Q2. (a) If the mean proper life-time of muons is 2.2 x 10 s, what average distance would they travel in vacuum before decaying in the reference frame in which its velocity is measured as 0.6
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- While in flight, an unstable particle decays into three pions (rest mass 140 MeV/c²) according to figure 1. The kinetic energies and angles are: K₁ = 190 MeV, K₂ = 321 MeV, K3 = 58 MeV 0₁ = 22.4°, 0₂ = 12.25° Calculate the mass of the unstable particle.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 Units3.4. Cosmic ray muons are produced high in the atmosphere (at 8000 m, say) and travel toward the earth at very nearly the speed of light (0.998 c, say). (a) Given the lifetime of the muon (2.2 x 10-6 sec), how far would it go before disintegrating, according to prerelativistic physics? Would the muons make it to ground level? (b) Now answer the same question using relativistic physics. (Because of time di- lation, the muons last longer, so they travel farther.) (c) Now analyze the same process from the perspective of the muon. (In its reference frame it only lasts 2.2 x 10-6 sec; how, then, does it make it to ground?) + (d) Pions are also produced in the upper atmosphere. [In fact, the sequence is proton (from outer space) hits proton (in atmosphere) → p + p + pions. The pions then decay into muons: ¯ → μ¯ + D µ; πt → μ† + vµ.] But the lifetime of the pion is much shorter, a hundredth that of the muon. Should the pions reach ground level? (Assume that the pions also have a speed of…
- Protons in the LHC accelerator in Geneva, Switzerland are accelerated to an energy of 4.0 TeV. What is this in joules? 6.4 x 10-7 J 6.4 x 10-19 J 6.4 x 10-13 J 6.4 x 10-16 J 6.4 x 10-⁹ JDetermine the rest energy (in MeV) for a neutron with mass 1.675×10-27 kg.1. A supertrain of proper length 195 m travels at a speed of 0.92c as it passes through a tunnel having proper length 90.0 m. How much longer is the tunnel than the train or vice versa as seen by an observer at rest with respect to the tunnel? meters
- A proton is traveling in an accelerator with a speed of 1.0 x108 m/sBy what factor does the proton’s kineticenergy increase if its speed is doubled?Derive an expression for E using the attached equation (Lorentz Force Law), and calculate a predicted value for E in N/C if a particle had v = 40 m/s, q = -0.001 C, m = 0.3 ⨉ 10 -3 kg, and B = 0.6 T.Suppose that you have found a way to convert the rest energy of any type of matter directly to usable energy with an efficiency of 49.0%49.0%. How many liters of water would be sufficient fuel to very slowly push the Moon 3.30 mm3.30 mm away from the Earth? The density of water is ?water=1.00kg/literρwater=1.00kg/liter, the Earth's mass is ?earth=5.97×1024 kgMearth=5.97×1024 kg, the Moon's mass is ?moon=7.36×1022 kgMmoon=7.36×1022 kg, and the separation of the Earth and Moon is ?E,M=3.84×108 mdE,M=3.84×108 m.
- 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).If ever the human race would need to leave Earth, the Trappist-1 system might make a good destination – the star there has seven temperate terrestrial planets, a few of which are close to Earth’s size and mass. It’s 39.6 light years away, though, so it could take a long time to get there. (a) If the spaceship had a speed of 0.95c, how long would the journey take from the Earth’s reference frame? (b) How long would the journey be for the passengers on the spaceship?The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6 10-8 s. (a) If the meson moves with a speed of 0.94c, what is its mean lifetime as measured by an observer on Earth? (b) What is the average distance it travels before decaying, as measured by an observer on Earth? (c) What distance would it travel if time dilation did not occur?