Relativity and Its Applications PDF

Chapter 3 Relativity and Its Applications Merged by Abdullah Al Sakib Monju Akter Mou Md. Roni Islam  Modern Physics | 1 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 2 Merged by: AAS|MAM|RIM Lecturer, De...

Chapter 3 Relativity and Its Applications Merged by Abdullah Al Sakib Monju Akter Mou Md. Roni Islam  Modern Physics | 1 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 2 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 3 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 4 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 5 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 6 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 7 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 8 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 9 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 10 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 11 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 12 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 13 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 14 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 15 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 16 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 17 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 18 Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 19 3.8 Applications of Relativity in Space Travel Space travel allows humanity to explore distant worlds and uncover the mysteries of the cosmos, but as we journey deeper into space, we must confront fundamental principles that govern our universe, particularly Einstein's Theory of Relativity. Proposed in 1905, the Theory of Special Relativity introduced spacetime—a four-dimensional framework combining space and time—and revealed that the laws of physics are constant for all observers moving at constant speeds relative to each other, regardless of their reference frames. One crucial aspect of this theory is time dilation, where time slows as an object approaches the speed of light, an effect that becomes significant in interstellar missions at relativistic velocities. General Relativity, introduced by Einstein in 1915, expanded on this by incorporating gravity, explaining that massive objects like planets warp spacetime, causing objects to follow curved paths—a phenomenon we observe as gravity. This concept has essential applications for space travel, affecting satellite navigation systems, which must account for time dilation due to their higher speeds and weaker gravitational fields compared to Earth, and for planning interplanetary missions that navigate the spacetime curvature near massive celestial bodies. While speculative concepts like warp drive, which involve bending spacetime for faster-than-light travel, remain within the realm of science fiction, Einstein's theories continue to fuel our imagination for what might one day be possible. Through each mission, we advance our understanding of the universe while honoring the brilliance of Einstein's work that shaped modern physics and underpins our progress in space exploration. Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU  Modern Physics | 20 Mathematical Problems for Practice 1. A woman at the age of 30 left in a spacecraft moving with velocity 0.98 c for trip to the space with leaving behind a daughter of 10 years old on earth. According to the counting of time she returned to the earth spending 30 years in space. After returning whose age was what among them? Ans: Daughter: 40y and women: 35.97 y 2. At what speed a hypothetical train should move so that its length will be one third of the stationary length? Ans: [same 4 below] 3. The length of a rocket on the ground is 100m. When the rocket moves with respect to a stationary observer on the ground its length appears to be 99.5m. Calculate the speed of the rocket. Ans: 29.96x106 ms-1 4. At what speed a spacecraft move so that 1 day in space will be equal to 2 days on earth? Ans:2.598x108 ms-1 5. Mass of a person is 99 kg. Inside a rocket of what speed his weight will be 100 kg from an observer on the ground? [Ans:4.23x107ms-1 ] 6. If an electron moves with a velocity of 0.99c, what is its mass? [Ans: 6.45x10-30kg] 7. Derive the formula of Mass dilation or increase according to the theory of relativity. [Hint: Use the momentum conservation law] 8. An astronaut, at the age of 30 years, went to investigate the Milky Way by a spaceship moving with a speed of 2.4 ×108 ms- 1 and returned after 50 years (according to the calendar of the earth). What will be his age? Ans: 60years. 9. The length of a rocket is 100 m on the earth. When it was flying a person on the earth measured its length as 99 m. What is the speed of the rocket? Ans ; 4.2 ×107 ms-1 10. An electron is moving at a speed of 0.99c, what is its moving mass? Rest mass of electron mo = 9.1 ×10-31 kg. Ans ; Ans: 64.5x10-31kg] 11. In the physics laboratory Mr. Hassan found the density of a 1 m long metallic object 19.3 × 10 3 kg m - 3.On the other hand Pabon determined the density of the object in the moving frame moving with a velocity 0.9 e along the length of the object. (a) Find the length of the object in the moving frame. Ans: 0.4359m (b) Will Mr. Hassan and Pabon get the density of the object the same? Analyze mathematically. Ans: 101.6 x 103 kgm-3 (not same) 12. The length and mass of a rocket on earth are 10 m and 5000 kg respectively. It started moving with a velocity 3× 107 ms¹ with respect to a stationary observer on earth. (a) Find the moving length of the rocket in the light of the stem. Ans: 9.95m (b) If the velocity of the rocket is doubled, what change in its mass will take place- explain with mathematical analysis. Ans: the mass will be increased by 77.915 kg. Merged by: AAS|MAM|RIM Lecturer, Dept. of CSE, DIU