Newton’s inverse-square law

Charles Augustin de Coulomb (1736-1806). French physicist. Coulomb did research in electricity and magnetism and ap-plied Newton s inverse square law to electricity. He also invented a torsion balance. 

Newton s Inverse-square Law Newton s calculation (Stirling, 1935) of the correct formula enabled the synthesis with Kepler s model. 

The conclusion from this brief discussion is that molecular adhesion is caused by electromagnetic forces, but not the simple forces that operate in electric motors or between magnets. Those Coulombic forces can be either attractions or repulsions and obey Newton s inverse square law. By contrast, molecular adhesion is caused by London forces which are always attractive and which fall off extremely rapidly with separation. 

The equation for Coulomb s Law resembles the inverse square law developed by Isaac Newton to calculate the gravitational attraction between two bodies... 

Some of the first steps toward understanding how the basic corpuscles of matter behaved came from what might seem like an unlike source meteorology. John Dalton (1766-1844), bom in Manchester, began to study weather in 1787. He also studied Newton s Principia and as a result was conversant with the concept of the inverse square law. Newton had used it to show that the attraction of gravity decreased as the square of the distance between objects. This mathematical relationship also applied to a range of other physical phenomena, such as luminosity. When considering questions about precipitation— why there was fog, rain, and snow—he discovered that the quantity of water vapor in a gas was independent of the type of gas but dependent on the temperature of the gas. 

Newton came across the Robert Hooke s famous book Micrographia that was published around 1964. Robert Hooke is famous for providing the law of elasticity in 1660. It states that for relatively small deformations of an object, the displacement or size of the deformation is directly proportional to the deforming force or load. It is said that Hooke got this idea while working with Robert Boyle (1627-1691) on whose name is a law that states that for a fixed amount of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional. In 1678, Hooke described the inverse square law to describe planetary motion. Later on Newton provided a universal law of gravitation that is stated as follows ... 

These are problem relative - there is a model for the blood system of a mammal and another for the nervous system, both abstracted from the body of the animal in question. To create an analytical model the anatomist must be able to observe the body of the animal in question as a concrete source of the abstract lay out of the various anatomical systems that can be represented in diagrams. Newton s model of the solar system as a system of perfect material spheres obeying Kepler s laws of motion and the inverse square law of gravitational attraction was derived by abstraction and ideahzation of observable fears of the actual solar system (Frigg 2010 251-268). Analytical models can be wholly pictorial as in anatomy or they can be abstract and partially mathematical as in the Newtonian cosmology. 

Newton s law of attraction states that the force of interaction of particles is inversely proportional to the square of the distance between them. However, in a general case of arbitrary bodies the behavior of the force as a function of a distance can be completely different. 

Assuming Newton s law of gravity given by the famous inverse squared relationship ... 

In the above calculation the system has been treated as though the nucleus were stationary and the electron moved in a circular orbit about the nucleus. The correct application of Newton s laws of motion to the problem of two particles with inverse-square force of attraction leads to the result that both particles move about their center of mass. The center of mass is the point on the line between the centers of the two particles such that the two radii are inversely proportional to the masses of the two particles. The equations for the Bohr orbits with consideration of motion of the nucleus are the same as those given above, except that the mass of the electron, m, is to be replaced by the reduced mass of the two particles, /, defined by the expression 1/m = 1/m + 1/M, where M is the mass of the nucleus. 

I. The calculation of the momentary states from the complete law. Before the instantaneous rate of change, dyjdx, can be determined it is necessary to know the law, or form of the function connecting the varying quantities one with another. For instance, Galileo found by actual measurement that a stone falling vertically downwards from a position of rest travels a distance of s = gt2 feet in t seconds. Differentiation of this, as we shall see very shortly, furnishes the actual velocity of the stone at any instant of time, V = gt. In the same manner, Newton s law of inverse squares follows from Kepler s third law and Ampere s law, from the observed effect of one part of an electric circuit upon another. 

The hydrogen atom consists of an electron and a proton. The interaction of their electric charges, —e and +e. respectively, corresponds to inverse-square attraction, in the same way that the gravitational interaction of the earth and the sun corresponds to inverse-square attraction. If Newton s laws of motion were applicable to the hydrogen atom we should accordingly expect that the electron, whose mass is small compared with that of the nucleus, would revolve about the nucleus in an elliptical orbit, in the same way that the earth revolves about the sun. The simplest orbit for the electron about the nucleus would be a circle, and Newton s laws of motion would permit the circle to be of any size, as determined by the energy of the system. 

The concept of a global gravity field is based on the basic principles of physics, which is at present largely Newtonian mechanics. Newton s Law of Gravitation states that the magnitude of the force between two masses M and m is inversely proportional to the square of the distance (r) between them and may be written as ... 

Examples.—(1) Assuming the Newton-Laplace formula that the square of the velocity of propagation, V, of a compression wave (e.g., of sound) in a gas varies directly as the adiabatic elasticity of the gas, E, and inversely as the density, p, or V2 cc E /p show that F2 oc yRT. Hints Since the compression wave travels so rapidly, the changes of pressure and volume may be supposed to take place without gain or loss of heat. Therefore, instead of using Boyle s law, pv = constant, we must employ pvy = constant. Hence deduce yp = v. dp/dv = Eq. Note that the volume varies inversely as the density of the gas. Hence, if... 

Many of the periodic trends in properties of the elements can be explained using Coulomb s law, which states that the force (F) between two charged objects (Qi and is directly proportional to the product of the two charges and inversely proportional to the distance (d) between the objects squared Force is inversely proportional to d, whereas energy is inversely proportional to d [W Section 5.1]. The SI unit of force is the newton (N = m kg/s ) and the SI unit of energy is the joule (J = m kg/s"). 

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