Proportional to force

A crystal material is excited by the force imposed on it by an internal I v mounted mass. A voltage is produced by the crystal proportional to accel eration. This voltage is then amplified by a charge amplifier type signal conditioner from whence the signal can be transmitted long distance. (1.000 feet is not uncommon) to the monitor/readout unit. It is calibrated in terms of gravitational units (g), which are proportional to force. Force is ttnc of the most reliable indicators of equipment distress. 

In the absence of factors dictating a specific choice, velocity waves are a good overall choice because (1) it is numerically easier to perform digital integration to get displacement than it is to differentiate displacement to get velocity, (2) slope waves are immediately computable from velocity waves. Slope waves are important because they are proportional to force waves. 

If a fluid (e.g., water) flows in direct proportion to the force applied, it is said to exhibit "Newtonian" flow. However, the flow of molten polyethylene is not directly proportional to force applied, and polyethylene is said to exhibit "non-Newtonian" flow. Polyethylene becomes less viscous at higher stress ("shear"). This is called "shear thinning" and is typical of molten polyethylene. 

Acceleration is directly proportional to force. Highei derivatives of the trqectory with respect to time do not enter this equation, and neither does fhe nature or cause of the force. The equation is also invariant with respect to any possible starting point (position, velocity, and mass). What remarkable simplicity and gmerality there is (within limits, see Chapter 31. 

Newton s law of motion n. Every body continues in its state of rest or of uniform motion in a straight line except in so far as it may be compelled to change that state by the action of some outside force. Change of motion is proportional to force applied and takes place in the direction of the line of action of the force. Also, to every action there is always an equal and opposite reaction. 

In the seventeenth century, the British physicist Robert Hooke (Purrington 2009) defined the basic relation between stress and strain as Ut tensio, sic vis. meaning extension is proportional to force. This so called Hooke s law is valid for many inorganic materials in the linear elastic region, where force-induced deformations are reversible and the material will completely return to its initial shape after removing the force without any delay or residual plastic deformations. 

Boyle s law At constant temperature the volume of a given mass of gas is inversely proportional to the pressure. Although exact at low pressures, the law is not accurately obeyed at high pressures because of the finite size of molecules and the existence of intermolecular forces. See van der Waals equation. 

A new, non destructive method has been developed for testing high strength bolts which is based on measuring the magnetic stress on the head of a bolt. The forces originating in the body of the bolt can be determined in this way since these forces are proportional to the stress state in the head of the bolt. 

During the tightening, stress changes also occur in the head of the bolt that are proportional to those in the body of the bolt, so, if measurements are carried out on the appropriate parts of the head the forces in the body can be determined (Fig. 6). 

An interesting aspect of friction is the manner in which the area of contact changes as sliding occurs. This change may be measured either by conductivity, proportional to if, as in the case of metals, it is limited primarily by a number of small metal-to-metal junctions, or by the normal adhesion, that is, the force to separate the two substances. As an illustration of the latter, a steel ball pressed briefly against indium with a load of IS g required about the same IS g for its subsequent detachment [37]. If relative motion was set in, a value of S was observed and, on stopping, the normal force for separation had risen to 100 g. The ratio of 100 IS g may thus be taken as the ratio of junction areas in the two cases. 

The leading order quantum correction to the classical free energy is always positive, is proportional to the sum of mean square forces acting on the particles and decreases with either increasing particle mass or mcreasing temperature. The next tenn in this expansion is of order This feature enables one to independently calculate the leading correction due to quanmm statistics, which is 0(h ). The result calculated in section A2.2.5.5 is... 

Figure Bl.19.23. Principle of simultaneous measurement of nomial and lateral (torsional) forces. The intensity difference of the upper and lower segments of the photodiode is proportional to the z-bending of the cantilever. The intensity difference between the right and left segments is proportional to the torsion, t, of the force sensor. (Taken from [110], figure 2.)...

Carpick et al [M] used AFM, with a Pt-coated tip on a mica substrate in ultraliigh vacuum, to show that if the defonnation of the substrate and the tip-substrate adhesion are taken into account (the so-called JKR model [175] of elastic adliesive contact), then the frictional force is indeed proportional to the contact area between tip and sample. Flowever, under these smgle-asperity conditions, Amontons law does not hold, since the statistical effect of more asperities coming into play no longer occurs, and the contact area is not simply proportional to the applied load. 

Migration is the movement of ions due to a potential gradient. In an electrochemical cell the external electric field at the electrode/solution interface due to the drop in electrical potential between the two phases exerts an electrostatic force on the charged species present in the interfacial region, thus inducing movement of ions to or from the electrode. The magnitude is proportional to the concentration of the ion, the electric field and the ionic mobility. 

The time-averaged force, equation (Cl.4.3), consists of two tenns tire first tenn is proportional to tire gradient of tire electric field amplitude tire second tenn is proportional to tire gradient of tire phase. Substituting equation (Cl.4.4) and equation (Cl.4.5) into equation (Cl.4.3), we have for tire two tenns. 

This expression shows diat if die detuning Acuj is negative (i.e. red detuned from resonance), dieii die cooling force will oppose die motion and be proportional to die atomic velocity. The one-diniensional motion of die atom, subject to an opposing force proportional to its velocity, is described by a damped haniionic oscillator. The Doppler damping or friction coefficient is die proportionality factor. 

Thus, under conditions of plastic defonnation the real area of contact is proportional to the nonnal force. If the shear force during sliding is proportional to that area, one has the condition that the shear force is proportional to the nonnal force, thus leading to the definition of a coefficient of friction. 

Equation (C3.5.2 ) is a function of batli coordinates only. The VER rate constant is proportional to tire Fourier transfonn, at tire oscillator frequency Q, of tire batli force-correlation function. This Fourier transfonn is proportional as well to tire frequency-dependent friction q(n) mentioned previously. For example, tire rate constant for VER of tire Emdamental (v = 1) to tire ground (v = 0) state of an oscillator witli frequency D is [54]... 

VER in liquid O 2 is far too slow to be studied directly by nonequilibrium simulations. The force-correlation function, equation (C3.5.2), was computed from an equilibrium simulation of rigid O2. The VER rate constant given in equation (C3.5.3) is proportional to the Fourier transfonn of the force-correlation function at the Oj frequency. Fiowever, there are two significant practical difficulties. First, the Fourier transfonn, denoted [Pg.3041]

Figure C3.5.6. The computed Fourier transfonn at frequency co, of tire classical mechanical force-force correlation function for liquid O2 at 70 K from [M]- The VER rate is proportional to the value of ( " at tire O2...

If there are no reactions, the conservation of the total quantity of each species dictates that the time dependence of is given by minus the divergence of the flux ps vs), where (vs) is the drift velocity of the species s. The latter is proportional to the average force acting locally on species s, which is the thermodynamic force, equal to minus the gradient of the thermodynamic potential. In the local coupling approximation the mobility appears as a proportionality constant M. For spontaneous processes near equilibrium it is important that a noise term T] t) is retained [146]. Thus dynamic equations of the form... 

Parallel molecular dynamics codes are distinguished by their methods of dividing the force evaluation workload among the processors (or nodes). The force evaluation is naturally divided into bonded terms, approximating the effects of covalent bonds and involving up to four nearby atoms, and pairwise nonbonded terms, which account for the electrostatic, dispersive, and electronic repulsion interactions between atoms that are not covalently bonded. The nonbonded forces involve interactions between all pairs of particles in the system and hence require time proportional to the square of the number of atoms. Even when neglected outside of a cutoff, nonbonded force evaluations represent the vast majority of work involved in a molecular dynamics simulation. 

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