Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
9th Edition
ISBN: 9781305266292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 39, Problem 9OQ
To determine
The statements regarding fundamental postulates of special theory of relativity.
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Which of the following are part of the first postulate of Einstein's Special Theory of Relativity?
Time and weight are relative to the motion of the observer.
All the laws of physics are the same in all inertial frames of reference.
Absolute motion can always be detected.
a
I only
b
II only
c
III only
d
I, II, and III
The factor y (gamma) appears throughout the expressions of special relativity. It depends only on
the (constant) relative velocity between two inertial frames of reference.
Calculate y for the case when rel=0.93 c (where c is the speed of light in vacuum = 3.0 x 108
m/s).
Y =
What is the difference between the velocity vrel and the speed of light c if y = 4.8? In other words,
what is c-Vrel?
C-Vrel=
What is this velocity Urel expressed as a fraction of the speed of light (as the case of the first
question above)?
Vrel=
m/s
C
Special relativity has become a fundamental theory in the 20th century and is crucial for ex-
plaining many astrophysical phenomena. A central aspect of special relativity is the transfor-
mation from one reference frame to another. The following Lorentz transformation matrix gives
the transformation from a frame at rest to a moving frame with velocity v along the z-axis:
0 0 YB
1 0
0 1
YB 0 0
where B = v/cwith c being the speed of light in a vacuum, and y is the Lorentz factor:
1
V1- 32
(a) State and explain the two traditional postulates from which special relativity originates.
(b) Draw a plot of the Lorentz factor for 0 < B< 0.9 to see how its value changes.
One of the many exciting phenomena of special relativity is time dilation. Imagine astronauts
in a spaceship that is passing by the Earth with a high velocity.
(c) Are clocks ticking slower for the people on Earth or for the astronauts on the spaceship?
(d) How fast must the spaceship travel such that the clocks go twice as…
Chapter 39 Solutions
Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
Ch. 39.1 - Which observer in Figure 38.1 sees the balls...Ch. 39.1 - Prob. 39.2QQCh. 39.4 - Suppose the observer O on the train in Figure 38.6...Ch. 39.4 - Prob. 39.4QQCh. 39.4 - Prob. 39.5QQCh. 39.4 - Prob. 39.6QQCh. 39.4 - You are observing a spacecraft moving away from...Ch. 39.6 - You are driving on a freeway at a relativistic...Ch. 39.8 - Prob. 39.9QQCh. 39 - Prob. 1OQ
Ch. 39 - A spacecraft zooms past the Earth with a constant...Ch. 39 - Prob. 3OQCh. 39 - Prob. 4OQCh. 39 - Prob. 5OQCh. 39 - Prob. 6OQCh. 39 - Prob. 7OQCh. 39 - Prob. 8OQCh. 39 - Prob. 9OQCh. 39 - Prob. 10OQCh. 39 - Prob. 1CQCh. 39 - Prob. 2CQCh. 39 - Prob. 3CQCh. 39 - Prob. 4CQCh. 39 - Prob. 5CQCh. 39 - Prob. 6CQCh. 39 - Prob. 7CQCh. 39 - Prob. 8CQCh. 39 - Prob. 9CQCh. 39 - Prob. 10CQCh. 39 - Prob. 11CQCh. 39 - Prob. 12CQCh. 39 - Prob. 13CQCh. 39 - Prob. 14CQCh. 39 - Prob. 1PCh. 39 - In a laboratory frame of reference, an observer...Ch. 39 - The speed of the Earth in its orbit is 29.8 km/s....Ch. 39 - Prob. 4PCh. 39 - A star is 5.00 ly from the Earth. At what speed...Ch. 39 - Prob. 6PCh. 39 - Prob. 7PCh. 39 - Prob. 8PCh. 39 - Prob. 9PCh. 39 - An astronaut is traveling in a space vehicle...Ch. 39 - Prob. 11PCh. 39 - Prob. 12PCh. 39 - Prob. 13PCh. 39 - Prob. 14PCh. 39 - Prob. 15PCh. 39 - Prob. 16PCh. 39 - Prob. 17PCh. 39 - A cube of steel has a volume of 1.00 cm3 and mass...Ch. 39 - Prob. 19PCh. 39 - Prob. 20PCh. 39 - Prob. 21PCh. 39 - Review. In 1963, astronaut Gordon Cooper orbited...Ch. 39 - Prob. 23PCh. 39 - Prob. 24PCh. 39 - Prob. 25PCh. 39 - Prob. 26PCh. 39 - Prob. 27PCh. 39 - Prob. 28PCh. 39 - Prob. 29PCh. 39 - Prob. 30PCh. 39 - Prob. 31PCh. 39 - Prob. 32PCh. 39 - Prob. 33PCh. 39 - Prob. 34PCh. 39 - Prob. 35PCh. 39 - Prob. 36PCh. 39 - Prob. 37PCh. 39 - Prob. 38PCh. 39 - Prob. 39PCh. 39 - Prob. 40PCh. 39 - Prob. 41PCh. 39 - Prob. 42PCh. 39 - Prob. 43PCh. 39 - Prob. 44PCh. 39 - Prob. 45PCh. 39 - Prob. 46PCh. 39 - Prob. 47PCh. 39 - (a) Find the kinetic energy of a 78.0-kg...Ch. 39 - Prob. 49PCh. 39 - Prob. 50PCh. 39 - Prob. 51PCh. 39 - Consider electrons accelerated to a total energy...Ch. 39 - Prob. 53PCh. 39 - Prob. 54PCh. 39 - Prob. 55PCh. 39 - Prob. 56PCh. 39 - Prob. 57PCh. 39 - Prob. 58PCh. 39 - Prob. 59PCh. 39 - Prob. 60PCh. 39 - Prob. 61PCh. 39 - An unstable particle with mass m = 3.34 1027 kg...Ch. 39 - Prob. 63PCh. 39 - Prob. 64PCh. 39 - Prob. 65PCh. 39 - Prob. 66APCh. 39 - Prob. 67APCh. 39 - Prob. 68APCh. 39 - Prob. 69APCh. 39 - Prob. 70APCh. 39 - Prob. 71APCh. 39 - Prob. 72APCh. 39 - Prob. 73APCh. 39 - Prob. 74APCh. 39 - Prob. 75APCh. 39 - Prob. 76APCh. 39 - Prob. 77APCh. 39 - Prob. 78APCh. 39 - Prob. 79APCh. 39 - Prob. 80APCh. 39 - Prob. 81APCh. 39 - Prob. 82APCh. 39 - An alien spaceship traveling at 0.600c toward the...Ch. 39 - Prob. 84APCh. 39 - Prob. 85APCh. 39 - Prob. 86APCh. 39 - Prob. 87APCh. 39 - Prob. 88CPCh. 39 - The creation and study of new and very massive...Ch. 39 - Prob. 90CPCh. 39 - Owen and Dina are at rest in frame S, which is...
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- Which of the following statements are fundamental postulates of the special theory of relativity? More than one statement may be correct. (a) Light moves through a substance called the ether. (b) The speed of light depends on the inertial reference frame in which it is measured. (c) The laws of physics depend on the inertial reference frame in which they are used. (d) The laws of physics are the same in all inertial reference frames. (e) The speed of light is independent of the inertial reference frame in which it is measured.arrow_forwardAs measured by observers in a reference frame S, a particle having charge q moves with velocity v in a magnetic field B and an electric field E. The resulting force on the particle is then measured to be F = q(E + v × B). Another observer moves along with the charged particle and measures its charge to be q also but measures the electric field to be E′. If both observers are to measure the same force, F, show that E′ = E + v × B.arrow_forwardJoe and Moe are twins. In the laboratory frame at location S1 (2.00 km, 0.200 km, 0.150 km). Joe shoots a picture for aduration of t= 12.0 s. For the same duration as measured inthe laboratory frame, at location S2 (1.00 km, 0.200 km,0.300 km), Moe also shoots a picture. Both Joe and Moe begintaking their pictures at t = 0 in the laboratory frame. Determine the duration of each event as measured by an observer ina frame moving at a speed of 2.00 108 m/s along the x axisin the positive x direction. Assume that at t = t = 0, the origins of the two frames coincide.arrow_forward
- According to special relativity, a particle of rest mass m0 accelerated in one dimension by a force F obeys the equation of motion dp/dt = F. Here p = m0v/(1 –v2/c2)1/2 is the relativistic momentum, which reduces to m0v for v2/c2 << 1. (a) For the case of constant F and initial conditions x(0) = 0 = v(0), find x(t) and v(t). (b) Sketch your result for v(t). (c) Suppose that F/m0 = 10 m/s2 ( ≈ g on Earth). How much time is required for the particle to reach half the speed of light and of 99% the speed of light?arrow_forwardAn astronaut is traveling in a spacecraft in outer space in a straight line at a constant speed of 0.500c. Which of the following effects would she experience? (a) She would feel heavier. (b) She would find it harder to breathe. (c) Her heart rate would change. (d) Some of the dimensions of her spacecraft would be shorter. (e) None of those answers is correct.arrow_forwardSpacecraft I, containing students taking a physics exam, approaches the Earth with a speed of 0.600c (relative to the Earth), while spacecraft II, containing professors proctoring the exam, moves at 0.280c (relative to the Earth) directly toward the students. If the professors stop the exam after 50.0 min have passed on their clock, for what time interval does the exam last as measured by (a) the students and (b) an observer on the Earth?arrow_forward
- Suppose our Sun is about to explode. In an effort to escape, we depart in a spaceship at v = 0.80c and head toward the star Tau Ceti, 12 lightyears away. When we reach the midpoint of our journey from the Earth, we see our Sun explode and, unfortunately, at the same instant we see Tau Ceti explode as well. (a) In the spaceship’s frame of reference, should we conclude that the two explosions occurred simultaneously? If not, which occurred first? (b) In a frame of reference in which the Sun and Tau Ceti are at rest, did they explode simultaneously? If not, which exploded first?arrow_forwardWhat happens to the density of an object as its speed increases, as measured by an Earth observer?arrow_forwardTwo powerless rockets are on a collision course. The rockets are moving with speeds of 0.800c and 0.600c and are initially 2.52 × 1012 m apart as measured by Liz, an Earth observer, as shown in Figure P1.34. Both rockets are 50.0 m in length as measured by Liz. (a) What are their respective proper lengths? (b) What is the length of each rocket as measured by an observer in the other rocket? (c) According to Liz, how long before the rockets collide? (d) According to rocket 1, how long before they collide? (e) According to rocket 2, how long before they collide? (f) If both rocket crews are capable of total evacuation within 90 min (their own time), will there be any casualties? Figure P1.34arrow_forward
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Time Dilation - Einstein's Theory Of Relativity Explained!; Author: Science ABC;https://www.youtube.com/watch?v=yuD34tEpRFw;License: Standard YouTube License, CC-BY