Definitions of force

The science of Mechanics is concerned with the strict definition of force and the consequences of this definition. 

When describing the effect of an external force, we must first define the force itself. A lay person s definition of a force is the amount of effort to get the desired effect. As scientists, we need a more precise definition of force. With a precise definition we can understand and quantify the effect of an applied force on a polymeric material. The mathematical definition of force is the work (which is a form of energy) required to move an object over some distance. Another way to define a force is in terms of the acceleration it creates when applied to some object of a mass m. In our everyday experiences, the first explanation is a simple idea to relate to. When we push a stalled car we exert a force on it. We could easily quantify the force from the weight of the car, the slope of the hill it is sitting on, and how far we must push it. Once we begin to talk about forces in polymer systems, the ideas become a bit more complicated. For example, the force required to open a bag of candy is defined by the work required to deform the bag until it ruptures by overcoming the intermolecular forces which hold the plastic together. 

In scientific systems, this is accepted as the definition of force that is, force is a derived dimension, being identical to ML/t2. 

For our purposes, work is done when a displacement occurs under the influence of a force the amount of work is taken as the product of a force by the displacement. Because force and displacement can be given suitable operational significance, the term work also will share this characteristic. The measurement of the displacement involves experimental determinations of a distance, which can be carried out, in principle, with a measuring rod. The concept of force is somewhat more complicated. It undoubtedly originated from the muscular sensation of resistance to external objects. A quantitative measurement is obtained readily with an elastic body, such as a spring, whose deformation can be used as a measure of the force. However, this definition of force is limited to static systems. For systems that are being accelerated, additional refinements must be considered. Because these considerations would take us far... 

Table I presents six basic equations in a general way. Those on the left apply to transfer within a phase A, and those on the right to transfer across a phase boundary AB. The top row expresses the mutual definition of force F, proportionality constant K, and potential . The second row expresses the phenomenological proportionality between flux J and force F. The bottom row states the conservation constraints. The left equation says merely that in a given volume the difference between the accumulation rate and the emanation rate must be attributed to a source S. As stated, these equations apply to any conserved quantity which is diffusing, either within a phase under the influence of a potential gradient or across a phase under the influence of a potential difference.

This Report is arranged as follows. Section 2 is concerned with the representation of force fields the definition of force constants, choice of units, etc. Section 3 is a brief discussion of the theory and interpretation of diatomic vibration-rotation spectra, and is intended to act as an introduction to the greater complications of polyatomic molecules. Section 4 is concerned with the theoretical and mathematical problems involved in relating the spectra of a polyatomic molecule to its force field, and in trying to calculate the force field from observed data. Finally, in Section 5 we discuss some of the calculations carried out at this time, with examples, and we consider some of the problems involved in finding useful model force fields. 

When we write F = ma, we are expressing a relation between measurable quantities, one which holds underspecified conditions, qualifications and limitations. There s more to it than the equation. One must, for example, specify that all measurements are made in an inertial frame, for if they aren t, this relation isn t correct as it stands, and must be modified. Many physical laws, including this one, also include definitions. This equation may be considered a definition of force, if m and a are previously defined. But if F was previously defined, this may be taken as a definition of mass. But the fact that this relation can be experimentally tested, and possibly be shown to be false (under certain conditions) demonstrates that it is more than a mere definition. 

Fundamental definition of force mass X acceleration. ifir... 

Jhe ambiguity in the definitions of force and pressure is related to the presence of long-range interactions in the medium. 

Since the potential Ep is a result of the force T and will decrease if the body is allowed to move, the terms are given opposite signs. Thus one definition of force could be that it is (the negative of) a space rate of change of energy, and the functional form in equation (5.17) is common to all potential quantities. Any change in the potential will appear as work, either done on the body to increase the potential, or by the body in lowering its potential. Thus... 

Consider now the case when the gap between particles is small in comparison with particle size, that is A 1. Since the forces acting on the particles are connected by Eq. (12.43), the problem may be hmited to the definition of force Fi. Taking advantage of Eq. (12.44), and dividing the surface of the particle, S2, into two parts, S and S2 S, where S is that part of the surface located close to the line joining the centers of the particles, we obtain ... 

For scientific purposes the weight of a body is not constant, because gravitational force varies from the Equator to the Poles in space a body would be weightless but here on Earth under the influence of gravity a 1 kg mass would have a weight of approximately 9.81 N (see also the definition of force ). 

Once the electric fields caused by displacement of atomic planes in polar crystals are understood. It is easy to calculate the phonon dispersion ab initio, using the method explained on Ge in Section 5. Fig. 7.0.1 shows the displacement pattern employed it is essentially the same one as in Ge, except that twice as many calculations are now needed the Ga and As atoms have to be interchanged and the calculation repeated with the As-planes displaced. The equivalent "linear chain" is shown in Fig. 7.0.2 together with the definition of force constants to make the definition of k ) clear, the displaced plane (Ga or As ) is shown in Fig. 7.0.2 aSways at origin. The orientation of the +[100] direction is the same as used in Ge (Section 5.3). With two types of atoms in each unit cell the force constants need an additional label "cation-cation" or "anion-anion" but the labels "cation-anion" or "anion-cation" at the odd-neighbor k are not needed since k is the same as k, to any order in u - a... 

The creator of mechanics, the great scientist Isaac Newton, was totally on the side of Descartes. He suggested the well-known definition of force... 

The SI unit of force is the Newton, derived from the base units by using the definition of force, F = ma. The dyne is a non-SI unit of force in which mass is measured in grams and time is measured in seconds. The relationship between the two units is 1 dyne = ICT N. Find the unit of length used to define the dyne. 

Let us assume that sizes of drops are essentially various / , << R. Then, it is possible to consider that the small corpuscle moves simply in a hydrodynamic field big, and at definition of force of resistance of medium to its motion by inhomogeneity of this field it is possible with sufficient accuracy to neglect. If the distance between surfaces of drops several times is more R, it is possible to neglect also forces of hydrodynamic interacting of moving sphere with a motionless flat wall. These assumptions allow to present the equation of motion of a small corpuscle in an aspect ... 

Modality as necessity can usefully be captured in the intuition that the statement in question cannot intelligibly be negated. This intuition can reflect two very different kinds of beliefs or presumptions as to what the function of the law statement could be. R may be that those who hold to the law believe that there is a stable natural mechanism that accounts for the regularity covered by it, as a matter of empirical fact. However, some universal statements are taken to be necessary because their function is not to describe the ways things must be with a pre-given vocabulary, but rather to express a rule which fixes some aspect of the meaning of the descriptive terms that appear in the law . It may be that the law only seems to be about material stuff in the material world. It expresses a semantic rule rather than a putative matter of fact. Newton s Second Law, that the force acting on a body is the product of mass and acceleration, has sometimes been treated as a definition of force as that which produces acceleration. Frederick Waismann once declared that all statements ever uttered by chemists, except the most recent, were necessary truths, since they served to amplify the criteria of identity for the substances in question. 

Other quantities are also used. For example, true stress is sometimes used as force/(actual area) rather than the more conventional definition of force/(original area). In ordinary calculations for steel, wood, and other materials of construction, the materials are regarded as linearly elastic and the modulus is a material property. In the case of polymers subject to larger deformations, the modulus is a function of deformation, deformation rate, and time. It is therefore no longer a material property and various formulas from theory or empirical practice are required to describe polymer elasticity. 

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