Two Particles Are Located On The X Axis

[Nolan Guyz]

Neutrinosrarely interact with other particles; they can pass through the entire planet as if it were empty space. In order to study such particles, scientists need to create an intense beam of them and send them continuously through a large detector for long periods of time. Because of the need for intense beams, these experiments are said to take place at the Intensity Frontier of particle physics.

Fermi National Accelerator Laboratory, which manages the NOvA project, generates a beam of neutrinos to send to a 14,000-ton detector in Ash River, Minnesota. The particles complete the 500-mile interstate trip in less than three milliseconds. Because neutrinos rarely interact with other matter, they travel straight through the Earth without a tunnel. Scientists detect a small fraction of the neutrinos in a near-detector at Fermilab and in a larger far-detector in Minnesota looking for signals that the neutrinos are changing from one type to another on their trip.

Scientists cannot catch the same neutrino in both detectors to check if it has changed, so they need to use statistics to determine what is happening. Most of the neutrinos detected in the near detector should be muon neutrinos. If scientists notice very few electron neutrinos passing through the near detector and a larger percentage of electron neutrinos passing through the far detector, that will let them know that some of the muon neutrinos from the NuMI beam have become electron neutrinos during the trip to Minnesota.

The Fermilab accelerator complex currently is capable of delivering 700 kilowatts of power to the NuMI beam, but part of the NOvA project will include an upgrade to the accelerator to allow it to provide up to 900 kilowatts of power to NuMI.

The NOvA experiment uses two detectors: a 300 metric-ton near detector at Fermilab and a much larger 14 metric-kiloton far detector in Minnesota just south of the U.S.-Canada border. The detectors are made up of 344,000 cells of extruded, highly reflective plastic PVC filled with liquid scintillator. Each cell in the far detector measures 3.9 cm wide, 6.0 cm deep and 15.5 meters long. When a neutrino strikes an atom in the liquid scintillator, it releases a burst of charged particles. As these particles come to rest in the detector, their energy is collected using wavelength-shifting fibers connected to photo-detectors. Using the pattern of light seen by the photo-detectors, scientists can determine what kind of neutrino caused the interaction and what its energy was.

A neutrino beam, much like a beam of light from a flashlight, gradually spreads apart as it travels. The width of the NuMI beam at Fermilab starts at about six feet and grows to several miles by the time it reaches the far detector in Minnesota. The NOvA detector is located slightly off the centerline of the neutrino beam coming from Fermilab. At this off-axis location, scientists find a large flux of neutrinos at an energy of 2 GeV, the energy at which oscillation from muon neutrinos to electron neutrinos is expected to be at a maximum.

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The effects of confinement on the director field configurations are studied for a spherical particle immersed in a nematic liquid crystal. The liquid crystal is confined in a cylindrical geometry and the particle is located on the axis of symmetry. A finite element method is used to minimize the Frank free energy for various sizes of the system. The liquid crystal is assumed to possess strong anchoring at all the surfaces in the system. Two structures are examined for strong homeotropic anchoring at the surface of the particle: configuration with a Saturn ring disclination line and configuration with a satellite point defect (hedgehog defect). It is shown that the equilibrium locations of the Saturn ring and of the hedgehog point defect change with confinement. It is also found that confinement induces an increase in the elastic free energy that differs substantially with the type of topological defect under consideration. In particular, the evaluation of the total free energy that includes an approximate contribution for the core defect shows that, for micrometer-sized particles in confined systems, the Saturn ring configuration appears to be more stable than the hedgehog defect. This result is in contrast to the bulk situation, where the hedgehog is more stable than the Saturn ring, and it helps explain recent experimental observations of Saturn ring defects around confined micrometer-sized solid particles.

We see from this equation that the kinetic energy of a rotating rigid body is directly proportional to the moment of inertia and the square of the angular velocity. This is exploited in flywheel energy-storage devices, which are designed to store large amounts of rotational kinetic energy. Many carmakers are now testing flywheel energy storage devices in their automobiles, such as the flywheel, or kinetic energy recovery system, shown in (Figure).

Six small washers are spaced 10 cm apart on a rod of negligible mass and 0.5 m in length. The mass of each washer is 20 g. The rod rotates about an axis located at 25 cm, as shown in (Figure). (a) What is the moment of inertia of the system? (b) If the two washers closest to the axis are removed, what is the moment of inertia of the remaining four washers? (c) If the system with six washers rotates at 5 rev/s, what is its rotational kinetic energy?

We can see the individual contributions to the moment of inertia. The masses close to the axis of rotation have a very small contribution. When we removed them, it had a very small effect on the moment of inertia.

A typical small rescue helicopter has four blades: Each is 4.00 m long and has a mass of 50.0 kg ((Figure)). The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length. The helicopter has a total loaded mass of 1000 kg. (a) Calculate the rotational kinetic energy in the blades when they rotate at 300 rpm. (b) Calculate the translational kinetic energy of the helicopter when it flies at 20.0 m/s, and compare it with the rotational energy in the blades.

Rotational and translational kinetic energies can be calculated from their definitions. The wording of the problem gives all the necessary constants to evaluate the expressions for the rotational and translational kinetic energies.

A person hurls a boomerang into the air with a velocity of 30.0 m/s at an angle of [latex] 40.0\text [/latex] with respect to the horizontal ((Figure)). It has a mass of 1.0 kg and is rotating at 10.0 rev/s. The moment of inertia of the boomerang is given as [latex] I=\frac112mL^2 [/latex] where [latex] L=0.7\,\textm [/latex]. (a) What is the total energy of the boomerang when it leaves the hand? (b) How high does the boomerang go from the elevation of the hand, neglecting air resistance?

In part (b), the solution demonstrates how energy conservation is an alternative method to solve a problem that normally would be solved using kinematics. In the absence of air resistance, the rotational kinetic energy was not a factor in the solution for the maximum height.

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The environmental dust particles characteristics and their removal removal from the solid surfaces are examined previously7,8,9,10. Several methods are introduced, including droplet rolling on inclined hydrophobic surfaces7, mechanical brushing of surfaces8, air jet blowing on surfaces9, electrostatic repelling10, etc. In general, the external influence is generated for the removal of the dust particles from the hydrophobic surfaces. However, the wetting state of the surface may become a major concern for the dust particles removal from the solid surfaces through applying the electrostatic forces. The application of the electrostatic forces for the dust removal from the photovoltaic active surfaces was presented by Kawamoto and Guo11. The findings revealed that the energy required repelling the small size dust particles is higher than that of the large size particles. However, applying the high voltage enhances the dust particles repelling and improves the surface cleaning efficiency. The electrostatic dust removal from the biomass flue gas was investigated by Cui et al.12. They showed that the cleaning efficiency of the dust particles improved when the dust particles were located in T-shape on the surface and increasing applied voltage enhanced the dust repelling from the surface. The importance of electrostatic charge on the repelling of the dust particles from the solid was studied by Sayyah et al.13. They indicated that the ratio of electrostatic charge over the dust particles mass was influenced by the electric field intensity; in which case, increasing electric field intensity improved the amount of dust particles repelled from the solid surface. The electrostatic traveling wave and the dust removal from surfaces are studied by Kawamoto and Hashime14. The findings reveal that low frequency of surface vibration improved the dust repelling from the surface under the applied electrostatic forces. The surface topography and the dust particles transport under electrostatic effects were examined by Poppe et al.15. They adopted the particle-in-cell model to investigate the influence of surface topography on the transport characteristics of the dust particles. The dust particles behavior and their separation in electrostatic field were studied by Hofer and Wolter16. They demonstrated that the dust mixture displayed precipitation properties, which were associated with the mineralogical structures of the dusts. The mechanical behavior of un-compacted dust aggregates was investigated by Pontius and Snyder17. The mechanical response of the dust aggregates demonstrated the complicated behavior, which was related to the heterogeneity of inter-particle forces due to varying sizes of the dust particles. The mechanics of charged dust particles in electric field were examined by Tedjojuwono et al.18. The dynamic motion of the dust particles was dependent on the strength of the applied voltage, which was more pronounced for the small dust particles. The influence of the electrostatic forces on the motion of charged particles was studied by Jianan et al.19. They showed that the motion of the charged dust particles was influenced by the electrostatic repulsion among the particles and the size of the charged dust layer formed on the charged surface.

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