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Chapter 37: Q1P (page 1145)

The mean lifetime of stationary muons is measured to be 2.2000μs. The mean lifetime of high-speed muons in a burst of cosmic rays observed from Earth is measured to be 16.000μs. To five significant figures, what is the speed parameter βof 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=2.20μs

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

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:

β=1-t0t2

Substitute all the values in equation.

β=1-2.20μs16μs2β=0.99050

Therefore, the speed parameter of cosmic ray muons is 0.99050

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Most popular questions from this chapter

A spaceship is moving away from Earth at speed 0.20c. A source on the rear of the ship emits light at wavelength 450 nm according to someone on the ship. What (a) wavelength and (b) color (blue, green, yellow, or red) are detected by someone on Earth watching the ship?

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Bullwinkle in reference frame S' passes you in reference frame S along the common direction of the x' and x axes, as in Fig. 37-9. He carries three meter sticks: meter stick 1 is parallel to the x' axis, meter stick 2 is parallel to the y' axis, and meter stick 3 is parallel to the z' axis. On his wristwatch he counts off 15.0 s, which takes 30.0 s according to you. Two events occur during his passage. According to you, event 1 occurs at x1=33.0mand t1=22.0ns, and event 2 occurs at x2=53.0mand t2=62.0ns. According to your measurements, what is the length of (a) meter stick 1, (b) meter stick 2, and (c) meter stick 3? According to Bullwinkle, what are (d) the spatial separation and (e) the temporal separation between events 1 and 2, and (f) which event occurs first?
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