Static, inclined plane

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. 

As it is practically impossible to compare slip resistance or static coefficients of friction of various WPC materials using the same experimental approach (Table 11.3), I have undertaken—while preparing this book for the publication—a simplified comparison using the standard incline-plane method. This method is a standard experiment in mechanical physics and involves tilting a platform to the point where movement of a material first occurs. The tangent of the angle of the plane at the point of movement is equal to the static coefficient of friction. 

TABLE 11.5 Static coefficient of friction for piastic or WPC deck boards, measured using a simplified inclined plane method. All measurements were done in the most slippery directions, that is, along the grain. Date for dry and wet pressure treated lumber are given for a comparison... 

Robbins [121] has also developed a procedure for determining dry static friction at low load (in the milligram range) by modification of the incline plane fiber loop method of Howell and Mazur [124]. This procedure attempts to measure those intimate fiber-fiber interactions associated with hair body and style retention, by determining the angle of slip for a small hair loop sitting on two parallel hair fibers. Above a 1-mg load, the frictional coefficient decreases very slowly with increasing load. However, below a... 

Static friction describes the force of friction of two surfaces that are in contact but do not have any motion relative to each other, such as a block sitting on an inclined plane. Kinetic friction describes the force of friction of two surfaces in contact with each other when there is relative motion between the surfaces. 

The static coefficient of friction was measure on the cured PCL flocked aluminum test samples using the inclined plane method. Starting from horizontal, the angle of the inclined plane slowly and steadily increased until the frictional surfaces begin to slide past each other. The angle of inclination at which sliding starts, q, is noted. The static coefficient of friction (ji) is then calculated from ... 

T0 compute the maximum work, we need tw o other idealizations. A reversible work source can change volume or perform work of any other kind quasi-statically, and is enclosed in an impermeable adiabatic waU, so 6g = TdS = 0 and dU = S w. A reversible heat source can exchange heat quasi-statically, and is enclosed in a rigid wall that is impermeable to matter but not to heat flow, so = pdV = 0 and dU = 6q = TdS. A reversible process is different from a reversible heat or work source. A reversible heat source need not have AS = 0. A reversible process refers to changes in a whole system, in w-hich a collection of reversible heat plus work sources has AS = 0. The frictionless weights on pulleys and inclined planes of Newtonian mechanics are reversible w ork sources, for example. The maximum possible work is achieved w hen reversible processes are performed with reversible heat and work sources. 

Coefficient of static friction of uncoated paper is determined by the inclined plane method. " One specimen of paper is clamped on an inclined plane and the... 

ASTM D4918-97(2007) Standard Test Method for Coefficient of Static Friction of Uncoated Writing and Printing Paper by Use of the Inclined Plane Method. 

One simple way to measure the static COF is to place a block of steel on a plaque of test material. The plaque is lifted on one end creating an inclined plane that is tilted higher and higher until the block starts to move as shown in Fig. 2.13. The angle of tilt can be used to resolve the forces to calculate the static COF as defined in Eq. (2.5) ... 

Figure 2.13 An inclined plane may be used to determine the static coefficient of friction the geometry is shown on the left and a testing machine using this approach on the right.

The horizontal force of acceleration is Fx = max. By D Alembert s principle the problem may be transformed into one of static equilibrium if the actual accelerating force is replaced by a fictitious inertia force of the same magnitude but the opposite direction, -Fx. The resultant of the gravity force Fy and -Fx is F, and the surface must be normal to the direction of F. Thus tan 0 + ajg. Hence the surface and all planes of equal hydrostatic pressure must be inclined at this angle 0 with the horizontal. 

The rocks with planar anisotropy exhibit the highest strength in the direction perpendicular to the anisotropy and the lowest at an inclination of 30°-45° with the plane of anisotropy in jointed samples. The anisotropy of the specimen influences the dynamic elastic modulus more than the static elastic modulus... 

Consider a layer of particles with homogeneous characteiisties (of size and shape) deposited on a plane which is inclined at an angle a on the horizontal. If the bed is at static equilibrium, the two components of the force exerted per unit surface by a surface layer of thickness h on the underlying layer are ... 

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