Concept explainers
(a) Determine the Lorentz transformation matrix giving position and time in frame
Explain this result.
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Modern Physics
Additional Science Textbook Solutions
The Cosmic Perspective (8th Edition)
The Cosmic Perspective Fundamentals (2nd Edition)
College Physics: A Strategic Approach (3rd Edition)
College Physics: A Strategic Approach (4th Edition)
Essential University Physics (3rd Edition)
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
- 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_forwardOwen and Dina are at rest in frame S, which is moving at 0.600c with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action (Fig. P9.63). Owen throws the ball to Dina at 0.800c (according to Owen), and their separation (measured in S) is equal to 1.80 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, (d) how fast is the ball moving, and (e) what time interval is required for the ball to reach Dina? Figure P9.63arrow_forwardAn observer in frame S sees lightning simultaneously strike two points 100 m apart. The first strike occurs at x1 = y1 = z1 = t1 = 0 and the second at x2 = 100 m, y2 = z2 = t2 = 0. (a) What are the coordinates of these two events in a frame S moving in the standard configuration at 0.70c relative to S? (b) How far apart are the events in S? (c) Are the events simultaneous in S? If not, what is the difference in time between the events, and which event occurs first?arrow_forward
- As seen from Earth, two spaceships A and B are approaching along perpendicular directions. If A is observed by an Earth observer to have velocity uy = 0.90c and B to have a velocity ux = +0.90c, find the speed of ship A as measured by the pilot of B.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_forwardA spacecraft moves at a speed of 0.900c. If its length is L as measured by an observer on the spacecraft, what is the length measured by a ground observer?arrow_forward
- Owen and Dina are at rest in frame S. which is moving at 0.600c with respect to frame S. They play a game of catch while Ed. at rest in frame S, watches the action (Fig. P39.91). Owen throws the ball to Dina at 0.800c (according to Owen), and their separation (measured in S') is equal to 1.80 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, (d) how fast is the ball moving, and (e) what time interval is required for the ball to reach Dina?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_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
- A yet-to-be-built spacecraft starts from Earth moving at constant speed to the yet-to-be-discovered planet Retah, which is 20 lighthours away from Earth. It takes 25 h (according to an Earth observer) for a spacecraft to reach this planet. Assuming that the clocks are synchronized at the beginning of the journey, compare the time elapsed in the spacecraft’s frame for this one-way journey with the time elapsed as measured by an Earth-based clock.arrow_forwardConsider an electron moving with speed 0.980c. a. What is the rest mass energy of this electron? b. What is the total energyof this electron? c. What is the kinetic energy of this electron?arrow_forwardAccording 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_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning