Spring, potential energy

The entropic force fs, given as the negative of the gradient of the spring potential energy, is represented by one of the various kinds of springs used in molecular models (Fig. 3). 

B A system of two balls attached by a spring. Potential energy is gained when the spring is stretched. It is converted to the kinetic energy of the moving balls as the spring relaxes. 

Potential energy stored in pressure vessels, gas tanks, hydraulic or pneumatic systems, such as pipelines, and springs (potential energy can be released as hazardous kinetic energy)... 

Here is the original, many-body potential energy fiinction, while Vq is a sum of single-particle spring potentials proportional to As X —> 0 the system becomes a perfect Einstein crystal, whose free energy... 

Suppose, for simplicity, that the masses in Fig. 5-lb are the same, tti = m2 = m, and all three springs are the same, but veloeities and displaeements of the masses may not be the same. Let one mass be displaeed by a distance x from its equilibrium position while the other is displaeed by a distanee X2- The only plaee the potential energy V... 

By hypothesis, the force eonstant of the eoupling spring is the same as k for the other two springs, so the potential energy ean be written... 

Springs made from coils of wire are used to store elastic energy which is a form of potential energy. The most common type of spring is cylindrically shaped, with coils evenly spaced and of the same diameter. A ballpoint pen uses a coil spring to hold the point in place for writing and to return it to the case for protection. 

The package has a mass of 2 kg or a weight of 4.415 lb. Assume a downward velocity of about 10 ft/s. The shock absorber develops a constant force (independent of the relative velocity) of 10 lb (44.48 N). The spring stiffness is 57.10 Ib/in. The potential energy due to gravity will be neglected. 

Here A is the amplitude, cp the initial phase, and coo the frequency of free vibrations. Thus, in the absence of attenuation free vibrations are sinusoidal functions and this result can be easily predicted since mass is subjected to the action of the elastic force only. In other words, the sum of the kinetic and potential energy of the system remains the same at all times and the mass performs a periodic motion with respect to the origin that is accompanied by periodic expansion and compression of the spring. As follows from Equation (3.105) the period of free vibrations is... 

A simple eigenvalue problem can be demonstrated by the example of two coupled oscillators. The system is illustrated in fug. 2. It should be compared with the classical harmonic oscillator that was treated in Section 5.2.2. Here also, the system will be assumed to be harmonic, namely, that both springs obey Hooke s law. The potential energy can then be written in the form... 

Figure 3.5 Potential energy (PE) exists between objects that either attract or repel each other. When the spring is either stretched or compressed, the PE of the two balls increases.

Potential energy of the normal spring and tangential spring... 

Differences in the potential energy t/ of a Hooke s Law spring can be calculated as the product of the restoring force (—/) and the distance dx over which the force acts. Thus, by substituting -kx in place of/, we get... 

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