5.1 (a) At what speed must an object move in order for its kinetic energy to be equal to its rest energy? (b) At what speed must an object move in order for its kinetic energy to be equal to twice its rest energy? (c) At what speed must an object move in order for its total energy to be twice its rest energy?
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- A deuteron, consisting of a proton and neutron and having mass 3.34 x 10-27 kg, is traveling at 0.950c relative the Earth in a linear accelerator. Calculate the deuteron's rest energy, y-factor, total energy, and kinetic energy. (a) rest energy (Give your answer to at least three significant figures.) (b) y-factor (c) total energy (d) kinetic energyWhat are (a) the kinetic energy, (b) the rest energy, and (c) the total energy of a 1.2 g particle with a speed of 0.80 c ? Part A Express your answer using two significant figures. ΜΕ ΑΣΦ Ekinetic=263 Submit Previous Answers Request Answer × Incorrect; Try Again; 5 attempts remaining Part B Express your answer using two significant figures. ΜΕ ΑΣΦ Erest = Submit Request Answer Part C Express your answer using two significant figures. ΜΕ ΑΣΦ Etotal = Submit Request Answer ? ? ? J J JConsider these 4 Particles: Particle. Rest energy. Total energy 1 A A 2 B 2B 3 2C 4C 4 3D 5D Rank in order, from largest to smallest, the particles’ speed u1 to u4 Order: Explanation:
- Michale is decided to buy a ticket to go to space. After meticulously planning his journey, he travels in his vessel at speed 7/10c from Earth to the nearby planet, Alfa-0 , 20 light-years away (as measured in the common rest frame of Earth and Alfa-0). He spends a year (as measured in Earth- Alfa-0 frame) on this foreign planet sharing stories of human history to aliens. Finally, he is ready to head home. His hosts, charmed by his friendliness and the stories of his wonderful home, give him their best space ship for the return voyage. In this new ship, he travels at speed 95/100 c. Let W be Michael's departure from Earth (which we can set as the origin of the reference frame), X his arrival to the Alfa-0, Y his departure from the Alfa-0, and Z his arrival back to Earth. a. Draw the spacetime diagram from the rest frame of the Earth - Alfa-0 system, indicating Michale's worldline, and the events, W, X, Y, Z. (A rough sketch will suffice - do not worry about the angles. b. Find the…Antimatter: When a particle and its anti-particle collide, energy and momentum are conserved. However, the particles can annihilate each other and produce two gamma rays - high energy photons. An electron and an anti-electron each have a rest mass of 9.11 × 10-31 kg. Suppose the particles are each accelerated to a speed of 0.98c in a particle accelerator with a length of 1543 m for a head on collision. (Each particle is moving at this speed with respect to the lab, and the particles are moving in opposite directions.) They collide head on and annihilate. What is the wavelength of the gamma rays produced in this collision?In special relativity, we introduced the momentum of a particle in a given Lorentz frame as pu = (E, pi ), where E is the energy of the particle and pi is the relativistic 3-momentum. Explain why, in general relativity, the energy of a particle measured by an observer is given, irrespective of the coordinate system used, by −p · uobs, where pu is the momentum of the particle and uuobs is the velocity of the observer in those coordinates.
- What is the speed of a proton when its kinetic energy is equal to twice its rest energy?An interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 70.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 15.0 years as measured in a rest frame. (a) How long do the batteries on the space probe last as measured by mission control on Earth? (b) How far is the probe from Earth when its batteries fail as measured by mission control? (c) How far is the probe from Earth as measured by its built-in trip odometer when its batteries fail? (d) For what total time after launch are data received from the probe by mission control? Note that radio waves travel at the speed of light and fill the space between the probe and Earth at the time the battery fails.a) How fast must an object travel for its total energy to be 1% more than its rest energy? b) How fast must an object travel for its total energy to be 99% more than its rest energy?
- Find the rest energy of an electron (m = 9.109 x 10-31 kg, q = -e = -1.602 x 10-19 C) in joules and in electron volts. (a) Find the speed of an electron that has been accelerated by an electric field, from rest, through a potential increase of 20.0 kV or of 5.00 MV (typical of a high-voltage x-ray machine).a) What is the kinetic energy of a 1.0 g particle with a speed of 0.800c? b) What is the rest energy of a 1.0 g particle with a speed of 0.800c? c) What is the total energy of a 1.0 g particle with a speed of 0.800c?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?