The third Newtonian law

Till now we have discussed the question of how other bodies act on a given body. Quantitatively, this action is defined by force. Experience shows that such an action cannot be unilateral, any action has the nature of interaction. Actions and counteraction are equal and indistinguishable. They simultaneously appear and simultaneously disappear, but are attributed to different bodies. All these facts form the essence of the third dynamics law or Newton s third law the forces with which bodies act on each other are always equal in magnitude and oppositely directed. This signifies that at the interaction of two bodies a force Pl2 with which the first body acts on the second, is of the absolute value and oppositely directed to the force with which the second body acts on the first. That is, 

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Solution To determine scale readings means to find the weight of the body mg (a), i.e., the force with which the body acts on a spring. This force, under the third Newtonian law in the inertial system connected to the earth, is equal on the modulo and is opposite in direction to the force of elasticity (force of a support reaction) from which the spring cup of the scales operates on a body N, P being the scale reading, that is mg = -N or in scalar form P = N. 

Any set of MPs (or bodies) is called a material points system. Each system s points can interact both with bodies of the same system and with bodies not belonging to it. Forces acting between the system s MP (bodies) are referred to as internal forces. Forces acting on the system s points from ontside are referred to as external forces. A system is called closed (or isolated) if it comprises all interacting bodies. Thus, in the closed system only internal forces are acting. They compensate each other according to the third Newtonian law. 

Solution Let us consider the forces working on the body. There are several forces acting in a vertical direction however, they all mutually compensate each other (according the third Newtonian law) and are therefore excluded from our consideration. Operating along the horizontal direction are (1) a periodically changing with frequency co external force F t) = Fq cos cot, (2) an elasticity force (3)... 

Classical mechanics is primarily the study of the consequences of these laws. It is sometimes called Newtonian mechanics. The first law is just a special case of the second, and the third law is primarily used to obtain forces for the second law, so Newton s second law is the most important equation of classical mechanics. 

The rheological data are given in Table 1. The second column of the table is the evaporation state of the oil in mass pereentage lost. The third column is the assessment of the stability of the emulsion based on both visual appearance and rheological properties. The power law constants, k and n, are given next. These are parameters from the Ostwald— de Waele equation which describes the Newtonian (or non-Newtonian) characteristics of the material. The viscosity of the emulsion is next and in column 7, the complex modulus which is the vector sum of the viscosity and elasticity. Column 8 lists the elasticity modulus and column 9, the viscosity modulus. In column 10, the isolated, low-shear viscosity is given. This is the viscosity of emulsion at very low shear rate. In column 9, the tan 5, the ratio of the viscosity to the elasticity component, is given. Finally, the water content of the emulsion is presented. 

Note that the force vector represented in the form of (2.5) is a fundamental hypothesis of Newtonian mechanics (i.e., the frame indifference of a force vector see Sect. 2.2.2). The third law gives the interacting forces for a two-body problem, and this will not be treated here. 

Newtonian mechanics that reduces dynamics to an equilibrium condition like statics by extending Newton s third law to the case of forces acting on bodies rather than just bodies in static equilibrium, i.e. it postulates that bodies are always in equilibrium even when they are acted on by a force because the force applied to the body minus the rate of change of the momentum with respect to time is always zero. It was proposed by the French mathematician Jean le Rond D Alembert (1717-83) in 1743. 

We now understand that the first law assures the existence of inertial frames, and the second and third laws are valid in the inertial frames. This is the essence of Newtonian mechanics. 

Here we introduced another tensor, of third rank, with components hijk- By using the distance Ar between r and the colloid at Vc as variable, it is expressed that the flow field moves together with the particle, i.e. is stationary in a particle fixed coordinate system. Importantly, the formulated dependence is of the linear type. Hence, it holds for Newtonian liquids which by definition obey linear laws. All low molar mass liquids behave in a Newtonian manner, at least within the limit of low velocities. 

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