Motion without external forces

Kinetics (Cord.) of centrifugation, 115-117 of cyclones, 117-120 electrostatic controlled (see Electrostatic controlled kinetics) equation of motion, 76-77 without external forces, 77-80 ideal stirred settling, 86-88 impaction (see Impaction) isokinetic sampling, 120-124 limitations on, 84 one-dimensional motion, 84-86 respirable sampling, 124-128 stop distance, 83... 

A hydrocarbon chain is in a constant thermal motion, and without external force field, the chains fluctuate around the most stable position given by the distribution of possible conformations at the temperature. The action of external forces at the ends of a molecule causes displacements of chains from their equilibrium conformations and evokes retractive forces. For a hydrocarbon chain of M = 14,000, extended length 125.5 nm, and the end-to-end distance r = 1 mn, the maximum exerted force is 10 MPa. The level of forces exerted by the random coil macromolecules are much lower than the theoretical strength of the primary bonds. The presence of strong intermolecular interactions, such as hydrogen bonds in polyamides, affects the retractive force substantially, causing a restriction of the number of possible chain conformations. In addition, the transitions... 

Oscillatory deformation of a material specimen with the motion generated without the continuous application of an external force. 

Fuoss and Kirkwood32 have obtained equations identical with Eqs. 31 and 32 without introducing, explicitly, the exponential decay function. Like Debye they reasoned as if the problem were mainly one of diffusion by Brownian motion under the influence of an external force. Treating this problem as a Sturm-Liouville equation, they developed /lt into a complete set of orthogonal functions yx. A relaxation time rx is associated with each of these functions. 

The speed of kinesin calculated as a function of the external force showed that applied forces influence the kinesin motion in a rather complicated way (Figure 3.2, left panel) The speed of kinesin shows a maximum at an intermediate external load ( 5pN) and even larger external load slows down the kinesin walking speed, consistent with the experimental results of Carter and Cross [51]. A hindering force slows down the speed of kinesin in the force range of 0 to about 8pN (for [ATP] = 1 mM), without changing the direction of the net motion and the stall force appears to be insensitive to the ATP concentration, which decreases from about 8pN at 5mM of ATP to 7 pN at 5 pM of ATP. 

The central nervous system (CNS) appropriately excites the muscle, and the generated tension is transferred to the skeletal system by the tendon to cause motion, stabilize the joint, and resist the effect of external forces on the body. Hence the functional evaluation of muscles cannot be performed without the characterization of the interfaced mechanical environment. 

Perpetual motion of the third kind. A form of motion that continues indefinitely but without doing any useful work. An example is the random molecular motion in a substance. This type postulates the complete elimination of friction. A mechanism consisting of frictionless bearings maintained in a vacuum could turn indefinitely, once started, without contravening the first or second laws of thermodynamics, provided it did no external work. Experience indicates that on the macroscopic scale such a condition cannot be achieved. On the microscopic scale, however, a superconducting ring of wire will apparently sustain a perpetual current flow without the application of an external force. This could be considered a form of... 

The frictional behaviour of polymers differs somewhat from that of perhaps more familiar materials. The frictional force tends to be proportional not to load (as in the classical case) but to speed. The coefficient of friction is very dependent on the nature of the two surfaces in contact, but is generally low, when suitable pairs are selected. This means that plastics gears can usually be run without external lubricants. Often the static friction coefficient is lower than the dynamic, which helps to explain the absence of slip-stick phenomenon exhibited by some plastics systems in motion this is especially marked with PTFE, which has an exceptionally low coefficient (around 0.02). The non-classical response of plastics materials results from their much lower modulus. Their frictional response is characterized by adhesion and deformation. 

It is important to note that the Stokes equation is linear, unlike the original equation. Therefore the sum of two solutions is a solution itself, and we can treat the case of each external force acting on the system independently. Hence, one can study sedimentation without Brownian motion and vice versa. Solving the Stokes equations for a sedimenting spherical colloidal particle yields the following expression for the velocity of the fluid surrounding the particle ... 

Derive the equations of motion for an isotropic solid without any external forces, Eq. (E.41), starting with the general relations Eq. (E.18) and using the relevant stress-strain relations,... 

Some special cases can be noted in this respect. A system is not closed, but the result of forces is zero. In this case the total momentum of the system is preserved. A system is not closed but one of the projections of external forces (e.g., F- ) is zero. Then Ap = 0 and = const. Hence, the law of conservation is valid only to the given motion direction. This case corresponds, for example, to the motion without friction in a field of a gravity along a horizontal axis with non-zero initial velocity (refer to Example El.4). 

In an elastic material medium a deformation (strain) caused by an external stress induces reactive forces that tend to recall the system to its initial state. When the medium is perturbed at a given time and place the perturbation propagates at a constant speed (or celerity) c that is characteristic of the medium. This propagating strain is called an elastic (or acoustic or mechanical) wave and corresponds to energy transport without matter transport. Under a periodic stress the particles of matter undergo a periodic motion around their equilibrium position and may be considered as harmonic oscillators. 

A fluid may be made to rotate as a solid body without relative motion theoretically between particles, either by the rotation of a containing vessel or by stirring the contained fluid so as to force it to rotate. Thus an external torque is applied. A common example is the rotation of fluid within the impeller of a centrifugal pump or the rotation of a gas within the impeller of a centrifugal fan or centrifugal compressor. 

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