measured by this observer to be 10 times longerthan its lifetime when at rest relative to the observer?3. The lifetime of a free neutron is 886 s. If a neutron moves with aspeed of 2.9 x 108m/s relative to an observer in the lab, what doesthe observer measure the neutron's lifetime to be?4. A computer in a laboratory requires 2.50 us to make a certain calcu-lation, as measured by a scientist in the lab. To someone movingpast the lab at a relative speed of 0.995c, how long will the same cal-culation take?5. The formula for length contraction gives the length of an interval ona ruler moving with velocity v relative to an observer as V1-v²/c²times the length of the same interval on a ruler at rest with respectto the observer. By what fraction is the length of a meter stickreduced if its velocity relative to you is measured to be 95 percentthe speed of light?6. If an electron is speeding down the two-mile-long Stanford LinearAccelerator at 99.98 percent the speed of light, how many meterslong is the trip as seen from the perspective of the electron? (SeeProblem 5.)(a(H((18. A7. Calculate the rest energy of a proton in joules and MeVs. What isthe mass of a proton in MeV/c²?8. The tau is the heaviest of all the known leptons, having a mass of1,777 MeV/c². Find the rest energy of a tau in MeVs and joules.What is the mass of the tau in kilograms? Compare your result withthe mass in kilograms of an electron.9. If a 1.0-kg mass is completely converted into energy, how muchenergy, in joules, would be released? Compare this value to theamount of energy released when 1.0 kg of liquid water at 0°C freezes.10. In a particular beam of protons, each particle moves with an averagespeed of 0.8c. Determine the total relativistic energy of each protonin joules and MeVs.19.202111. A particle of rest energy 140 MeV moves at a sufficiently high speedthat its total relativistic energy is 280 MeV. How fast is it traveling?12. If the relativistic kinetic energy of a particle is 9 times its rest energy,at what fraction of the speed of light must the particle be traveling?oth at rest, were to completely anni-

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The lifetime of a free neutron is 886 s. If a neutron moves with a peed of 2.9 X 108m/s relative to an observer in the lab, what does the observer measure the neutron's lifetime to be? V

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter26: Relativity

Section: Chapter Questions

Problem 9P: A muon formed high in Earth's atmosphere travels toward Earth at a speed v = 0.990c for a distance...

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Concept explainers

Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience this effect in everyday life. This effect is only observed when an object moves with some velocity comparable to the velocity of light. This velocity is termed relativistic velocity.

Question

measured by this observer to be 10 times longer
than its lifetime when at rest relative to the observer?
3. The lifetime of a free neutron is 886 s. If a neutron moves with a
speed of 2.9 x 108m/s relative to an observer in the lab, what does
the observer measure the neutron's lifetime to be?
4. A computer in a laboratory requires 2.50 us to make a certain calcu-
lation, as measured by a scientist in the lab. To someone moving
past the lab at a relative speed of 0.995c, how long will the same cal-
culation take?
5. The formula for length contraction gives the length of an interval on
a ruler moving with velocity v relative to an observer as V1-v²/c²
times the length of the same interval on a ruler at rest with respect
to the observer. By what fraction is the length of a meter stick
reduced if its velocity relative to you is measured to be 95 percent
the speed of light?
6. If an electron is speeding down the two-mile-long Stanford Linear
Accelerator at 99.98 percent the speed of light, how many meters
long is the trip as seen from the perspective of the electron? (See
Problem 5.)
(a
(H
(
(
18. A
7. Calculate the rest energy of a proton in joules and MeVs. What is
the mass of a proton in MeV/c²?
8. The tau is the heaviest of all the known leptons, having a mass of
1,777 MeV/c². Find the rest energy of a tau in MeVs and joules.
What is the mass of the tau in kilograms? Compare your result with
the mass in kilograms of an electron.
9. If a 1.0-kg mass is completely converted into energy, how much
energy, in joules, would be released? Compare this value to the
amount of energy released when 1.0 kg of liquid water at 0°C freezes.
10. In a particular beam of protons, each particle moves with an average
speed of 0.8c. Determine the total relativistic energy of each proton
in joules and MeVs.
19.
20
21
11. A particle of rest energy 140 MeV moves at a sufficiently high speed
that its total relativistic energy is 280 MeV. How fast is it traveling?
12. If the relativistic kinetic energy of a particle is 9 times its rest energy,
at what fraction of the speed of light must the particle be traveling?
oth at rest, were to completely anni-

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