An unstable particle with a mass of 3.34'10-" kg is initially at rest. The particle decays into two fragments that fly off along the x-axis with velocity components 0.987c and -0.868c. Determine the masses of the fragments.
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- 1. You and your lab partner are making measurements on particle decay in the lab. You make the following measurements on particle A: m₁ = 498 MeV/c² and ₁ = 0.462c î. You observe VA particle A decay to particles B and C. Your lab partner makes the following measurements: MB = mc = = 140 MeV/c² and ✓ = −0.591c î. (a) Calculate the total energy for each particle. (b) Find the velocity (magnitude and direction) of particle C. (c) Spock is in a ship moving with VB a velocity of vs = 0.635c î observing the same particle decay. What values does he measure for the velocities of particle B and particle C?A particle at rest decays into two corfu particles, each with a mass of 200.0 MeV/c². One of the corfu particles is measured to have a kinetic energy of 98.3 MeV. - Find the mass in MeV/c² of the original particle which decayeds 98.3x2 Ke=Chapter 37, Problem 045 In a high-energy collision between a cosmic-ray particle and a particle near the top of Earth's atmosphere, 110 km above sea level, a pion is created.The pion has a total energy E of 1.68 x 105 MeV and is traveling vertically downward. In the pion's rest frame, the pion decays 35.0 ns after its creation. At what altitude above sea level, as measured from Earth's reference frame, does the decay occur? The rest energy of a pion is 139.6 MeV. Number Units
- (17%) Problem 6: Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v = 0.94c. The muon then travels at constant speed and lives 1.525 us as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.) Randomized Variables v = 0.94 c t = 1.525 µs Part (a) How many kilometers does the muon travel according to an Earth-bound observer? Lo = |A kaon with a speed 0.8c in the laboratory decays into two pions, one positively charged and the other negatively charged. The rest mass of the kaon is 498 MeV/c2 and the rest mass of the pion is 140 MeV/c2. (a) What is the total energy of the kaon in the laboratory frame? (b) In the rest frame the two pions must go off in opposite directions to conserve momentum. What is the energy of each of the pions in the kaon rest frame? (c) Assume that the positive pion continues to travel in the same direction as the kaon was traveling. What is the total energy of each of the pions in the laboratory? (d) In what direction, relative to the kaon’s original direction of travel, does the negatively charged pion travel?What is the momentum of the alpha particle that is moving at 0.5c. with mass equal to 7.0*10-27 kg.
- At the Stanford Linear Accelerator Center (SLAC; see Fig. 33.9), subatomic particles are accelerated to high energies over a straight path whose length, in Earth's reference frame, is 3.2 km. For an electron traveling at 0.9999995c, how long does the trip take as measured (a)in Earth's frame and (b) in the electrons' frame?The star 61 Cygni A is 11.4 light-years from Earth. Imagine a spaceship that travels from Earth to 61 Cygni A at a constant speed of 0.921c. On Earth, we would measure the time it takes for the ship to reach the star to be 11.4 ly 0.921c = 12.4 years. (a) How much time (in years) would it take the ship to travel from the Earth to the star as measured by a traveler aboard the ship? years (b) What is the distance to the star (in light years) as measured by a traveler aboard the ship? lyA particle known as a pion lives for a short time before breaking apart into other particles. Suppose a pion is moving at a speed of 0.986c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 2.8 × 10-8 s. (a) What is the lifetime according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the laboratory move before the pion breaks apart? (a) Number (b) Number MO Units Units
- There is a free neutron that is at rest. It decays into a proton (mass energy is 938.30 MeV), an electron (mass energy is 0.50 MeV, and an antineutrino (mass energy is negligible on the scale of MeV). What is the total kinetic energy of the decay products?1. You are an observer in a 100-m long spacecraft traveling from the earth to the moon at 0.8c. (a)What is the proper length of the spacecraft? (b) For a proper time interval of 1 sec., the relativistic time interval for the spacecraft measured from the earth reference frame would be: (c)Time dilation does not apply to all time-dependent physical and biological processes. T/F? (c) What is the relativistic length, DL measured from the reference frame of earth? (d) An APOLLO crew left a flat mirror reflector on the surface of the moon (for all you deniers out there, in the 50th anniversary year of APOLLO 11!). If the average surface-to-surface distance from the earth to the moon is 3.83 x 10^8 m, then how long does it take moonlight to reach earth?Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v = 0.765c. The muon then travels at constant speed and lives 1.6 μs as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.)Randomized Variablesv = 0.765 ct = 1.6 μs Part (a) How many kilometers does the muon travel according to an Earth-bound observer? part (b) How many kilometers of the Earth pass by as viewed by an observer moving with the muon? Base your calculation on its speed relative to the Earth and its lifetime (proper time).