Opposing force

From Eq. (9.1) we see that the viscous force associated with this motion equals [i7(dv/dr)] (area), where the pertinent area is proportional to the surface of the sphere and varies as. This qualitative argument suggests that the viscous force opposing the relative motion of the liquid and the sphere is propor tional to [t7(v /R)] (R ). The complete solution to this problem reveals that both pressure and shear forces arising from the motion are proportional tc 77Rvj., and the total force of viscous resistance is given by... 

We prove this by a virtual work calculation. We equate the work done by the applied stress when the dislocation moves completely through the crystal to the work done against the force / opposing its motion (Fig. 9.12). The upper part is displaced relative to the lower by the distance b, and the applied stress does work (7/1/2) moving... 

Figure 4.3. Energy versus bond rotation in methylsuccinic acid (schematic). The diagram shows the greater stability of staggered as compared with eclipsed forms, and the effect of size and dipole moment of substituents on the barriers. The slope of the curve at any point represents the force opposing rotation there. ( = energy of activation of rotation.) (After Gordon )...

The only force opposing the downward flow of the heated air or upward flow of the cooled air is a buoyancy force. In their analysis, Helander and Jakowatz also suggested accounting for inertial forces due to the entrainment of room air. However, this suggestion is not in an agreement with a principle of momentum conservation used in most of the existing models for isothermal jets. 

Sandberg et al. conducted similar tests with a heated linear jet so that the buoyancy forces opposed the forces due to the lower pressure in the circulation zone (bubble). Based on the results of these tests, it was concluded that... 

First, we consider the expansion work done by a system consisting of a gas in a cylinder. The external pressure acting on the outer face of the piston provides the force opposing expansion. We shall suppose that the external pressure is constant, as when the piston is pressed on by the atmosphere (Fig. 6.5). We need to find how the work done when the system expands through a volume AV is related to the external pressure Pcx. 

We can relate pressure to the work of expansion against a constant pressure by using the fact that pressure is the force divided by the area to which it is applied P = PI A (Section 4.2). Therefore, the force opposing expansion is the product of the pressure acting on the outside of the piston, Pex, and the area of the piston, A (P = P(XA). The work needed to drive the piston out through a distance d is therefore... 

Figure 8. For any set of conditions, the greatest velocity that a muscle can shorten is attained when the total force opposing shortening is zero. Empirically, the maximum velocity of shortening increases with the degree of phosphorylation of myosin. This is seen as the straight line in the velocity-phosphorylation plane. The maximum force that a smooth muscle can develop is not increased by phosphorylation beyond about 25% phosphorylation. It seems therefore that past a point, phosphorylation regulates the rate at which work is being done rather than the force that can be developed. The force a muscle can develop if 25% myosin is phosphorylated is maximal and saturated however, the rate of doing work is not saturated and continues to increase with further phosphorylation.

At short interparticle distances, the van der Walls forces show that two metallic particles will be mutually attracted. In the absence of repulsive forces opposed to the van der Walls forces the colloidal metal particles will aggregate. Consequently, the use of a protective agent able to induce a repulsive force opposed to the van der Walls forces is necessary to provide stable nanoparticles in solution. The general stabihzation mechanisms of colloidal materials have been described in Derjaguin-Landau-Verway-Overbeck (DLVO) theory. [40,41] Stabilization of colloids is usually discussed... 

Whichever method is followed, a protective agent able to induce a repulsive force opposed to the van der Waals forces is generally necessary to prevent agglomeration of the formed particles and their coalescence into bulk material. Since aggregation leads to the loss of the properties associated with the colloidal state, stabilization of metallic colloids - and therefore the means to preserve their finely dispersed state - is a cmcial aspect for consideration during their synthesis. 

Various anionic compounds such as halides, carboxylates or polyoxoanions, generally dissolved in aqueous solution, can establish electrostatic stabilization. Adsorption of these compounds onto the metallic surface and the associated countercations necessary for charge balance produces an electrical double-layer around the particles (Scheme 9.1). The result is a coulombic repulsion between the particles. At short interparticle distances, if the electric potential associated with the double layer is sufficiently high, repulsive forces opposed to the van der Waals forces will be significant to prevent particle aggregation. 

In crystal NaCl, each Na+ or Cl- ion is surrounded by 6 nearest neighbors of opposite charge and 12 nearest neighbors of the same charge. Two sets of forces oppose each other the coulombic attraction and the hard-core repulsion. The potential energy u(r) of the crystal is given by the Lennard-Jones potential expression,... 

As the pore sizes are reduced, the frictional forces opposing the movement of water through these pores and waists may become significant, so that equation 16.19 is more accurately represented by ... 

The testing of battery separators and control of their pore characteristics are important requirements for proper functioning of batteries. Mercury porosim-etry has been historically used to characterize the separators in terms of percentage porosity, mean pore size and pore size distribution. In this method, the size and volume of pores in a material are measured by determining the quantity of mercury, which can be forced into the pores at increasing pressure. Mercury does not wet most materials, and a force must be applied to overcome the surface tension forces opposing entry into the pores. 

Contraction does not necessarily imply shortening but refers only to activation of the force-generating process. In order for shortening to occur, the force generated by a muscle must be greater than the force opposing the shortening. If the two forces are equal, there will be an increase... 

How do we know there are attractions and repulsions between molecules First, gases condense to liquids when cooled or compressed, so their molecules must attract one another. Second, liquids are very difficult to compress, so there must be powerful forces opposing molecules being squashed together into a tiny volume. 

In order to specify a pump to meet the required operating conditions it is necessary to calculate the forces opposing the pumping of this fluid, i.e. the pressure or head which makes pumping necessary. Calculations were performed for normal flow conditions and also for design conditions 20% above the normal. The pump specification is based on the larger design values. 

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