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$\bullet$ Why are we bombarded by muons? Muons are unstablesubatomic particles (more on them in Chapter 30 ) that decay toelectrons with a mean lifetime of 2.2$\mu \mathrm{s}$ . They are producedwhen cosmic rays bombard the upper atmosphere about 10 $\mathrm{km}$above the earth's surface, and they travel very close to the speedof light. The problem we want to address is why we see any ofthem at the earth's surface. (a) What is the greatest distance amuon could travel during its 2.2$\mu$ s lifetime? (b) According toyour answer in part (a), it would seem that muons could nevermake it to the ground. But the 2.2$\mu$ lifetime is measured in theframe of the muon, and they are moving very fast. At a speedof $0.999 c,$ what is the mean lifetime of a muon as measured byan observer at rest on the earth? How far could the muon travelin this time? Does this result explain why we find muons in cos-mic rays? (c) From the point of view of the muon, it still livesfor only $2.2 \mu s,$ so how does it make it to the ground? What isthe thickness of the 10 $\mathrm{km}$ of atmosphere through which themuon must travel, as measured by the muon? Is it now clearhow the muon is able to reach the ground?

$-\sqrt{447} \log$

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

Cornell University

University of Winnipeg

McMaster University

Lectures

03:55

In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

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Sir Isaac Newton described the law of universal gravitation in his work "Philosophiæ Naturalis Principia Mathematica" (1687). The law states that every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

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Muons are unstable subatom…

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Elementary particles calle…

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Muons are subatomic partic…

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About 10,000 cosmic-ray pr…

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Particles called muons exi…

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Integrated ConceptsPar…

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Muons are created in the u…

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Muons are elementary parti…

Que? The lifetime of um yuan at rest is 2.2 times 10 to the negative six, and they travel close to the speed of light. So if there was no time dilation, then the distance of new one would be able to travel before it decayed would be about 2.2 times 10 to the negative, six times the speed of light, and this comes out to 660 meters. Yet we know that they travel 10 kilometers from the upper atmosphere down to the surface of the earth. And what makes this possible is time dilation. So in our reference frame, because the moon's moving so fast, it, it appears to us, is having a longer life span. No, and this new life span is 4.9 times 10 to the negative five seconds. So the distance that we're able to see a travel is 0.999 times, three times 10 to the times, 4.9 times 10 to the negative five cool. And this comes out to 1.5. We're sorry it comes out to 15 kilometers, So that's more than enough for the Mulan to reach the ground. Technically in part A. I should have introduced another factor of 0.999 But that's not going to change the answer much, and the point was that it's much less than 10 kilometers. So in the naive picture, the muon shouldn't be able to make it to the ground. Now to keep everything consistent, we need to understand how the Mu one reaches the ground from the Mu won's perspective because from the mules perspective, it's only lives 2.2 times sent the negative six. And the resolution to that is that from the Mu won's perspective, the distance it has to travel gets length contracted. So, um, if the initial distance, if the distance and our frame is 10 kilometers than in the Mulan's frame, it would be 10 times the square root of 0.999 squared. And this comes out to 15 kilometers, which is the same answer we gotten be so everything's consistent

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