Find the fraction of decrease of the kinetic energy of a neutron of mass m, in head-on collision with an atomic nucleus of mass m2 which is initially at rest 4m?m? (m1+m2)² 2m2 M1 (m,+m2)² 4m2 m1 (m,+m2)² 2m2 m² (m,+m2)²
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- Six identical particles have a speed 2m/s except for the last ( which is the seventh) particle which has a speed of 4m/s. What is the vavg of these particles?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,…Electron capture is a variant on beta-radiation. The lightest nucleus to decay by electron capture is 7Be -- beryllium-7. The daughter nucleus is 7Li -- lithium-7. The electron is transformed into a massless particle (a neutrino): e − + 7 B e + ⟶ 7 L i + ν The initial electron is bound in the atom, so the beryllium mass includes the electron. In fact, since the electron starts bound in the atom, a more-accurate statement of the nuclear reaction is probably: 7 B e ⟶ 7 L i + ν The masses are beryllium: 7.016929 u, and lithium: 7.016003 u, and refer to the neutral atom as a whole. (Use uc and uc2 as your momentum and energy units -- but carry them along in your calculation.) The initial beryllium atom is stationary. Calculate the speed of the final lithium nucleus in km/s. (all the energy released goes into the lighter particle. c = 300,000 km/s)
- Electron capture is a variant on beta-radiation. The lightest nucleus to decay by electron capture is 7Be -- beryllium-7. The daughter nucleus is 7Li -- lithium-7. The electron is transformed into a massless particle (a neutrino): e − + 7 B e + ⟶ 7 L i + ν The initial electron is bound in the atom, so the beryllium mass includes the electron. In fact, since the electron starts bound in the atom, a more-accurate statement of the nuclear reaction is probably: 7 B e ⟶ 7 L i + ν The masses are beryllium: 7.016929 u, and lithium: 7.016003 u, and refer to the neutral atom as a whole. (Use uc and uc2 as your momentum and energy units -- but carry them along in your calculation.) The initial beryllium atom is stationary. Calculate the speed of the final lithium nucleus in km/s. (You will make life much easier for yourself if you recognize that practically all the energy released goes into the lighter particle. c = 300,000 km/s)A Carbon-14 nucleus is initially at rest but emits two particles of radiation; one with momentum 5.8x10-21kgm/s[E], and another with momentum 4.5x10-21kgm/s[S]. If the residual Carbon-14 mass is 2.3x10-26kg; a. Determine the residual Carbon 14 momentum magnitude b. Determine the residual Carbon 14 momentum direction c. determine the residual Carbon 14 velocity.13
- a) What is the magnitude of energy (in MJ) that must be removed to freeze 377 L of water with a density of 999.8 Kg/m3 that is already at 0˚C [round your final answer to one decimal place]? {latent heats of water: Lf = 33.5 × 104 J/kg, and Lv = 22.6 × 105 J/kg} b) The magnitude of energy that must be added to melt the same mass of ice (already at 0˚C) would be greater than the amount of energy that had to be removed in order to freeze it. TRUE OR FALSE {latent heats of water: Lf = 33.5 × 104 J/kg, and Lv = 22.6 × 105 J/kg}b & c2. An alternative derivation of the mass-energy formula E, = moc² also given by Einstein, is based on the principle that the location of the center of mass (CM) of an isolated system cannot be changed by any process that occurs inside the system. The Figure below shows a rigid box of length L that rests on a frictionless surface; the mass M of the box is equally divided between its two ends. A burst of electromagnetic radiation of energy E, is emitted by one end of the box. According to classical physics, the radiation has the momentum p = "0%c , and when it is emitted, the box recoils with the speed v z Eo/ so that the total momentum of Mc the system remains zero. After a time t z L/c the radiation reaches the other end of the box and is absorbed there, which brings the box to a stop after having moved the distance S. If the CM of the box is to remain in its original place, the radiation must have transferred mass from one end to the other. Show that this amount of mass is m, = c2.