Frictional force defined

The electrical force acting on a positive charge is proportional to the intensity of the electric field at that point. The electric field, on the other hand, is equal to the negative value of the electrical potential grMient, dK/dx, at that point. For charges moving with a constant mean velocity t/, the size of the electrical force equals that of the frictional force. Defining electrical conductivity of the medium as the ratio between the current density and the electric field at that point. 

The coefficient of friction /x between two solids is defined as F/W, where F denotes the frictional force and W is the load or force normal to the surfaces, as illustrated in Fig. XII-1. There is a very simple law concerning the coefficient of friction /x, which is amazingly well obeyed. This law, known as Amontons law, states that /x is independent of the apparent area of contact it means that, as shown in the figure, with the same load W the frictional forces will be the same for a small sliding block as for a laige one. A corollary is that /x is independent of load. Thus if IVi = W2, then Fi = F2. 

The atomic force microscope (ATM) provides one approach to the measurement of friction in well defined systems. The ATM allows measurement of friction between a surface and a tip with a radius of the order of 5-10 nm figure C2.9.3 a)). It is the tme realization of a single asperity contact with a flat surface which, in its ultimate fonn, would measure friction between a single atom and a surface. The ATM allows friction measurements on surfaces that are well defined in tenns of both composition and stmcture. It is limited by the fact that the characteristics of the tip itself are often poorly understood. It is very difficult to detennine the radius, stmcture and composition of the tip however, these limitations are being resolved. The AFM has already allowed the spatial resolution of friction forces that exlribit atomic periodicity and chemical specificity [3, K), 13]. 

If all the PES coordinates are split off in this way, the original multidimensional problem reduces to that of one-dimensional tunneling in the effective barrier (1.10) of a particle which is coupled to the heat bath. This problem is known as the dissipative tunneling problem, which has been intensively studied for the past 15 years, primarily in connection with tunneling phenomena in solid state physics [Caldeira and Leggett 1983]. Interaction with the heat bath leads to the friction force that acts on the particle moving in the one-dimensional potential (1.10), and, as a consequence, a> is replaced by the Kramers frequency [Kramers 1940] defined by... 

For a monolayer film, the stress-strain curve from Eqs. (103) and (106) is plotted in Fig. 15. For small shear strains (or stress) the stress-strain curve is linear (Hookean limit). At larger strains the stress-strain curve is increasingly nonlinear, eventually reaching a maximum stress at the yield point defined by = dT Id oLx x) = 0 or equivalently by c (q x4) = 0- The stress = where is the (experimentally accessible) static friction force [138]. By plotting T /Tlx versus o-x/o x shear-stress curves for various loads T x can be mapped onto a universal master curve irrespective of the number of strata [148]. Thus, for stresses (or strains) lower than those at the yield point the substrate sticks to the confined film while it can slip across the surface of the film otherwise so that the yield point separates the sticking from the slipping regime. By comparison with Eq. (106) it is also clear that at the yield point oo. 

The frictional properties of plastics are of particular importance to applications in machine products and in sliding applications such as belting and structural units such as sliding doors. The range of friction properties are rather extensive. The relationship between the normal force and the friction force is used to define the coefficient of static friction. 

The frictional properties of TPs, specifically the reinforced and filled types, vary in a way that is unique from metals. In contrast to metals, even the highly reinforced plastics have low modulus values and thus do not behave according to the classic laws of friction. Metal-to-thermoplastic friction is characterized by adhesion and deformation resulting in frictional forces that are not proportional to load, because friction decreases as load increases, but are proportional to speed. The wear rate is generally defined as the volumetric loss of material over a given unit of time. Several mechanisms operate simultaneously to remove material from the wear interface. However, the primary mechanism is adhesive wear, which is characterized by having fine particles of plastic removed from the surface. 

The same nano scratch tester was used to carry out the friction tests. The Rockwell diamond tip (radius 2 /u.m) was used to draw at a constant speed 3 mm/min across the sample surface under a constant load of 20 mN for which no scratches occurred for all the samples. Feedback circuitry in the tester ensures the applied load is kept constant over the sample surface. The sliding distance is 3 mm. The friction coefficient is defined normally as the ratio of the friction force and the applied load. 

Abrasion can be defined as the loss of material from a surface due to frictional forces and is most often the result of two surfaces being rubbed together. Abrasion resistance is then the resistance to wear resulting from mechanical action on the surface. 

The sign of the frictional force is negative because it acts in the direction opposite the flow. We have defined left to right as the positive direction. 

This is a surprising result in view of the following argument [51], due to Hiickel. Defining Q and D to be respectively the net charge and the translational diffusion coefficient of the polyelectrolyte, the balance of frictional force ksT/D) p, and electrical force gE gives... 

A mathematical expression that defines how an ensemble average fluctuates with time. An example is the analysis of Brownian motion, where one may seek to understand the nature of the frictional force. If one considers T as a time interval that is very small on the macroscopic scale, but large on the microscopic scale, then... 

Spring-bead models relate frictional force to the relative velocity of the medium at the point of interaction. The entanglement friction coefficient above is defined in terms of the relative velocity of the passing chain. Since the coupling point lies, on the average, midway between the centers of the two molecules involved, the macroscopic shear rate must be doubled when applying the result to a spring-bead model. Substitution of 2 CE for Con in the Rouse expression for viscosity yields... 

Defining 6 = tan-1 p/q and ( ) - dB/dt [ (/) is periodic but time dependent], the frequency of spiraling in phase space is modulated by the frictional force. Moreover, the rate of energy dissipation,... 

As particles sediment under the influence of the centrifugal field, their movement is countered by a resistance force, the frictional force. The frictional force is defined by Equation 7.5. 

The first recorded systematic studies on static friction have been carried out by Leonardo da Vinci.1 He had already stated that friction does not depend on the contact area and that doubling the weight doubles the friction. The most important empirical law found for describing friction was published in 1699 by Guillaume Amontons.2 Like da Vinci he measured the force Ff required to slide a body over a solid surface at a given load Fp (Fig. 11.1). The load is usually the weight of the body but it can also contain an additional external force pushing the body down. Amonton found that the frictional force is proportional to the load and does not depend on the contact area. For example, in Fig. 11.1 the loads F[ = Fp are equal, then the frictional forces are also equal Fp = Fp. In other words the coefficient of friction p defined by... 

Classical, macroscopic devices to measure friction forces under well-defined loads are called tribometers. To determine the dynamic friction coefficient, the most direct experiment is to slide one surface over the other using a defined load and measure the required drag force. Static friction coefficients can be measured by inclined plane tribometers, where the inclination angle of a plane is increased until a block on top of it starts to slide. There are numerous types of tribometers. One of the most common configurations is the pin-on-disk tribometer (Fig. 11.6). In the pin-on-disk tribometer, friction is measured between a pin and a rotating disk. The end of the pin can be flat or spherical. The load on the pin is controlled. The pin is mounted on a stiff lever and the friction force is determined by measuring the deflection of the lever. Wear coefficients can be calculated from the volume of material lost from the pin during the experiment. 

In order to take particle-particle interactions into account, a stability ratio W is included which relates the collision kernel /So to the aggregation kernel /3agg. The stability ratio W depends on the interaction potential aggregation rate without to the rate with interactions additional to the omnipresent van der Waals forces. For Brownian motion as dominant reason for collisions, the stability ratio W can be calculated according to Eq. (6) taken from Fuchs [ 10]. In case of shear as aggregation mechanism, the force dip/dr relative to the friction force should rather be considered instead of the ratio of interaction energy relative to thermal energy. 

In another type of experiment with the ultracentrifuge, the sedimentation coefficient of the particle is obtained. If the centrifugal force greatly exceeds the force due to the osmotic field, the particles will sediment, forming a boundary that will move down from the surface of the solution for positive values of (dp/dc2)v.. This movement will be opposed by the buoyancy of the particles and by the frictional force generated by their motion. It can be shown that this leads to a constant velocity (dr/dt) of the boundary and a sedimentation coefficient, s, is defined for the particle by s = (drldt)l(n2r, where r is the distance to the center of rotation (Schachman, 1959). For vanishing particle concentration,... 

In other words, it is assumed here that the particles are surrounded by a isotropic viscous (not viscoelastic) liquid, and is a friction coefficient of the particle in viscous liquid. The second term represents the elastic force due to the nearest Brownian particles along the chain, and the third term is the direct short-ranged interaction (excluded volume effects, see Section 1.5) between all the Brownian particles. The last term represents the random thermal force defined through multiple interparticle interactions. The hydrodynamic interaction and intramolecular friction forces (internal viscosity or kinetic stiffness), which arise when the macromolecular coil is deformed (see Sections 2.2 and 2.4), are omitted here. 

The friction parameter generally measured is the coefficient of friction. To measure the friction coefficient, a surface is brought into contact with another and moved relative to it. When the two surfaces are brought into contact, the perpendicular force is defined as the normal force (N). The friction force (F) is that force, which opposes relative movement between the two surfaces. From Amonton s law, the coefficient of friction (/u.) is defined as the ratio of the friction force to the normal force ... 

The friction coefficient can be measured in two ways the static friction coefficient Qus) and the dynamic or kinetic friction coefficient (fikX The static friction coefficient is defined as the ratio of the force required to initiate relative movement and the normal force between the surfaces the dynamic or kinetic friction coefficient is defined as the ratio of the friction force to the normal force when the two surfaces are moving relative to each other. For simplicity, much of the research has focused on the dynamic friction coefficients wherein the two surfaces move at a relative constant velocity. Most of the friction studies on skin have dealt with the dynamic friction coefficient and the subscript k is usually dropped. This overview references the dynamic coefficient of friction unless otherwise noted. 

Suppose that in a second experiment the piston is no longer frictionless, again the temperature is constant, now to achieve the same expansion more heat will be needed to overcome the frictional forces which oppose the expansion. So here q > qlev(q = <7rev + q ) but the work performed will be the same for the expansion process. qlev is a particular value of the heat absorbed by the gas and it is only this value which defines the entropy change, AS. This shows, as was seen in Frame 1, that q and w depend on the specific parameters of the experiment or path and are not state functions in contrast to the entropy change, AS. 

The friction coefficient is defined as the ratio of the tangential friction force, resisting relative motion of the surfaces, to the normal load pressing the surfaces together. In the case of high adhesion of wet smooth surfaces, the normal load shall be considered as a sum of the externally applied normal force and the internal adhesion (stiction) between surfaces. For simplification, the normal load is usually considered equal to the externally applied normal force. 

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