Force dependency

The method seirsibility depeird essentially on the poles force attraction which exists at the position of the defect. This attraction force depend on the value of the leakage field, so of the magnetic exciting field which has created them. 

Small drops or bubbles will tend to be spherical because surface forces depend on the area, which decreases as the square of the linear dimension, whereas distortions due to gravitational effects depend on the volume, which decreases as the cube of the linear dimension. Likewise, too, a drop of liquid in a second liquid of equal density will be spherical. However, when gravitational and surface tensional effects are comparable, then one can determine in principle the surface tension from measurements of the shape of the drop or bubble. The variations situations to which Eq. 11-16 applies are shown in Fig. 11-16. 

The equations of motion are integrated using a modified velocity Verlet algorithm. The modification is required because the force depends upon the velocity the extra step involves... 

Figure 9.5a shows a portion of a cylindrical capillary of radius R and length 1. We measure the general distance from the center axis of the liquid in the capillary in terms of the variable r and consider specifically the cylindrical shell of thickness dr designated by the broken line in Fig. 9.5a. In general, gravitational, pressure, and viscous forces act on such a volume element, with the viscous forces depending on the velocity gradient in the liquid. Our first task, then, is to examine how the velocity of flow in a cylindrical shell such as this varies with the radius of the shell.

The term load means either mass or force, depending on its use. A load that produces a vertically downward force because of the influence of gravity acting on a mass may be expressed in mass units. Any other load is expressed in force units. 

Coefficient A and exponent a must be evaluated experimentally. Experiments have shown that A and a are themselves functions of the Reynolds number. Equation 47 shows that the resistance force increases with increasing velocity. If the force field (e.g., gravity) has the same potential at all points, a dynamic equilibrium between forces P and R develops shortly after the particle motion begins. As described earlier, at some distance from its start the particle falls at a constant velocity. If the acting force depends on the particle location in space, in a... 

Note, in contrast to both an isotropic layer and a specially orthotropic layer, that extensional forces depend on shearing strain as well as on extensional strain. Also, the resultant shearing force, N y, depends on the extensional strains, and e, as well as on the shear strain, Similarly, the moment resultants all depend on both the bending curvatures, Kx and Ky, and on the twist curvature, k. ... 

After a fragment has attained a certain initial velocity, the forces acting upon it during flight are those of gravity and fluid dynamics. Fluid-dynamic forces are subdivided into drag and lift components. The effects of these forces depend on the fragment s shape and direction of motion relative to the wind. 

A force is required to rotate an object. The response to the force depends not only the size of the force, but also on the manlier in which the force is applied. A bicyclist must push down on a pedal to cause the sprocket to rotate. But if the shaft to which the pedal is attached is vertical, no rotation results. The greatest response occurs when the bicyclist pushes down on the pedal when the shaft is horizontal. The concept of torque is used to describe rotational motion. The bicyclist pushing down on the pedal when the shaft is vertical produces zero torque. The maxiniuiii torque is produced when the shaft is horizontal. In this case the torque is the product of the force and the length of the shaft. For any other position between vertical and horizontal, the torque is the product of the force, shaft length, and sine of the angle made by the shaft and direction of the force. A force develops power when linear motion is involved and a torque develops power when rotational motion is involved. The power developed by a force is the product of force and linear velocity (P = Fv) and the power developed by a torque is the product of torque and angular velocity (P = Tw). 

All molecules have dispersion forces. The strength of these forces depends on two factors—... 

It is relatively easy to summarize how nuclear stability (and hence the attractive nuclear forces) depends upon the numbers of protons and neutrons in the nucleus. For atoms with atomic number less than 20, the most stable nuclei are those in which there are equal numbers of protons and neutrons. For atoms with atomic numbers between 20 and 83, the most stable nuclei have more neutrons than protons. For atoms of atomic number greater than 83, no nucleus can be considered stable by our definition. These... 

Among the causes producing irreversibility w7e may instance the forces depending on friction in solids, viscosity of liquids imperfect elasticity of solids inequalities of temperature (leading to heat conduction) set up by stresses in solids and fluids generation of heat by electric currents diffusion chemical and radio-active changes and absorption of radiant energy. 

F, is related to the distance dependence of the potential energy, p, by F = —dEp/dr. How does the intermolecular force depend on separation for a typical intermolecular interaction that varies as 1/r6 ... 

The magnitude of the pull-off force depends on the natnre of the tip-sample interaction during contact. Adhesion depends on the deformation of the tip and the sample, because attractive forces are proportional to the contact area. Quantifying the work of adhesion is difficult. The measured magnitude of A7 is strongly dependent on environment, surface roughness, the rate of pull-off, and inelastic deformation surrounding the contact. 

FIG. 1 Schematic representation of the operation of the scanning polarization force microscope (SPFM). An electrically biased AFM tip is attracted toward the surface of any dielectric material. The polarization force depends on the local dielectric properties of the substrate. SPFM images are typically acquired with the tip scanning at a height of 100-300 A. (From Ref. 32.)... 

As we have shown, the polarization force depends not only on the topography [through the f(R z) term] and dielectric constant e, but also on the local contact potential 4). As we shall see now, ac bias modulation and lock-in detection allow these contributions to be separated. 

FIG. 12 Plot of the effective contact angle 0 of the glycerol drops on contaminated mica vs. drop height e. A rapid increase occurs up to 200 A (corresponding to a drop with a base diameter of 2.2 p.m), where it reaches a constant value Gq. Inset Plot of (Go - 0 )/(l + e/8) vs. e. This plot shows that the potential due to the long-range forces depends exponentially on the distance. (From Ref. 9.)... 

In the liquid state, the molecules are still free to move in three dimensions but stiU have to be confined in a container in the same manner as the gaseous state if we expect to be able to measure them. However, there are important differences. Since the molecules in the liquid state have had energy removed from them in order to get them to condense, the translational degrees of freedom are found to be restricted. This is due to the fact that the molecules are much closer together and can interact with one another. It is this interaction that gives the Uquid state its unique properties. Thus, the molecules of a liquid are not free to flow in any of the three directions, but are bound by intermolecular forces. These forces depend upon the electronic structure of the molecule. In the case of water, which has two electrons on the ojQ gen atom which do not participate in the bonding structure, the molecule has an electronic moment, i.e.- is a "dipole". 

In order to determine the force with which an arbitrary body acts on a particle located around the point p, we mentally divide the volume of the body into many elementary volumes, so their dimensions are much smaller than the corresponding distance from the particle p. It is clear that the magnitude and direction of each force depends on the position of the point q inside a body. Now, applying the principle of superposition, we can find the total force acting on the particle p. Summation of elementary forces gives ... 

In 1749, D Alembert pointed out that there is a connection between the theory of precession and a figure of the earth. As is well known, precession is caused by the fact that the resultant force of attraction due to celestial bodies, such as Sun and Moon, does not pass through the center of the earth. Correspondingly, there are couple of forces, which tend to turn Earth in such way that the plane of an equator would go through an attracting body and produce a precession. If the earth had a spherical form, then due to spherical symmetry the resultant force passes through the center. However, the spheroidal form does not have such symmetry. Points of the equator or polar axes are exceptions, since the resultant force passes through the earth s center. For all other points this condition is not met. Besides, the position of the resultant force depends also on the distribution of a density inside the earth. Let... 

Temperature Programmed Desorption (TPD). Chemisorbed molecules are bonded to the surface by forces dependent on the nature of the sites. For instance, ammonia will be strongly adsorbed on acid sites, whereas it is only weakly adsorbed on basic sites. Consequently, the adsorbate complex formed with the basic sites will decompose at lower temperatures than that formed with the acid sites. The following example regarding the NH.i-zeolite H-ZSM-5 system will illustrate this. 

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