A particle with mass M at rest decays into two particles, one with mass m, and the other with mass m₂. Use conservation of energy and momentum to show that (M²+ m²-m²) c² E₁ = 2M
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- What is the rest energy (in joules) of a subatomic particle whose (rest) mass is 6.7×10−31 kg? How many MeV’s of energy is this?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 69.0%69.0%. How many liters of water would be sufficient fuel to very slowly push the Moon 3.10 mm3.10 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.The very massive Higgs particle (mass 125 GeV/c2) is created when two protons traveling at equally high speeds but in opposite directions collide head‑on. The mass of a proton is 938.27 MeV/c2. In order to make a Higgs particle when they collide, each proton must have a minimum kinetic energy of 62.5 GeV. What is the minimum total energy E(min) of each proton? E(min) = ? eV In terms of the speed c of light, what speed v is each proton traveling? Calculate your answer to five significant figures. v = ? c
- 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.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=
- 06 (a) A stationary particle 1 decays into particles 2 and 3, which move off with equal but oppositely directed momenta. Show that the kinetic energy K2 of particle 2 is given by K, -[(E, - E) – E, 2E, where E1, E2, and Ez are the rest energies of the particles. (b) A stationary positive pion + (rest energy 139.6 MeV) can de- cay to an antimuon ut (rest energy 105.7 MeV) and a neutrino v (rest energy approximately 0). What is the resulting kinetic energy of the antimuon?(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?
- SS f6 8. An electron travels at a speed of 8.80 × 107 m/s. What is its 9.11 × 10-³1 kg) MeV 60 ssf60 ssi of t energy? (The rest mass of an electron 50 ssf60 ss ssf60 ssf6ůProtons 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 JA proton and anti-proton with rest energy of, E0 = 931 MeV/c2 was traveling in the opposite direction at a speed of, V = 0.9995*c (where c is a speed of light equal to 3.0 * 108 m/s). After traveling in a vacuum chamber, the two particles collide head-on to produce a new massive particle in the center of the chamber. What is the new Energy (in GeV) of the proton and anti-proton after reaching V = 0.9995*c? What is the new kinetic energy (in GeV) of the proton and anti-proton after reaching the new speed? If the collision of the two particles produced a stationary massive particle, what is the stationary mass of the new particle in GeV/c2?