A new type of force was discovered by physicists with the following expression: α Fnew = + Be* + 3xª where alpha & beta are constants, and x is the position. The expression above was obtained from the interaction of a massless Higgs Boson (a type of particle) and a black hole, Quantum physicists then decides to design and build a machine that is able to move the Higgs Boson from x2 to x1. How much work should the machine do to achieve this feat? (For simplicity, consider that no energy is lost in the process) Solution To determine the work done we apply the following W = dx X; Evaluating the above, we get W = for the limits from xj to xf substituting x1 and x2 as the limits, the work done is expressed as W = | + BI x1 ( x15 - x25 )

A new type of force was discovered by physicists with the following expression: α Fnew = + Be* + 3xª where alpha & beta are constants, and x is the position. The expression above was obtained from the interaction of a massless Higgs Boson (a type of particle) and a black hole, Quantum physicists then decides to design and build a machine that is able to move the Higgs Boson from x2 to x1. How much work should the machine do to achieve this feat? (For simplicity, consider that no energy is lost in the process) Solution To determine the work done we apply the following W = dx X; Evaluating the above, we get W = for the limits from xj to xf substituting x1 and x2 as the limits, the work done is expressed as W = | + BI x1 ( x15 - x25 )

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter5: Relativity

Section: Chapter Questions

Problem 112AP: Nuclear-powered rockets were researched for some years before safety concerns paramount. (a) What...

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A positron is an antimatter version of the electron, having exactly the same mass. When a positron and an electron meet, they annihilate, converting all of their mass into energy. (a) Find the energy released, assuming negligible kinetic energy before the annihilation. (b) If this energy is given to a proton in the form of kinetic energy, what is its velocity? (c) If this energy is given to another electron in the form of kinetic energy, what is its velocity?
Nuclear-powered rockets were researched for some years before safety concerns paramount. (a) What fraction of a rocket's mass would have to be destroyed to get it into a low Earth orbit, neglecting the decrease in gravity? (Assume an orbital altitude of 250 km, and calculate both the kinetic energy (classical) and the gravitational potential energy needed.) (b) If the ship has a mass of 1.00×105kg (100 tons), what total yield nuclear explosion in tons of TNT is needed?
(a) Verify from its quark composition that the particle could be an excited state of the proton. (b) There is a spread of about 100 MeV in the decay energy of the interpreted as uncertainty due to its short lifetime. What is its approximate lifetime? (c) Does its decay proceed via the strong or weak force?
Plans for ail accelerator that produces a secondary beam of K mesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of 500 MeV. (a) What would the relativistic quantity =11v2/c2be for these particles? (b) How long would their average lifetime be in the laboratory? (c) How far could they travel in this time?
A muon formed high in Earth's atmosphere travels toward Earth at a speed v = 0.990c for a distance of 4.60 km as measured by an observer at rest with respect to Earth. It then decays into an electron, a neutrino, and an antineutrino. (a) How long does the muon survive according to an observer at rest on Earth? (b) Compute the gamma factor associated with the muon. (c) How much time passes according to an observer traveling with the muon? (d) What distance does the muon travel according to an observer traveling with the muon? (e) A third observer traveling toward the muon at c/2 measures the lifetime of the particle. According to this observer, is the muons lifetime shorter or longer than the lifetime measured by the observer at rest with respect to Earth? Explain.
Models are particularly useful in relativity and quantum mechanics, where conditions are outside those normally encountered by humans. What is a model?
(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.
In supei novae, neutrinos are produced in huge amounts. They were detected from the 1987A supernova in the Magellanic Cloud, which is about 120,000 light- years away from Earth (relatively close to our Milky Way Galaxy). If neutrinos have a mass, they cannot travel at the speed of light, but if their mass is small, their velocity would be almost that of light, (a) Suppose a neutrino with a 7eV/c2mass has a kinetic energy of 700 keV. Find the relativistic quantity =11v2/c2for it. (b) If the neutrino leaves the 1987A supernova at the same time as a photon and both travel to Earth, how much sooner does the photon arrive? This is not a large time difference, given that it is impossible to know which neutrino left with which photon and the poor efficiency of the neutrino detectors. Thus, the fact that neutrinos were observed within hours of the brightening of the supernova only places an upper limit on the neutrino’s mass. (Hint: You may need to use a series expansion to find v for the neutrino, since its is so large.)
A muon formed high in Earth's atmosphere travels toward Earth at a speed v = 0.990c for a distance of 4.60 km as measured by an observer at rest with respect to Earth. It then decays into an electron, a neutrino, and an antineutrino. (a) How long does the muon survive according to an observer at rest on Earth? (b) Compute the gamma factor associated with the muon. (c) How much time passes according to an observer traveling with the muon? (d) What distance does the muon travel according to an observer traveling with the muon? (e) A third observer traveling toward the muon at c/2 measures the lifetime of the particle. According to this observer, is the muons lifetime shorter or longer than the lifetime measured by the observer at rest with respect to Earth? Explain.
A chain of nuclear reactions in the Suns core converts four protons into a helium nucleus. (a) What is the mass difference between four protons and a helium nucleus? (b) How much energy in MeV is released during the conversion of four protons into a helium nucleus?
Integrated Concepts Plans for an accelerator that produces a secondary beam of Kmesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of 500 MeV. (a) What would the relativistic quantity be for these particles? (b) How long would their average lifetime be in the laboratory? (c) How far could they travel in this time?
(a) Calculate the relativistic quantity =11v2/c2for 1.00-TeV protons produced at Fermilab. (b) If such a proton created a +having the same speed, how long would its life be in the laboratory? (c) How far could it travel in this time?