The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6 x 10-8 s. (a) If the meson moves with a speed of 0.99c, what is its mean lifetime as measured by an observer on Earth? (b) What is the average distance it travels before decaying, as measured by an observer on Earth? m (c) What distance would it travel if time dilation did not occur? m

The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6 x 10-8 s. (a) If the meson moves with a speed of 0.99c, what is its mean lifetime as measured by an observer on Earth? (b) What is the average distance it travels before decaying, as measured by an observer on Earth? m (c) What distance would it travel if time dilation did not occur? m

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter1: Relativity I

Section: Chapter Questions

Problem 10P: The average lifetime of a pi meson in its own frame of reference is 2.6 × 10−8 s. If the meson moves...

See similar textbooks

Similar questions

The average lifetime of a pi meson in its own frame of reference is 2.6 × 10−8 s. If the meson moves with a speed of 0.95c, what is (a) its mean lifetime as measured by an observer on Earth and (b) the average distance it travels before decaying, as measured by an observer on Earth?
What is the kinetic energy in MeV of a meson that lives s as measured in the laboratory, and when at rest relative to an observer, given that its rest energy is 135 MeV?
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?
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.
A muon has a rest mass energy of 105.7 MeV, and it decays into an electron and a massless particle. (a) If all the lost mass is converted into the electron's kinetic energy, find for the electron. (b) What is the electron's velocity?
Check Your Understanding a. A particle travels at 1.90108m/sand lives 2.10108swhen at rest relative to an observer. How long does the particle live as viewed in the laboratory? b. Space craft A and B pass in opposite directions at a relative speed of 4.00107m/s . An internal clock in space craft A causes it to emit a radio signal for 1.00 s. The computer in spacecraft B corrects for the beginning and end of the signal having traveled different distances, to calculate the time interval during which ship A was emitting the signal. What is the time interval that the computer in spacecraft B calculates?
If two spaceships are heading directly toward each other at 0.800c, at what speed must a canister be shot from the first ship to approach the other at 0.999c as seen by the second ship?
At what speed does a clock move if it is measured to run at a rate one-half the rate of a clock at rest with respect to an observer?
An observer sees two events 1.5108s apart at a separation of 800 m. How fast must a second observer be moving relative to the first to see the two events occur simultaneously?
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. 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 P9.63
Suppose the primed and laboratory observers want to measure the length of a rod that rests on the ground horizontally in the space between the helicopter and the tower (Fig. 39.8B). To derive the length transformation L = L (Eq. 39.5), we had to assume that the positions of the two ends were determined simultaneously. What happens to the length transformation equation if both observers measure the end below the helicopter at one time t1 and the other end at a later time t2?
A spacecraft is launched from the surface of the Earth with a velocity of 0.600c at an angle of 50.0° above the horizontal, positive x-axis. Another spacecraft is moving past with a velocity of 0.700c in the negative x direction. Determine the magnitude and direction of the velocity of the first spacecraft as measured by the pilot of the second spacecraft.