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(a) How far does the muon in Example 28.1 travel according to the Earth-bound observer?

(b) How far does it travel as viewed by an observer moving with it? Base your calculation on its velocity relative to the Earth and the time it lives (proper time).

(c) Verify that these two distances are related through length contraction .

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Rochelle Enrera
Rochelle EnreraLv10
4 Mar 2021

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

(a) How long does it take the astronaut in Example 28.2 to travel at (as measured by the Earth-bound observer)? (b) How long does it take according to the astronaut? (c) Verify that these two times are related through time dilation with  as given.

Example 28.2 Calculating Length Contraction: The Distance between Stars Contracts when You Travel at High Velocity Suppose an astronaut, such as the twin discussed in Simultaneity and Time Dilation, travels so fast that . (a) She travels from the Earth to the nearest star system, Alpha Centauri, away as measured by an Earth-bound observer. How far apart are the Earth and Alpha Centauri as measured by the astronaut? (b) In terms of c , what is her velocity relative to the Earth? You may neglect the motion of the Earth relative to the Sun. (See Figure 28.11.)

Muons are unstable subatomic particles that decay to electrons with a mean lifetime of 2.2 μs . They are produced when cosmic rays bombard the upper atmosphere about 11.4 km above the earth's surface, and they travel very close to the speed of light. The problem we want to address is why we see any of them at the earth's surface.

What is the greatest distance a muon could travel during its 2.2 μs lifetime?

According to your answer in part A, it would seem that muons could never make it to the ground. But the 2.2 μs lifetime is measured in the frame of the muon, and muons are moving very fast. At a speed of 0.999 c, what is the mean lifetime of a muon as measured by an observer at rest on the earth?

Express your answer using two significant figures.

How far would the muon travel in this time?

Express your answer using two significant figures.

From the point of view of the muon, it still lives for only 2.2 μs , so how does it make it to the ground? What is the thickness of the 11.4 km of the atmosphere through which the muon must travel, as measured by the muon?

Express your answer using two significant figures.

There two general consequences of relativity: moving clocksrunslow, and moving lengths contract (although you need tocarefullyapply the definitions of proper time and proper length toavoidgetting yourself stuck in an infinite thought loop).

Please look at the problem below and explain, carefully, howthe"moving clocks run slow" and "moving lengths contract" rulesapplyto parts a, b, and c. That is, why are you not surprised atthesizes of your answers in these three parts?


Aninterstellar space probe is launched from Earth. After abriefperiod of acceleration it moves with a constantvelocity, 72.0%of the speed of light. Its nuclear-poweredbatteries supply theenergy to keep its data transmitter activecontinuously. Thebatteries have a lifetime of 15.9 years as measured in a restframe.
(a) How long dothe batteries on the space probe last as measured bymissioncontrol on Earth?
yr
(b) How far is the probe from Earth when its batteries fail,asmeasured by mission control?
ly
(c) How far is the probe from Earth, as measured by itsbuilt-intrip odometer; when its batteries fail?
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(d) For what total time after launch is data received from theprobeby mission control? Note that radio waves travel at the speedoflight and fill the space between the probe and Earth at the timethebattery fails.
yr

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