Friction coefficient force

Since U equals force/friction coefficient, and the force on the charged species is given as z E by Eq. 8.8, we have... 

Friction force = (friction coefficient)(normal force)... 

Important Terms and Concepts. It is useful to clearly separate the various terms and concepts associated with friction, such as friction force, friction coefficient, frictional energy, and frictional heating. These terms are defined subsequently in the context of solid friction, which can be defined as the resistance to movement of one solid body over another. The movement may be by sliding or by rolling. 

Fig. 7 shows the torque necessary to obtain the specified body force under construction conditions and in tbe state when removed from the bridge. It can well be seen that the change of the friction coefficient causes a very big scattering, and the necessary torque is much bigger than specified. The distribution of the results of a measurement performed on 1,127 bolts is presented in Figure 8. An average of 80% of nominal body force was found by the new method. The traditional method found the nuts could be swivelled much further than specified on 42 bolts, these bolts were found to have 40 - 60 % body force by the new method. 

The traditional method for investigating the forces originating in the body of the bolt, which is based on measuring the torque of the nut, can detect only the bolts with a very great lack of body force since tbe friction coefficient worsens with time. 

Thus, the requirement that the Brownian particle becomes equilibrated with the surrounding fluid fixes the unknown value of, and provides an expression for it in tenns of the friction coefficient, the thennodynamic temperature of the fluid, and the mass of the Brownian particle. Equation (A3.1.63) is the simplest and best known example of a fluctuation-dissipation theorem, obtained by using an equilibrium condition to relate the strengtii of the fluctuations to the frictional forces acting on the particle [22]. 

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. 

The effective moment of inertia / and the friction coefficient / could easily be estimated. The force constant k associated with the relative motion of the lobes was determined from an empirical energy function. To do so, the molecule was opened in a step-wise fashion by manipulating the hinge region and each resulting structure was energy minimized. Then, the interaction energy between the two domains was measured, and plotted versus 0. 

The two sources of stochasticity are conceptually and computationally quite distinct. In (A) we do not know the exact equations of motion and we solve instead phenomenological equations. There is no systematic way in which we can approach the exact equations of motion. For example, rarely in the Langevin approach the friction and the random force are extracted from a microscopic model. This makes it necessary to use a rather arbitrary selection of parameters, such as the amplitude of the random force or the friction coefficient. On the other hand, the equations in (B) are based on atomic information and it is the solution that is approximate. For ejcample, to compute a trajectory we make the ad-hoc assumption of a Gaussian distribution of numerical errors. In the present article we also argue that because of practical reasons it is not possible to ignore the numerical errors, even in approach (A). 

Here, y is the friction coefficient of the solvent, in units of ps and Rj is the random force imparted to the solute atoms by the solvent. The friction coefficient is related to the diffusion constant D of the solvent by Einstein s relation y = kgT/mD. The random force is calculated as a random number, taken from a Gaussian distribu-... 

Let. F > 0 be a given friction coefficient, and > 0 be a known friction force at the boundary. The conditions of given friction along the normal implies... 

Methods for determining fiber-to-fiber friction have been developed (29—31). The friction coefficient can also be measured in terms of the force required to pull entwined fibers apart (32—34) or the force necessary to remove a single fiber from a mass of fibers under pressure (35). Another test involves an apparatus wherein one or a series of parallel fibers are mounted across a small bridge similar to a violin bridge. This is then pressed against a surface that may be another fiber or some other material, and the fibers alternately sHp and stick as they sHde across each other (36,37). 

Friction and Adhesion. The coefficient of friction p. is the constant of proportionality between the normal force P between two materials in contact and the perpendicular force F required to move one of the materials relative to the other. Macroscopic friction occurs from the contact of asperities on opposing surfaces as they sHde past each other. On the atomic level friction occurs from the formation of bonds between adjacent atoms as they sHde past one another. Friction coefficients are usually measured using a sliding pin on a disk arrangement. Friction coefficients for ceramic fibers in a matrix have been measured using fiber pushout tests (53). For various material combinations (43) ... 

Other spectral densities correspond to memory effects in the generalized Langevin equation, which will be considered in section 5. It is the equivalence between the friction force and the influence of the oscillator bath that allows one to extend (2.21) to the quantum region there the friction coefficient rj and f t) are related by the fluctuation-dissipation theorem (FDT),... 

The friction force can formally be expressed with the aid of the friction coefficient... 

Second, we take account of the frictional drag as the solute molecule moves through the solvent. The frictional force is taken to be proportional to the velocity of the particle, with a proportionality constant called the friction coefficient... 

The friction coefficient of 0.03 used above is so low due to the advantage of a wheel on an axle. The friction force at the axle of the pulley wheel is overcome by a smaller force applied at the rim in accord with the principle of the lever. 

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