Acceleration constant

If only ions with a single charge (z = 1) are considered, then with a constant magnetic field strength and constant accelerating voltage, the radius of arc depends on mass and, from Equation 24.3, Equation 24.4 is obtained. 

In addition to secondarv resistance control, other devices such as reactors and thyristors (solid-state controllable rectifiers) are used to control wound-rotor motors. Fixed secondary reactors combined with resistors can provide veiy constant accelerating torque with a minimum number of accelerating steps. The change in slip frequency with speed continually changes the effective reac tance and hence the value of resistance associated with the reactor. The secondaiy reactors, resistors, and contacts can be varied in design to provide the proper accelerating speed-torque curve for the protection of belt conveyors and similar loads. 

If the acceleration is variable, as in sinusoidal movement, piezoelectric systems are ideal. In case of a constant acceleration, and hence a force that is also constant, strain gages may be employed. For petroleum applications in boreholes, however, it is better to use servo-controlled accelerometers. Reverse pendular accelerometers and single-axis accelerometers are available. 

Mossbauer spectra are usually recorded in transmission geometry, whereby the sample, representing the absorber, contains the stable Mossbauer isotope, i.e., it is not radioactive. A scheme of a typical spectrometer setup is depicted in Fig. 3.1. The radioactive Mossbauer source is attached to the electro-mechanical velocity transducer, or Mossbauer drive, which is moved in a controlled manner for the modulation of the emitted y-radiation by the Doppler effect. The Mossbauer drive is powered by the electronic drive control unit according to a reference voltage (Fr), provided by the digital function generator. Most Mossbauer spectrometers are operated in constant-acceleration mode, in which the drive velocity is linearly swept up and down, either in a saw-tooth or in a triangular mode. In either case. 

Fig. 3.2 Triangular velocity reference signal top) and drive error signal bottom) of a Mossbauer drive operating in constant acceleration mode. The error signal is taken from the monitor output F of the drive control unit (see Fig. 3.1). Usually it is internally amplified by a factor of 100. Here, the deviations, including hum, are at the 2%o level of the reference. The peaks at the turning points of the triangle are due to ringing of the mechanical component, induced by the sudden change in acceleration (there should be no resonance line at the extremes of the velocity range)...

Fig. 3.10 Variation of the spectrometer aperture as a function of the source motion for Mossbauer spectrometers operated in constant acceleration mode with triangular velocity profile, and the resulting nonlinear baseline distortion of the unfolded raw spectra. For simplicity a point-source is adopted, in contrast to most real cases (Rib mm active spot for Co in Rh)...

A particle falling freely in vacuum is subjected to a constant acceleration, and its velocity increases continuously. The velocity at any point depends only on the distance from the starting point, and is independent of the size and the density of the particle. Thus a heavy stone and a feather fall at exactly the same rate in an evacuated system. However, in the event of a particle falling in a fluid medium, there is resistance to this fall or movement. The resistance increases as the velocity of the particle increases, and this continues until the forces tending to accelerate the particle and the fluid resistance forces become equal. The particle is then said to have attained its terminal velocity it continues to fall, but with a uniform velocity. 

It is necessary to postulate a dynamic charge distribution as in the well-known, but unrealistic planetary model of the atom. A stable electronic orbit can only be maintained by a constantly accelerated electron, which according to the principles of electrodynamics constitutes a source of radiation. The stability of the atom can simply not be accounted for in terms of classical mechanics. A radically different description of electronic behaviour is required. As a matter of fact, a radically different system of mechanics is required to describe electronic motion correctly and this is where a theoretical understanding of chemistry must start. 

Now I can look upon my life as spread before the scanner of memory and understand all those moments that foreshadowed this one. It is easy to look beyond the personal history to the events of human history and discern therein the prefiguration of this last moment. As a phenomenon it has always existed and it will continue, for it is the moving edge of phenomenal understanding that was generated in the era before physics and it has gathered momentum—a constant acceleration ever since. What we are moving... 

Further identification of the particles is made with 57Fe Mossbauer spectroscopy. Mossbauer spectra were recorded with a conventional constant acceleration spectrometer with 57Co in Rh matrix as a y-ray source. Velocity calibration was made using a 5-pm a-Fe foil at 293 K. Figure 1.6.10 shows the Mossbauer spectra of the sample recorded at 293 K and 4.2 K. Spectra were fitted with theoretical... 

Dose rate Dose per unit time, expressed in Gy s = J kgr s E At a constant accelerating voltage, it is proportional to the electron beam current. 

The deflagration cannot be scaled in terms of charge size since the flame constantly accelerates. A computation was carried out for the large charge only, so that the dimensionless flame position was described by... 

Constant acceleration approximation. An approximation introduced to the time-dependent intermolecular correlation function G, which was commonly referred to as the constant acceleration approximation (CAA), was used to compute the line shapes of collision-induced absorption spectra of rare gas mixtures, but the computed profiles were found to be unsatisfactory [286], It does not give the correct first spectral moment. 

A simple extension of the constant acceleration approximation was later introduced which gave results that agree rather well with the measured spectral profiles and moments [71]. The model has no free parameters although the required value of the derivative of the potential may be used as an adjustable parameter if desired. The computational efforts are minor and the extended constant acceleration approximation should be useful for all types of short-range induction components. 

By setting the derivative of the potential equal to zero in the lower Eq. 5.101, Oppenheim and Bloom s constant acceleration approximation is obtained a more appropriate name would be zero acceleration approximation . By avoiding neglect of the derivative of the potential, one has a simple and certainly more accurate approximation [71]. 

In practical terms, the quality of approximation obtained with the extended constant acceleration approximation is comparable to that of the best ad hoc model profiles to be discussed at the end of this Chapter. This approximation does not make any ad hoc assumptions concerning the line shapes. It may be considered a one-parameter profile (when the derivative of the potential is replaced by an adjustable parameter) and is as such somewhat inferior to the alternative three-parameter profiles mentioned in the cases where a direct comparison is possible. It is noteworthy that the CAA theory can be further refined in a number of ways that will doubtlessly be investigated in the future. 

J. Borysow, M. Moraldi, L. Frommhold, and J.D. Poll. Spectral line shape in collision induced absorption An improved constant acceleration approximation. J. Chem. Phys., 84 4277, 1986. 

M. S. Miller, D. A. McQuarrie, G. Birnbaum, and J. D. Poll. Constant acceleration approximation in collision induced absorption. J. Chem. Phys., 57 618, 1972. 

The data which yield a spectrum can be obtained with a system in which measurements are made at one velocity at a time (the transducer motion during the measurement is held at constant velocity) or, preferably, by changing the velocity through a range at constant acceleration and electronically sorting the y-ray intensity data obtained as a function of the changing source velocity. 

Consider, for example, a car undergoing a journey with an initial speed u and moving with a constant acceleration a. The speed, v, and distance, s, travelled after time t are given by ... 

Fig. 11. MBssbauer spectrum in the constant-acceleration mode. Zero velocity is with respect to 57Co in copper source. Figure according to Boudart el til. (215).

The Basset force can be substantial when the particle is accelerated at a high rate. The total force on a particle in acceleration can be many times that in a steady state [Hughes and Gilliland, 1952]. In a simple model with constant acceleration, the ratio of the Basset force to the Stokes drag, / gs> was derived [Wallis, 1969] and rearranged to [Rudinger, 1980]... 

In extracting square roots, remember that you always obtain two answers a positive root and a negative root. This is a mathematical reality, but in science typically only one of these answers has a physical reality. For example, starting from rest, the distance (x) an object travels, when undergoing constant acceleration (a) for a time interval (t), is given by x = 1/2 at2. Let s solve this equation for t when x = 6 and a = 3 ... 

Take, for illustrative purposes, the equation relating the distance s, covered by an object in time t, travelling at an initial velocity u, when subject to a constant acceleration a ... 

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