE DELA
TORRE
4. MADHAY,CHRISTINE LUSAYAN
V
VI
VII
4. ALBERT EINSTEIN
- was the first person to understand the
relationship between space and time. At a
very young age of 26, he showed how
measurements of time and space are
affected by motion between observer and
what is being observed. Einstein stated in
1905 that in moving through space, we
also change our rate of proceeding into
the future time itself.
5. * Meron na ba sa inyong nakakakita na ng jet
plane na lumilipad sa himpapawid?
* Anong napansin ninyo sa jet plane?
* Sino ba sa inyo ang nakapunta na ng ibang
bansa? Ano yung sinasakyan n’yo?
* Ano yung napapansin nyo pagtingin ninyo sa
ibaba?
* By the way, ano bang rason bakit pumunta
kayo ng ibang bansa? Anong bansa yun?
Nararamdaman n’yo ba ang pagka-espesyal?
* May kaugnayan ba ang galaw sa paglipad ng
sasakyang panhimpapawid mula sa iyong
6. The First Postulate of Special Relativity
Relativity. Presentation Express. Conceptual Physics
7. Einstein reasoned all motion is relative and all frames of reference are
arbitrary.
Example 1: Spaceman A considers himself at rest and sees spacewoman B
pass by,
while spacewoman B considers herself at rest and sees spaceman A pass
by.
Spaceman A and spacewoman B will both observe only the relative
motion.
The First Postulate of Special Relativity
8. THE SECOND POSTULATE OF
SPECIAL RELATIVITY
Relativity. Presentation Express.
Conceptual Physics
9. EXAMPLE 2:
A spaceship departing from the space station. The
speed of a light flash emitted by either the spaceship
or the space station is measured as c by observers on
the ship or the space station.
Relativity. Presentation Express.
Conceptual Physics
10. QUICK CHECK: ITS ALL
RELATIVE!
1. What does the first postulate of special relativity state?
_______________________________________________________
_______________________________________________________
_______________________________________________________
_______________________________________________________
2. What does the second postulate of special relativity state?
_______________________________________________________
_______________________________________________________
_______________________________________________________
_______________________________________________________
11. QUICK CHECK: ITS ALL
RELATIVE!
1. What does the first postulate of special relativity state?
The first postulate of special relativity states that the laws of
physics are the same in every initial frame of reference.
2. What does the second postulate of special relativity
state?
The second postulate of special relativity states that the
speed of light is the same in all inertial frames of reference
and is independent of the motion of the source.
13. INSTEIN’S SPECIAL THEORY OF
RELATIVITY
has two main postulates:
1) The laws of physics are the
same in every initial frame of
reference; and
2) The speed of light is the
same in all inertial frames of
reference and is independent of
the motion of the source.
18. TRUTH or
BLUFF
Directions: Please raise the
letter T if the statement is
correct and raise the letter B
if the statement is a bluff. If
the statement is a bluff,
state the word or words
19. TRUTH OR BLUFF
____1. Albert Einstein is the
proponent of the Special
Theory of Relativity.
T
20. TRUTH OR BLUFF
____2. The Special Theory of
Relativity has three main
postulates.
B
three
21. TRUTH OR BLUFF
____3. The first postulate states
that the speed of light is the same
in all inertial frames of reference
and is independent of the motion
of the source.
B first
22. TRUTH OR BLUFF
____4. A non-inertial frame of
reference is non-accelerating
and non-rotating frame of
reference.
B non-
24. TRUTH OR BLUFF
____6. In Relativity of Simultaneity,
if two distinct events are separated
in space, then it can be said that
they occur at the same time.
B can
33. TRUTH OR BLUFF
____15. Two events
happening at the same time
in a frame of reference is a
property known as the
relativity of simultaneity.
T
34. CONSEQUENCES OF THE
THEORY OF SPECIAL
RELATIVITY
Special Relativity implies a wide
range of consequences which have
been experimentally verified such
as relativity of simultaneity, time
dilation, length contraction,
relativistic mass, mass-energy
equivalence and cosmic speed limit.
35. RUBRICS
Category 3 4 5
Mastery and
correctness of
information
The group
demonstrate
Knowledgeof
somecontent
oftheir assigned
topic.
The group
demonstrate
knowledge of
important contents
of their assigned
topic.
The group
demonstrate
Totalknowledge
ofcontents of
topic
Delivery and
presentation of topic
The group delivers
their ideas orally
and with visual
materials .
The group delivers
a creative
presentation of the
topic.
The group
delivers a very
creative
presentation of
the topic.
Cooperation and other
preparation
Three or four
members of the
group are inactive
in the preparation
and presentation of
the topic
One or two
members of the
group are inactive
in the preparation
and presentation of
the topic
All the
members of the
group are
active in the
preparation and
presentation of
the topic
36. RELATIVITY OF
SIMULTANEITY
Two events happening at the same time in a
frame of reference is a property known as
the relativity of simultaneity. According to
Eintein’s theory of relativity, simultaneity is
not an absolute property between events. If
two distinct events are separated in space,
then it cannot be said absolutely that they
occur at the same time. It does not
necessarily follow what is simultaneous in
one frame is also simultaneous in another.
37. RELATIVITY OF SIMULTANEITY
To inside observer, light beams hit top and bottom
simultaneously while to outside observer, downward beam
38. TIME DILATION
Einstein proposed that time can be stretched depending
on the motion between the observer and the events
being observed.
The stretching of time is time dilation.
A moving clock ticks more slowly than a clock at rest.
To further
understand this, lets consider a light clock at a moving
ship. A stationary light clock is shown here. Imagine an
empty tube with a mirror at each end.
A flash of light bounces back and forth between the
42. From the outside, one tick of the light clock takes
longer than it takes for occupants of the spaceship.
The spaceship’s clock has slowed down. However,
for occupants of the spaceship, it has not slowed.
The slowing of time is not peculiar to the light
clock. It is time itself in the moving frame of
reference, as viewed from our frame of reference
that slows.
• The heartbeats of the spaceship occupants will
have a slower rhythm.
• All events on the moving ship will be observed by
us as slower.
43. THE TWIN PARADOX
A dramatic illustration of time dilation
is afforded by identical twins, one an
astronaut who takes a high-speed
round-trip journey while the other
stays home on Earth.
When the traveling twin returns, he is
younger than the stay-at-home twin.
How much younger depends on the
46. THE TWIN PARADOX
Einstein showed the relation between the time t0 in the
observer’s own frame of reference and the relative time t
measured in another frame of reference is:
where v represents the relative velocity between the
observer and the observed and c is the speed of light.
47. EXAMPLE 1:
Astronauts traveling at 99% of speed of light could
go to star Procyon (11.4 light-years distant) and
back in 23.0 years in Earth time. How long would
be is the travel if we apply the time dilation?
I.
List all the given.
v = 0.99 c
t = 23.0 years
t0 = ?
48. II. SUBSTITUTE
t0 = 𝑡√1 − ( 𝑣𝑐 )² (Derived formula on how to get t0 . )
t0 = 23.0 years √1 − (0.99𝑐/𝑐) ² (Substitute all the
given.Cancel out c.)
t0 = 23.0 years√1 − (0.99) ² (Get the value of the square
root .)
t0 = 23.0 years (0.14) (Multiply.)
t0 = 3.22 years
49. EXAMPLE 2:
We discovered an Earth-like
planet 20.5 lightyears away.
Suppose that you are chosen as
one of the astronauts to go along
as the first explorers. How long
will be is your round trip to the
planet if you can travel 87% of the
50. EXAMPLE 2:
v= 0.87 c
t = ?
t0 = 20.5 years
t = 20.5 years / √1- (0.87 c / c)2
t = 20.5 years / √1- (0.87)2
t = 20.5 years / √1- (0.76)
t = 20.5 years / 0.24
t = 85.4 years
51. LENGTH CONTRACTION
For moving objects, space as well
as time undergoes change.
The observable shortening of
moving objects approaching the
speed of light is called length
contraction.
The amount of contraction is
related to the amount of time dilation.
For everyday speeds, the amount of
contraction is much too small to be
52. The contraction of speeding
objects is the contraction of space
itself. Space contracts in only one
direction, the direction of motion.
Lengths along the direction
perpendicular to this motion are the
same in the two frames of reference.
As relative speed increases,
contraction in the direction of motion
increases. Lengths in the
perpendicular direction do not change.
54. RELATIVISTIC LENGTH
CONTRACTION IS STATED
MATHEMATICALLY:
v is the speed of the object relative to the
observer
c is the speed of light
L is the length of the moving object as
measured by the observer L0 is the measured
length of the object at rest
55. EXAMPLE 1:
An earth-bound observer
measures the distance to star
Sirius as 8.7 light years ( Ly). What
distance between the Earth and
Sirius would be measured by an
observer on a spaceship moving at
speed of 0.8 c?
56. GIVEN:
L = ?
Lo = 8.7 Ly
v = 0.8 c
L = 8.7 Ly √1-(0.8 c /c)2
L = 8.7 Ly √1-(0.64)L = 8.7 Ly
√0.36
L = 8.7 Ly (0.6)
L = 5.2 Ly
Solution:
57. EXAMPLE 2:
An observer on Earth sees a
rocket zoom by at 0.95 c. If the
rocket is measured to be 5.5 m
in length, how long is the
rocket ship as measure by the
astronaut inside the rocket?
58. GIVEN:
L = 5.5 m
v = 0.95 c
Lo = ? Lo = L / √1-(v/c)2
Lo = 5.5 m / √1-(0.95 c /
c)2
Lo = 5.5 m / √1-(0.9025
)
Lo = 5.5 m / √0.0975
Lo = 5.5 m / 0.312
Solution:
59. MASS ENERGY
EQUIVALENCE
A remarkable insight of Einstein’s
special theory of relativity is his
conclusion that mass is simply a form
of energy.
A piece of matter has an “energy of
being” called rest energy. Einstein
concluded that it takes energy to
make mass and that energy is
released when mass disappears. Rest
mass is, in effect, a kind of potential
60. The amount of rest energy E is
related to the mass m by the most
celebrated equation of the twentieth
century:
Special Relativity.
pdf
61. where c is again the speed of light. This equation gives
the total energy content of a piece of stationary matter of
mass m.
Rest energy can be converted to other forms. F or
example, when we strike a match, a chemical reaction
occurs and heat is released. A change in energy of any
object at rest is accompanied by a change in its mass.
The equation E = mc2 is more than a formula for the
conversion of rest massinto other kinds of energy, or vice
62. EXAMPLE:
Two grams of helium are
completely converted into
energy and used to power a
100 kg man. If all of this energy
is converted into kinetic energy
of the man, how fast will he
move?
63. ANSWER:
E = ?
m = 0.002 kg (Note! Always express mass into
kg.)
c = 3 x 108 m/s
E = mc2
E = 0.002 kg (3 x 108 m/s )2
E = 0.002 kg ( 9x 1016 m2/s2)
E = 1.8 x 1014 kg*m2/s2 (Note! 1 kg*m2/s2 =
1 Joule J)
64. THIS ENERGY COMPUTED CAN
BE EQUATED TO MAN’S KINETIC
ENERGY, WHICH CAN BE THEN
USED TO FIND THE MAN’S
VELOCITY.
Now, let us now get the man’s
velocity using the formula on
how to get the Kinetic Energy
(KE).
KE = mv2/2
where in, m is the mass
65. ANSWER:
KE = 1.8 x 1014 J
m = 100 kg
v = ?
KE = mv2/2
1.8 x 1014 J = 100 kg
(v2)/2
v = √ KE (2) / m
v = √ 1.8 x 1014 J (2) /
100 kg
v = √ 1.8 x 1014
kg*m2/s2 (2) / 100 kg
v =√ 3.6 x 1014
kg*m2/s2/2/100 kg
v = √ 3.6 x 1012 m2/s2
66. RELATIVISTIC MASS
The relative change in mass is
perceived when the body is in motion.
This concept is relativistic mass.
Moving objects appear to be more
massive.
Special Relativity. pdf
67. RELATIVISTIC MASS IS GIVEN
AS
m = m0 / √1-(v2/c2)
where m – relativistic mass
m0 – mass of the object at rest
(rest mass)
The mass of an object moving at the speed v
relative to an observer is larger than its mass
when at rest relative to the observer relative to
the factor 1 / √1-(v2/c2). Increase in
relativistic mass is significantly only at speeds
approaching that of light.
68. EXAMPLE:
An object in motion
has a mass of 12 kg and
travels in the air with
velocity of 0.82 c. What
would be its rest mass?
69. ANSWER:
m = 12 kg
v = 0.82 c
m0 = ?
m = m0 / √1-(v2/c2)
m0 = m * √1-(v2/c2)
m0 = 12 kg * √1-(0.822 c2/c2)m0 = 12 kg *
√1-(0.67)
m0 = 12 kg * √0.33
m0 = 12 kg * 0.57
m0 = 6.8 kg
70. COSMIC SPEED LIMIT
Einstein showed that the universe
has a speed limit which is the speed
of light in vacuum. Nothing can
travel faster than 300 000 km/s.
It is impossible for any material
object to travel faster than the speed
of light because the faster the object
travels, the more it becomes massive
and it takes more energy to increase
its speed.
71. REASON OUT!
3. How does the length of an
object change when it is moving
at a very high speed relative to
an observer?
________________________________
________________________________
4. Can we look at the equation E
= mc2 in another way and say
that matter transforms into pure
energy when it is traveling at the
speed of light squared?
________________________________
________________________________
5. Is it possible to travel faster
than the speed of light?
________________________________
________________________________
Directions: Answer or explain the
following questions correctly.
1. What are the two postulates of
Special Theory of Relativity?
______________________________________
______________________________________
2. If you were moving in a spaceship at
a high speed relative to Earth, would
you notice a difference in your pulse
rate? In the pulse rate of the people
back on Earth?
______________________________________
______________________________________
72. REASON OUT!
1. What are the two postulates of Special Theory of Relativity?
The two postulates of Special Theory of Relativity presented by
Albert Einstein are:
* the laws of physics are the same in every initial frame of
reference; and
* the speed of light is the same in all inertial frames of references
and is independent of the motion of the source.
2. If you were moving in a spaceship at a high speed relative to
Earth, would you notice a difference in your pulse rate? In the
pulse rate of the people back on Earth?
I would have noticed a difference in my pulserate, it will seem
normal at all. However, in the pulse rate of the people back on
Earth, it will seem slower than mine/normal.
73. REASON OUT!
3. How does the length of an object change when it is moving at
a very high speed relative to an observer?
The length of an object change when it is moving at a very high
speed relative to an obeserver by:
* 87% of c = 0.5 m
* 99.5% at c = 0.1 m
* And when the speed nearing to c or at exactly c, the length of
the object will be contracted to zero.
4. Can we look at the equation E = mc2 in another way and say
that matter transforms into pure energy when it is traveling at
the speed of light squared?
No, no no! Matter cannot be made to move at the speed of light,
let alone the speed of light squared (which is not speed)! The
equation E = mc2 simply means that energy and mass are “two
sides of the same coin.
5. Is it possible to travel faster than the speed of light?
74. MAY KAUGNAYAN BA ANG
GALAW SA PAGLIPAD NG
SASAKYANG PANHIMPAPAWID
MULA SA IYONG KINALALAGYAN
OR INUUPUAN?
Wala , as based on the first postulate of
the special theory of relativity which
states that the laws of physics are the
same in every initial frame of reference;
and
* the second theory which states that the
speed of light is the same in all inertial
frames of references and is independent
75. LEARNING COMPETENCY
Explain the consequences of
the postulates of Special
Relativity (e.g. relativity of
simultaneity, time dilation,
length contraction , mass
energy equivalence, and cosmic
speed limit (S11/12PS-IVi-j-
76. LEARNING OBJECTIVES: AT
THE END OF THE LESSON,
YOU ARE ABLE TO:
* Internalize the concept of the Theory of
Special Relativity based on the main
postulates stated by ALBERT EINSTEIN;
* Explain the consequences of the
postulates of Special Relativity (e.g.
relativity of simultaneity, time dilation,
length contraction , mass energy
equivalence, and cosmic speed limit; and
* Solve problems applying the concept of
the consequences of the postulates of
77. QUIZ #1-2 DIRECTIONS: READ THE
QUESTIONS CAREFULLY. ENCIRCLE THE
LETTER OF THE CORRECT ANSWER.
1. What property that illustrates that two events happening at the
same time in a frame of reference is a property known as the
relativity of simultaneity.
A. Time Dilation B. Relativistic Mass C. Cosmic Speed Limit D.
Relativity of Simultaneity
2. What is true about the special theory of relativity?
A. The laws of physics are the same in every initial frame of
reference; and the speed of light is the same in all inertial frames
of reference and is independent of the motion of the source.
B. The laws of physics are different in every initial frame of
reference; but the speed of light is the same in all inertial frames
of reference and is independent of the motion of the source.
C. The laws of physics are the same in every initial frame of
reference; but the speed of light is different in all inertial frames
of reference and is independent of the motion of the source.
D. The laws of physics are different in every initial frame of
reference; and the speed of light is different in all inertial frames
78. QUIZ
# 3-5Solve the following problems. Find your correct
answer in the choices. Encircle the letter of the correct
answer on your paper.
3. The NASA discovered an exo planet 14.3 lightyears
away from Earth.
A. 8.55 years B. 8.56 years C. 8.57 years D.
8.58 years
4. The NASA Spacecraft is travelling at 97% of the speed
of light to go there and back in 35.2 years. How long
would be is the travel if time dilation is applied?
A. 0.85 c B. 0.86 c C. 0.87 c D.
0.88 c
5. A spacewoman travels by a spherical planet so fast
that it appears to her to be an ellipsoid (egg shaped). If
she sees the short diameter as half the long diameter,
79. ANSWE
R:
1. What property that illustrates that two events happening at the same
time in a frame of reference is a property known as the relativity of
simultaneity.
A. Time Dilation B. Relativistic Mass C. Cosmic Speed Limit D. Relativity
of Simultaneity
2. What is true about the special theory of relativity?
A. The laws of physics are the same in every initial frame of reference;
and the speed of light is the same in all inertial frames of reference and
is independent of the motion of the source.
B. The laws of physics are different in every initial frame of reference;
but the speed of light is the same in all inertial frames of reference and
is independent of the motion of the source.
C. The laws of physics are the same in every initial frame of reference;
but the speed of light is different in all inertial frames of reference and
is independent of the motion of the source.
D. The laws of physics are different in every initial frame of reference;
and the speed of light is different in all inertial frames of reference and
is independent of the motion of the source.
80. ANSWE
R:
3. The NASA discovered an exo planet 14.3
lightyears away from Earth.
A. 8.55 years B. 8.56 years C. 8.57 years D.
8.58 years
4. The NASA Spacecraft is travelling at 97% of the
speed of light to go there and back in 35.2 years.
How long would be is the travel if time dilation is
applied?
A. 0.85 c B. 0.86 c C. 0.87 c D.
0.88 c
5. A spacewoman travels by a spherical planet so
fast that it appears to her to be an ellipsoid (egg
shaped). If she sees the short diameter as half the
long diameter, what is her speed relative to the
81. PROBLEMS. WRITE THE
SOLUTION THAT SUPPORTS YOUR
ANSWER.
1. IF THE COMBINATION OF PROTONS AND
NEUTRONS IN AN ATOM’S NUCLEUS RESULTS
IN MASS DEFECT OF 0.528 AMU ( 1 AMU =
1.66 X 10-27 KG ), WHAT IS THE BINDING
ENERGY FOR THIS ATOM?
2. A PARTICLE MASS OF 1.67 X 10-24 KG
TRAVELS WITH VELOCITY OF 0.65
C.COMPUTE ITS REST MASS.
REFLECT:
OBSERVE THE DIFFERENT SITUATIONS AT
HOME OR IN SCHOOL WHERE THE
DIFFERENT CONSEQUENCES OF SPECIAL
THEORY OF RELATIVITY ARE SHOWN. WRITE
Assignm
ent
82. REFERENCES
Padolina, Padua, Crisostomo and Alumaga. Physical Science, Vibal
Group Inc.,
2016.
Sears, Zemansky, and Young. University Physics,Seventh Edition,
Addion-Wesly
Publishing Company, 1987.
Special Relativity Presentation EXPRESS
https://www.phas.ubc.ca
uw.physics.wisc.edu
https.//byjus.com
varsitytutors.com
