Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 2, Problem 30P
To determine
In perfectly inelastic collision of fast moving proton with the similar target particle, the energy available to create a product particle is given by
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A tau lepton is a particle that decays into a muon and two particles of negligible mass. The tau lepton has a rest mass energy of 1777 MeV, and the muon has a rest mass energy of 105.7 MeV. Suppose the tau lepton is at rest and all of the missing mass goes into the muon's kinetic energy. How fast will the muon move? (Enter your answer in terms of c to at least four significant figures.)
Consider the inelastic collision. Two lumps of matter are moving directly toward each other. Each lump has a mass of 0.500 kgand is moving at a speed of 0.910?. The two lumps collide and stick together. Answer the questions, keeping in mind that relativistic effects cannot be neglected in this case.
What is the final speed ?f of the combined lump, expressed as a fraction of ??
?f=
?
What is the final mass ?f of the combined lump immediately after the collision, assuming that there has not yet been significant energy loss due to radiation or fragmentation?
?f=
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
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…
Chapter 2 Solutions
Modern Physics
Ch. 2 - A particle is moving at a speed of less than c/2....Ch. 2 - Give a physical argument showing that it is...Ch. 2 - Prob. 3QCh. 2 - Prob. 4QCh. 2 - Prob. 5QCh. 2 - Prob. 6QCh. 2 - Prob. 8QCh. 2 - Prob. 9QCh. 2 - Calculate the momentum of a proton moving with a...Ch. 2 - Prob. 2P
Ch. 2 - Consider the relativistic form of Newtons second...Ch. 2 - A charged particle moves along a straight line in...Ch. 2 - Prob. 5PCh. 2 - Prob. 6PCh. 2 - Prob. 7PCh. 2 - A proton moves at a speed of 0.95c. Calculate its...Ch. 2 - An electron has a kinetic energy 5 times greater...Ch. 2 - Find the speed of a particle whose total energy is...Ch. 2 - A proton in a high-energy accelerator is given a...Ch. 2 - An electron has a speed of 0.75c. Find the speed...Ch. 2 - Protons in an accelerator at the Fermi National...Ch. 2 - How long will the Sun shine, Nellie? The Sun...Ch. 2 - Electrons in projection television sets are...Ch. 2 - Prob. 16PCh. 2 - Prob. 17PCh. 2 - Prob. 18PCh. 2 - Prob. 19PCh. 2 - Prob. 20PCh. 2 - An electron having kinetic energy K = 1.000 MeV...Ch. 2 - The K0 meson is an uncharged member of the...Ch. 2 - An unstable particle having a mass of 3.34 1027...Ch. 2 - As measured by observers in a reference frame S, a...Ch. 2 - An object having mass of 900 kg and traveling at a...Ch. 2 - Prob. 27PCh. 2 - Prob. 28PCh. 2 - Prob. 29PCh. 2 - Prob. 30PCh. 2 - A particle of mass m moving along the x-axis with...Ch. 2 - Prob. 32PCh. 2 - Energy reaches the upper atmosphere of the Earth...
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- (a) What is the momentum of a 2000 kg satellite orbiting at 4.00 km/s? (b) Find the ratio of this momentum to the classical momentum. (Hint: Use the approximation that =1+(1/2)v2/c2 at low velocities.)arrow_forwardConsider an electron moving with speed 0.980c. a. What is the rest mass energy of this electron? b. What is the total energyof this electron? c. What is the kinetic energy of this electron?arrow_forwardThe muon is an unstable particle that spontaneously decays into an electron and two neutrinos. If the number of muons at t = 0 is N0, the number at time t is given by , where τ is the mean lifetime, equal to 2.2 μs. Suppose the muons move at a speed of 0.95c and there are 5.0 × 104 muons at t = 0. (a) What is the observed lifetime of the muons? (b) How many muons remain after traveling a distance of 3.0 km?arrow_forward
- Two powerless rockets are on a collision course. The rockets are moving with speeds of 0.800c and 0.600c and are initially 2.52 × 1012 m apart as measured by Liz, an Earth observer, as shown in Figure P1.34. Both rockets are 50.0 m in length as measured by Liz. (a) What are their respective proper lengths? (b) What is the length of each rocket as measured by an observer in the other rocket? (c) According to Liz, how long before the rockets collide? (d) According to rocket 1, how long before they collide? (e) According to rocket 2, how long before they collide? (f) If both rocket crews are capable of total evacuation within 90 min (their own time), will there be any casualties? Figure P1.34arrow_forwardSuppose our Sun is about to explode. In an effort to escape, we depart in a spaceship at v = 0.80c and head toward the star Tau Ceti, 12 lightyears away. When we reach the midpoint of our journey from the Earth, we see our Sun explode and, unfortunately, at the same instant we see Tau Ceti explode as well. (a) In the spaceship’s frame of reference, should we conclude that the two explosions occurred simultaneously? If not, which occurred first? (b) In a frame of reference in which the Sun and Tau Ceti are at rest, did they explode simultaneously? If not, which exploded first?arrow_forwardA Van de Graaff accelerator utilizes a 50.0 MV potential difference to accelerate charged particles such as protons. (a) What is the velocity of a proton accelerated by such a potential? (b) An electron?arrow_forward
- A box is cubical with sides of proper lengths L1 = L2 = L3, as shown in Figure P26.14, when viewed in its own rest frame. If this block moves parallel to one of its edges with a speed of 0.80c past an observer, (a) what shape does it appear to have to this observer? (b) What is the length of each side as measured by the observer? Figure P26.14arrow_forwardA muon has a rest mass energy of 105.7 MeV, and it decays into an electron and a massless particle. (a) If all the lost mass is converted into the electron's kinetic energy, find for the electron. (b) What is the electron's velocity?arrow_forward(a) What is the effective accelerating potential for electrons at the Stanford Linear Accelerator, if =1.00105 for them? (b) What is their total energy (nearly the same as kinetic in this case) in GeV?arrow_forward
- (a) Beta decay is nuclear decay in which an electron is emitted. If the electron is given 0.750 MeV of kinetic energy, what is its velocity? (b) Comment on how the high velocity is consistent with the kinetic energy as it compares to the rest mass energy of the electron.arrow_forward(a) Using data from Table 7.1, find the mass destroyed when the energy in a barrel of crude oil is released. (b) Given these barrels contain 200 liters and assuming the density of crude oil is 750 kg/m3, what is the ratio of mass destroyed to original mass, m/m ?arrow_forwardAn enemy spacecraft moves away from the Earth at a speed of v = 0.800c (Fig. P9.19). A galactic patrol spacecraft pursues at a speed of u = 0.900c relative to the Earth. Observers on the Earth measure the patrol craft to be overtaking the enemy craft at a relative speed of 0.100c. With what speed is the patrol craft overtaking the enemy craft as measured by the patrol crafts crew? Figure. P9.19arrow_forward
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