BackThe mean lifetimes listed in Table 43–2 are in terms of proper time, measured in a reference frame where the particle is at rest. If a tau lepton is created with a kinetic energy of 920 MeV, how long would its track be as measured in the lab, on average, ignoring any collisions?
(I) Calculate the rest energy of an electron (m = 9.11 x 10⁻³¹ kg) in joules and in MeV (1 MeV = 1.60 x 10⁻¹³ J) .
(I) The total annual energy consumption in the United States is about 1 x 1020 J How much mass would have to be converted to energy to fuel this need?
(II) What is the Schwarzschild radius for a typical galaxy (like ours)?
(II) What is the maximum sum-of-the-angles for a triangle on a sphere?
The nearest star to Earth is Proxima Centauri, 4.3 light-years away. At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 5.5 years, as measured by travelers on the spacecraft?
What is the speed of a galaxy with z = 0.068?
A particle of mass m travels at a speed v = 0.32 c. At what speed will its momentum be doubled?
What is the momentum of a proton traveling at v = 0.72c?
How much work is required to accelerate a proton from rest up to a speed of 0.995c?
Estimate the speed of a galaxy, and its distance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as being 625 nm.
What is the time for one complete revolution for a very high-energy proton in the 27-km LHC circumference?
Escape velocity from the Earth is 11.2 km/s. What would be the percent decrease in length of a 73.6-m-long spacecraft traveling at that speed as seen from Earth?
Estimate the wavelength shift for the 656.3-nm line in the Balmer series of hydrogen emitted from a galaxy whose distance from us is 6.0 x 106 ly.
Two spaceships leave Earth in opposite directions, each with a speed of 0.50c with respect to Earth.
(a) What is the velocity of spaceship 1 relative to spaceship 2?
(b) What is the velocity of spaceship 2 relative to spaceship 1?