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Government PropertyNOT FOR SALE NOTPhysical ScienceQuarter 2 - Module 8Einstein’s Special and General RelativityDepartment of Education ● Republic of the PhilippinesSenior High SchoolPhysical Science- Grade 12 Alternative Delivery Mode Quarter 2 - Module 8: Einstein’s Special and General Relativity ...

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NOT FOR SALE

Senior High School

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Physical Science Quarter 2 - Module 8 Einstein’s Special and General Relativity

Department of Education ● Republic of the Philippines

Physical Science- Grade 12 Alternative Delivery Mode Quarter 2 - Module 8: Einstein’s Special and General Relativity First Edition, 2020 Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalty. Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this book are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them. Published by the Department of Education – Division of Cagayan de Oro Schools Division Superintendent: Dr. Cherry Mae L. Limbaco, CESO V Development Team of the Module Author/s: Doris D. Pabalate, Maribeth T. Auman, Lelibeth D. Igtos Reviewers: Illustrator and Layout Artist: Management Team Chairperson: Dr. Arturo B. Bayocot, CESO III Regional Director Co-Chairpersons:

Dr. Victor G. De Gracia Jr. CESO V Asst. Regional Director Cherry Mae L. Limbaco, PhD, CESO V Schools Division Superintendent Alicia E. Anghay, PhD, CESE Assistant Schools Division Superintendent Mala Epra B. Magnaong, Chief ES, CLMD

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Senior High School

Physical Science Quarter 2 - Module 8 Einstein’s Special and General Relativity

This instructional material was collaboratively developed and reviewed by educators from public and private schools, colleges, and or/universities. We encourage teachers and other education stakeholders to email their feedback, comments, and recommendations to the Department of Education at action@ deped.gov.ph. We value your feedback and recommendations.

Department of Education ● Republic of the Philippines

Table of Contents What This Module is About................................................................................................... i What I Need to Know ............................................................................................................ ii How to Learn from this Module ........................................................................................... ii Icons of this Module ............................................................................................................. iii What I Know ........................................................................................................................ iii

Lesson 1: Special Relativity ......................................................................................................................... 1 What I Need to Know.......................................................................................... 1 What’s New: Observing Light ........................................................................... 2 What Is It .............................................................................................................. 3 What’s More: Special Relativity experiment .................................................. 4 What I Have Learned: Test your Analysis ........................................................ 5 What I Can Do: Reflection Paper ...................................................................... 6

Lesson 2: Consequences of Postulate of Special Relativity .................................. 7 What’s In ....................................................................................................... 7 What I Need to Know.................................................................................... 7 What’s New: Guessing Time ..................................................................... ..9 What Is It: .................................................................................................... .10 What’s More: Perform Me Correctly .......................................................... .14 What I Have Learned: Explain Briefly……………………………………..15 What I Can Do: Reaction Paper … ............................................................ ..16

Lesson 3: Consequences of Postulate of General Relativity ................................ 17 What’s In ....................................................................................................... 17 What I Need to Know.................................................................................... 17 What’s New: Find A Partner ...................................................................... ..18 What Is It: .................................................................................................... 18 What’s More: I am Bent .............................................................................. . 21 What I Have Learned: Expound Me ……………………………………… 22 What I Can Do: Let’s React ………………………………………………22

Lesson 4: Speeds and Distances of Far-off Objects ....................................................... 23 What I Need to Know.................................................................................... 23 What’s New: Knowing Parallax…………. ................................................. ..24 What Is It:…… ............................................................................................ ..24 What’s More: Show It To Me! ................................................................... ..30 What I Have Learned: Test Your Analysis ……………………………..…31 What I Can Do: How far? How Powerful? …………..……………………32

Lesson 5: The Expanding Universe ..................................................................................................... 35 What’s In ....................................................................................................... 35 What I Need to Know.................................................................................... 35 What’s New: Think Pair-Share ................................................................... ..36 What Is It: ................................................................................................... ..36 What’s More:The Expanding Universe- Galaxies … ...................................... ..41 What I Have Learned: Test Your AnalysisCalculating the age of the Universe ……………....42 What I Can Do: Sketch Me Up!……………………………………………42 Summary………………………………………..…………………………………………43 Assessment: (Post-Test)…………………………………………………………………...44 Key to Answers……………………………………………………………………………46 References…………………………………………………………………………………48

What This Module is About This Module in Physical Science attempts to supplement the students’ knowledge in Einstein’s Special and General Theory of Relativity as well as the Understanding on the Expanding Universe and to develop their science process skills. It is designed to make students’ study time more profitable and to provide a better understanding of Physical Science. Each lesson should be read thoroughly before answering the activities in each topic in order to be successful and efficient in every task given. The introductory remarks at the beginning of lesson provide a brief review of the background upon which the activity is predicated. The questions appearing in the activity are designed to check the student’s understanding of the quantitative principle learned inside and outside the classroom. The authors took into consideration the adequacy and endeavors needed as well as the suitability of equipment and materials involved in making this module. It is hope that this module will not only make the activities instructional but also more enjoyable. The following are the lessons contained in this module: 1. Einstein’s Special Relativity 2. Einstein’s General Relativity. 3. Expanding Universe

What I Need to Know

At the end of this module, you should be able to: 1. Explain how special relativity resolved the conflict between Newtonian mechanics

and Maxwell’s electromagnetic theory (S11/12PS-IVi-68); 2. 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-69); 3. Explain the consequences of the postulates of General Relativity (e.g., correct

predictions of shifts in the orbit of Mercury, gravitational bending of light, and black holes) (S11/12PS-IVi-70); 4. Explain how the speeds and distances of far-off objects are estimated (e.g.,

doppler effect and cosmic distance ladder) (S11/12PS-IVi-71);

5. Explain how we know that we live in an expanding universe, which used to be hot

and is approximately 14billion years old (S11/12PS-IVi-72).

How to Learn from this Module To achieve the objectives cited above, you are to do the following: • Take your time reading the lessons carefully. • Follow the directions and/or instructions in the activities and exercises diligently. • Answer all the given tests and exercises.

Icons of this Module What I Need to Know

This part contains learning objectives that are set for you to learn as you go along the module.

What I know

This is an assessment as to your level of knowledge to the subject matter at hand, meant specifically to gauge prior related knowledge This part connects previous lesson with that of the current one.

What’s In

What’s New

An introduction of the new lesson through various activities, before it will be presented to you

What is It

These are discussions of the activities as a way to deepen your discovery and understanding of the concept.

What’s More

These are follow-up activities that are intended for you to practice further in order to master the competencies.

What I Have Learned

Activities designed to process what you have learned from the lesson

What I can do

These are tasks that are designed to showcase your skills and knowledge gained, and applied into real-life concerns and situations.

What I Know (Pre-Test) Multiple Choice. Select the letter of the best answer from among the given choices. 1. At what rate do the EM waves travel according to Maxwell's electromagnetic wave theory? A. 3.00 x 108ms-1

C. 3.00 x 10-8ms-1

B. 6.00 x 108 ms-1

D. 6.00 x 10-8 ms-1

2. Which among the following resolves the conflict between Newtonian mechanics and Maxwell's electromagnetic theory? A. Theory of general relativity B. Theory of special relativity

C. Law of universal gravitation D. Law of conservation of energy

3. Einstein's theory of special relativity corrected the laws of motion first proposed by: A. Hertz C. Maxwell B. Galileo D. Newton 4. One of two identical twins becomes an astronaut, while the other becomes a real estate broker. The astronaut embarks on high-speed space travel and is gone for several years. Upon the astronaut's return, the two twins are reunites and observe their physical appearances. The result will be that A. both have aged the same. B. the astronaut has aged less.

C. the real estate broker has aged less. D. None of the above

5. Clocks in a stationary reference frame, compared to identical Clocks in a moving reference frame, appear to run A. at the same rate. B. backward in time.

C. faster. D. slower.

6. An object that looks green in empty space is positioned near but not in a black hole. From the black hole far from the observer, the object would appear A. black. C. green. B. blue.

D. red.

7. The Principle of Equivalence in the General Theory of Relativity states that inertial and gravitational masses are

A. identical. B. increasing.

C. not significant. D. varied.

8. Which of the following is not a consequence of General Theory of Relativity? A. Black Hole

C. Precession in the Orbit of Mercury

B. Gravitational Lensing Effect

D. Time Dilation

9. The Einstein Cross is an evidence of A. Black Hole B. Gravitational Lensing Effect

C. Increased gravity D. Shifting of orbit

Lesson

1

SPECIAL RELATIVITY

What I Need to Know

Relativity is not new. Galileo explained that motion is a relative way back around the year 1600. Wherever you happen to be, it seems like you are at a fixed point, and that everything moves with respect to you. Everyone else feels the same way. With respect to a fixed point motion is always measured. This is what we called establishing a frame of reference. In the discussion of relativity light is always involved for theories related to electromagnetism are inconsistent with Galileo’s and Newton’s explanation of relativity. The true nature of light was a hot topic of discussion and controversy in the late nineteenth century and it is now explain how special relativity resolved the conflict between Newtonian mechanics and Maxwell's electromagnetic theory. Newtonian Mechanics is also called as classical mechanics containing concepts that do not entirely agree with other known theories in Physics like electromagnetic theory of Maxwell but when Einstein presented his theory of special relativity, the conflict between the two great physicists was resolved. Maxwell’s theory is in fact contradicts with Newtonian Mechanics, and in trying to find the resolution to this conflict so, Einstein, lead to his theory of special relativity. Maxwell’s equation withstood the conflict, but it was Newtonian mechanics that were corrected by relativistic mechanics. But how the theory of special relativity resolved the conflict between the two famous physicists? What is Einstein’s theory of special relativity?

1

What’s New

Activity 8.1.1. Observing Light What can you tell about the picture below? Which theory regarding light is correct the Newtonian’s Theory or Maxwell Theory? Why?

https://doi.org/10.1119/1.4895355

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What Is It Newtonian mechanics discusses the everyday motion of the objects of normal size around us including the force that causes these motions. The concepts under Newtonian mechanics are mainly based on ideas of Newton about motion which correctly describes the state of motion of an object whether at rest or moving in a straight path and the forces that maintain and can cause changes in the body’s states of motion. Furthermore, Newtonian mechanics is based on the assumption of absolute space and time. This means that the distance between two points, and the time that passes between two events don’t depend on the coordinate system you choose. Therefore, a coordinate transformation must leave them unchanged. Maxwell’s electromagnetic theory consists of four formulas from the different works of Faraday and other physicists that unite all the concepts of electricity and magnetism that had the findings that electric and magnetic fields spread as waves. In 1886, Hertz proved that these waves really exist and the propagation speed of these waves can be calculated using the formula:

·

https://www.facebook.com/notes/physical-science/91-theory-of-specialrelativity/3390893954260139/

Moreover, Maxwell observed that the value of the above expression is equivalent to the speed of light c (3.0 x 108 m/s) which implies that speed of light c must also be constant in which the conflict between Newtonian mechanics and Maxwell’s theory starts.

If we consider a moving object with the of speed 100 m/s and switched on the flashlight, according to Newtonian mechanics the speed of the light from the flashlight would be 100 m/s + c and dispute what Maxwell’s theory stating that the speed of light is a constant value. Which is true between these two concepts? 3 The theory of special relativity proposed by Einstein in 1905, is a theory in physics that concern the relationship between space and time objects that are moving at a consistent speed in a straight line. Simply placing an object approaching the speed of light, its mass becomes infinite, and it is unable to go any faster than light travels. It is the generally accepted and experimentally confirmed. The two main postulates of special relativity are: 1. The laws of physics are the same in all reference frames that are moving at a constant velocity (not accelerating). 2. The speed of light is the same in all of these reference frames, even if the source of the light is moving. The second postulate clearly tells that Maxwell’s theory is correct but does imply that Newtonian mechanics is wrong. But not totally, the postulates of Einstein tell us that Newtonian mechanics has limitations in terms of its application. Considering moving objects with speed very small compared to the speed of light, Newtonian mechanics applies like the speeds of a flying ball and running car but considering a speed that is near to the speed of light, a new concept must be included to supply the limit of Newtonian mechanics and that is the Lorentz transformation the counterpart of the Galilean transformation of the Newtonian mechanics.

What’s More Activity 8.1.2. Special Relativity Experiment Do this activity with a partner. Mrs. Yap is standing in a ground while Mr. Yap is riding on a truck that is moving with velocity v. Mr. Yap switched on the flashlight in the direction in which he is moving.

https://aether.lbl.gov/www/classes/p139/exp/gedanken.html

Question: What happens? What was the observation of the Mrs. Einstein on the light as it travels? How about to Mr. Einstein what was his observation to the light? Do they have the same observation? Answer: ___________________________________________________________________________ ___________________________________________________________________________ _

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