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Chapter 37: Q1P (page 1145)

The mean lifetime of stationary muons is measured to be 2.2000渭s. The mean lifetime of high-speed muons in a burst of cosmic rays observed from Earth is measured to be 16.000渭s. To five significant figures, what is the speed parameter 尾of these cosmic-ray muons relative to Earth?

Short Answer

Expert verified

The speed parameter of cosmic ray muons is 0.99050.

Step by step solution

01

Identification of given data 

The mean life time for stationary muons is t0=2.20渭s

The mean life time for high-speed muons is t=16渭s

The speed parameter in the above problem is found by considering the Lorentz factor as the ration of mean life time for stationary muons to mean life time of high-speed muons.

02

Determination of speed parameter of cosmic ray muon relative to Earth 

The speed parameter of cosmic ray muons is given as:

尾=1-t0t2

Substitute all the values in equation.

尾=1-2.20渭s16渭s2尾=0.99050

Therefore, the speed parameter of cosmic ray muons is 0.99050

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Most popular questions from this chapter

Figure 37-20 shows the triangle of Fig 37-14 for six particles; the slanted lines 2 and 4 have the same length. Rank the particles according to (a) mass, (b) momentum magnitude, and (c) Lorentz factor, greatest first. (d) Identify which two particles have the same total energy. (e) Rank the three lowest-mass particles according to kinetic energy, greatest first.

In fig. 37-9, the origins of the two frames coincide at t=t'=0 and the relative speed is 0.950c. Two micrometeorites collide at coordinates x=100km and t=200渭s according to an observer in frame S. What are the (a) spatial and (b) temporal coordinate of the collision according to an observer in frame S' ?

In Fig. 37-35, three spaceships are in a chase. Relative to an x-axis in an inertial frame (say, Earth frame), their velocities are vA=0.900c, vB, and vc=0.900c. (a) What value of vBis required such that ships A and C approach ship B with the same speed relative to ship B, and (b) what is that relative speed?

A relativistic train of proper length 200 m approaches a tunnel of the same proper length, at a relative speed of 0.900c. A paint bomb in the engine room is set to explode (and cover everyone with blue paint) when the front of the train passes the far end of the tunnel (event FF). However, when the rear car passes the near end of the tunnel (event RN), a device in that car is set to send a signal to the engine room to deactivate the bomb. Train view: (a) What is the tunnel length? (b) Which event occurs first, FF or RN? (c) What is the time between those events? (d) Does the paint bomb explode? Tunnel view: (e) What is the train length? (f) Which event occurs first? (g) What is the time between those events? (h) Does the paint bomb explode? If your answers to (d) and (h) differ, you need to explain the paradox, because either the engine room is covered with blue paint or not; you cannot have it both ways. If your answers are the same, you need to explain why?

Question: The mass of an electron is 9.10938188脳10-31kg. To eight significant figures, find the following for the given electron kinetic energy: (a)localid="1663051516359" 纬and (b)尾localid="1663053404383" 尾forK=1.0000000keV, (c)localid="1663051781874">纬and (d)localid="1663051803695" 尾for, K=1.0000000MeVand then (e)localid="1663051835448" 纬and (f)localid="1663051820843" 尾forK=1.0000000GeV.
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