The Physics
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Opus in profectus

# Mass-Energy

## Problems

### practice

1. Write something.
2. Write something.
3. Write something.
4. Write something completely different.

### numerical

1. The luminosity of the sun is 3.85 × 1026 W.
1. Determine the mass of the sun converted to energy in one second.
2. How many elephants is this?
2. Fermi National Accelerator Laboratory (a.k.a. Fermilab) in Batavia, Illinois is a US Department of Energy National Laboratory and home of the world's most powerful particle accelerator, the Tevatron, which accelerates beams of protons and antiprotons to ultra-high energy and brings them into head-on collision. Protons in the Tevatron's accelerator ring acquire energies on the order of 1012 elevtronvolts — a teraelectron volt (TeV).
1. From the Tevatron's energy…
1. determine the speed of a proton in the accelerator
2. and then verify (or contradict) the laboratory's claim that protons "circle the four-mile [6.4 km] ring 57,000 times each second."
2. Determine the mass increase of a proton in the Tevatron in…
1. atomic mass units and
2. multiples of the proton's rest mass
3. ﻿Read the following excerpts about the the world's largest and most powerful particle accelerator, the Large Hadron Collider (LHC) at the European Organization for Nuclear Research (still called by its old acronym CERN) in Geneva, Switzerland.

LHC stands for Large Hadron Collider. Large due to its size (approximately 27 km in circumference), Hadron because it accelerates protons or ions, which are hadrons, and Collider because these particles form two beams travelling in opposite directions, which collide at four points where the two rings of the machine intersect.

The accelerator complex at CERN is a succession of machines with increasingly higher energies. Each machine injects the beam into the next one, which takes over to bring the beam to an even higher energy, and so on. In the LHC — the last element of this chain — each particle beam is accelerated up to the record energy of 7 TeV. In addition, most of the other accelerators in the chain have their own experimental halls, where the beams are used for experiments at lower energies.

No particle can move with speeds faster than the speed of light in a vacuum; however, there is no limit to the energy a particle can attain. In high-energy accelerators, particles normally travel very close to the speed of light. In these conditions, as the energy increases, the increase in speed is minimal. As an example, particles in the LHC move at 0.999997828 times the speed of light at injection (energy = 450 GeV) and 0.999999991 times the speed of light at top energy (energy = 7000 GeV). Therefore, particle physicists do not generally think about speed, but rather about a particle's energy.

 quantity number circumference 26 659 m dipole operating temperature 1.9 K (−271.3 ℃) number of magnets 9593 number of main dipoles 1232 number of main quadrupoles 392 number of RF cavities 8 per beam nominal energy, protons 7 TeV nominal energy, ions 2.76 TeV/u* peak magnetic dipole field 8.33 T min. distance between bunches ~7 m design luminosity 1034 cm−2 s−1 no. of bunches per proton beam 2808 no. of protons per bunch (at start) 1.1 × 1011 number of turns per second 11 245 number of collisions per second 600 million

The total energy in each beam at maximum energy is about 350 MJ, which is about as energetic as a 400 t train, like the French TGV, travelling at 150 km/h. This is enough energy to melt around 500 kg of copper. The total energy stored in the LHC magnets is some 30 times higher (11 GJ).

CERNfaq LHC the guide, 2008

Verify the following claims made in this FAQ.

1. "…particles in the LHC move at… 0.999999991 times the speed of light at top energy…"
1. Do it once using the dimensions of the LHC (easy, but less precise).
2. Do it again using the top energy value (not so easy, but more precise).
2. "The total energy in each beam at maximum energy is about 350 MJ…"
3. "…which is about as energetic as a 400 t train, like the French TGV, travelling at 150 km/h…"
4. "This is enough energy to melt around 500 kg of copper."