Certain types of particle detectors can be used to reconstruct the tracks left by unstable, fast-moving sub-atomic particles. Assumethat a track with a length of L=2.97 mm in the laboratory frame of reference has been observed. Further assume that youdetermined from other detector data that the particle moved at a speed of L=0.910 ⚫ c, also in the laboratory frame of reference. cdenotes the speed of light in vacuum. What proper lifetime would you determine for this particle from the data given?T= 4.0S

This completes the full solution with explanations for each part.

Answered: Certain types of particle detectors can…

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter5: Relativity

Section: Chapter Questions

Problem 31P: A spaceship, 200 m long as. seen on board, moves by the Earth at 0.970c. What is its length as...

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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?
A neutron lives 900 s when at rest relative to a observer. How fast is the neutron moving relative to a observer who measures its life span to be 2065 s?
(a) How long would the mum] in Example 5.3 have lived as observed on Earth if its velocity was. 0.0500c? (b) How far would it have traveled as observed on Earth? (c) What distance is this in the muon’s frame?
The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. If the number of muons at t = 0 is N0, the number at time t is given by , where τ is the mean lifetime, equal to 2.2 μs. Suppose the muons move at a speed of 0.95c and there are 5.0 × 104 muons at t = 0. (a) What is the observed lifetime of the muons? (b) How many muons remain after traveling a distance of 3.0 km?
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?
Calculate the momentum of a proton moving with a speed of (a) 0.010c, (b) 0.50c, (c) 0.90c. (d) Convert the answers of (a)(c) to MeV/c.
Check Your Understanding Shaw that if a time increment dt elapses for an observer who sees the particle moving with velocity v, it corresponds to a proper lime particle increment for the particle of d=dt.
Check Your Understanding A particle is traveling through Earth’s atmosphere at a speed of 0.750c. To an earthbound observer, the distance it travels is 2.50 km. How far does the particle travel as viewed from the particle’s reference frame?
. If the relativistic kinetic energy of a particle is 9 times its rest energy, at what fraction of the speed of light must the particle be traveling?
Check Your Understanding What is the kinetic energy of an electron if its speed is 0.992c?
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 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?

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