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One of the many fundamental particles in nature is the muon μ. This particle acts very much like a "heavy electron." It has a mass of 106 MeV/c².compared to the electron's mass of just 0.511 MeV/c². (We are using E=mc² to obtain the mass in units of energy and the speed of light c). Unlike the electron, though, the muon has a finite lifetime, after which it decays into an electron and two very light particles called neutrinos (v). We'll ignore the neutrinos throughout this problem. If the muon is at rest, the characteristic time that it takes it to decay is about 2.2 µs (Tμ = 2.2 x 10-6 s). Most of the time, though. particles such as muons are not at rest and, if they are moving relativistically, their lifetimes are increased by time dilation. In this problem we will explore some of these relativistic effects. Figure Earth μ 27 Proton 1 of 1 > into the upper atmosphere, they can convert into particles called pions (T), which subsequently decay into muons. These muons can then continue toward the earth until they, too, decay. Let us consider the effects of time dilation on the cosmic rays. Suppose that a cosmic-ray proton crashes into a nitrogen molecule in the upper atmosphere, 45 km above the earth's surface, producing a pion that decays into a muon. Assume that the muon has a downward velocity of 99.9943% the speed of light. ▾ Part C How far (du) would the muon travel before it decayed, if there were no time dilation? Express your answer in meters to three significant figures. [5] ΑΣΦ d₂=14745.24 Submit Part D C Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining d₁ = 4 ? Now, let us consider the effects of time dilation. How far would the muon travel, taking time dilation into account? Express your answer in kilometers to two significant figures. ΠΑΣΦ P Pearson m ? km

One of the many fundamental particles in nature is the muon μ. This particle acts very much like a "heavy electron." It has a mass of 106 MeV/c².compared to the electron's mass of just 0.511 MeV/c². (We are using E=mc² to obtain the mass in units of energy and the speed of light c). Unlike the electron, though, the muon has a finite lifetime, after which it decays into an electron and two very light particles called neutrinos (v). We'll ignore the neutrinos throughout this problem. If the muon is at rest, the characteristic time that it takes it to decay is about 2.2 µs (Tμ = 2.2 x 10-6 s). Most of the time, though. particles such as muons are not at rest and, if they are moving relativistically, their lifetimes are increased by time dilation. In this problem we will explore some of these relativistic effects. Figure Earth μ 27 Proton 1 of 1 > into the upper atmosphere, they can convert into particles called pions (T), which subsequently decay into muons. These muons can then continue toward the earth until they, too, decay. Let us consider the effects of time dilation on the cosmic rays. Suppose that a cosmic-ray proton crashes into a nitrogen molecule in the upper atmosphere, 45 km above the earth's surface, producing a pion that decays into a muon. Assume that the muon has a downward velocity of 99.9943% the speed of light. ▾ Part C How far (du) would the muon travel before it decayed, if there were no time dilation? Express your answer in meters to three significant figures. [5] ΑΣΦ d₂=14745.24 Submit Part D C Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining d₁ = 4 ? Now, let us consider the effects of time dilation. How far would the muon travel, taking time dilation into account? Express your answer in kilometers to two significant figures. ΠΑΣΦ P Pearson m ? km

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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One of the many fundamental particles in nature is the muon μ. This particle acts very much like a "heavy electron." It has a mass of 106 MeV/c².compared to the electron's mass of just 0.511 MeV/c². (We are using E=mc² to obtain the mass in units of energy and the speed of light c). Unlike the electron, though, the muon has a finite lifetime, after which it decays into an electron and two very light particles called neutrinos (V). We'll ignore the neutrinos throughout this problem. If the muon is at rest, the characteristic time that it takes it to decay is about 2.2 μs (Tμ = 2.2 × 10 s). Most of the time, though, particles such as muons are not at rest and, if they are moving relativistically, their lifetimes are increased by time dilation. In this problem we will explore some of these relativistic effects. Figure Earth μ 27 <1 of 1 > Proton A stream of particles, often called cosmic rays, is constantly raining down on the earth from outer space. (Figure 1) Most cosmic-ray particles are protons. When they crash into the upper atmosphere, they can convert into particles called pions (), which subsequently decay into muons. These muons can then continue toward the earth until they, too, decay. Let us consider the effects of time dilation on the cosmic rays. Suppose that a cosmic-ray proton crashes into a nitrogen molecule in the upper atmosphere, 45 km above the earth's surface, producing a pion that decays into a muon. Assume that the muon has a downward velocity of 99.9943% the speed of light. Part C How far (du) would the muon travel before it decayed, if there were no time dilation? Express your answer in meters to three significant figures. ΠΙΑΣΦΑ d=14745.24 Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining Part D OF ? du = Now, let us consider the effects of time dilation. How far would the muon travel, taking time dilation into account? Express your answer in kilometers to two significant figures. ΠΙΑΣΦ A P Pearson m ? Review km
Transcribed Image Text:One of the many fundamental particles in nature is the muon μ. This particle acts very much like a "heavy electron." It has a mass of 106 MeV/c².compared to the electron's mass of just 0.511 MeV/c². (We are using E=mc² to obtain the mass in units of energy and the speed of light c). Unlike the electron, though, the muon has a finite lifetime, after which it decays into an electron and two very light particles called neutrinos (V). We'll ignore the neutrinos throughout this problem. If the muon is at rest, the characteristic time that it takes it to decay is about 2.2 μs (Tμ = 2.2 × 10 s). Most of the time, though, particles such as muons are not at rest and, if they are moving relativistically, their lifetimes are increased by time dilation. In this problem we will explore some of these relativistic effects. Figure Earth μ 27 <1 of 1 > Proton A stream of particles, often called cosmic rays, is constantly raining down on the earth from outer space. (Figure 1) Most cosmic-ray particles are protons. When they crash into the upper atmosphere, they can convert into particles called pions (), which subsequently decay into muons. These muons can then continue toward the earth until they, too, decay. Let us consider the effects of time dilation on the cosmic rays. Suppose that a cosmic-ray proton crashes into a nitrogen molecule in the upper atmosphere, 45 km above the earth's surface, producing a pion that decays into a muon. Assume that the muon has a downward velocity of 99.9943% the speed of light. Part C How far (du) would the muon travel before it decayed, if there were no time dilation? Express your answer in meters to three significant figures. ΠΙΑΣΦΑ d=14745.24 Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining Part D OF ? du = Now, let us consider the effects of time dilation. How far would the muon travel, taking time dilation into account? Express your answer in kilometers to two significant figures. ΠΙΑΣΦ A P Pearson m ? Review km
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