Apparent force

Thus, the two bosons have an inereased probability density of being at the same point in spaee, while the two fermions have a vanishing probability density of being at the same point. This eonelusion also applies to systems with N identieal partieles. Identical bosons (fermions) behave as though they are under the influence of mutually attractive (repulsive) forces. These apparent forces are called exchange forces, although they are not forces in the mechanical sense, but rather statistical results. 

Electrons with the same spin behave as if there is a repulsive force acting between them. This apparent force is sometimes called the Pauli force. However, it is preferable not to speak of Pauli forces, since they are only apparent forces, not real forces like electromagnetic or gravitational forces. In fact, the Pauli principle implies that there is an intimate interconnection between the constituent parts of matter in the universe. Strictly speaking, no part can be isolated from the rest, except in an idealized way. The Pauli force acts at any time and over huge distances, much larger than atomic dimensions, but its effect becomes dramatic only when electrons of the same spin happen to be close to each other. 

Coriolis effect The apparent force acting on moving particles that results from Earth s rotation. The Coriolis Effect causes freely moving bodies to be deflected to the tight of their direction of motion in the northern hemisphere and to the left in the southern hemisphere. 

Irradiation of (S )-tropolone 2-methyl butyl ether in solution yields a 4-electron electrocyclization product as a 1 1 diastereomeric mixture (Sch. 8) [106]. In solution the presence of the chiral auxiliary in proximity to the reactive center has no influence on the product stereochemistry. When irradiated within NaY zeolite, however, the same molecule affords the cyclized product in 53% diastereomeric excess. The restricted space of the zeolite supercage apparently forces communication between the chiral center and the reaction site. 

If the large body from which the observations are made has an acceleration, the small body will appear to have an equal and opposite acceleration, and so will appear to be acted on by a force. Such apparent forces are exactly like gravitational forces, so that a body moving with an acceleration seems to produce a gravitational field. For example, the acceleration with which all bodies fall towards the earth is only partly due to the gravitational field of the earth. Part of it is due to the acceleration of the earth due to its rotation. It is easy to see that all gravitational fields are not merely appar-... 

In most textbooks the apparent forces, like the Coriolis and the centrifugal forces, are derived with the help of the framework of classical mechanics of a point particle. 

Assuming that Dw/Dt is equal to the local force acting per unit mass on a fluid parcel, the apparent forces in the rotating frame are derived. The above derivation can be called a Lagrangian approach since it exploits the concept of the fluid parcel . In this framework we define ... 

The body forces, like the gravity term, are integrated over the grid volume. Usually, the mean value approach is used, so that the value at the grid center is multiplied by the grid volume. The apparent forces that may occur in particular coordinate systems, are often considered as body forces and integrated in the same way as the gravity term. 

The second term is readily identified ( + l)h2/2mr2 = M2/2mr2, and thus, for circular motion, there is an apparent force ... 

The Vanishing of Apparent Forces The Galilean Transformation The Michelson-Morley Experiment The Galilean Transformation Crashes The Lorentz Transformation New Law of Adding Velocities The Minkowski Space-Time Continuum How do we Gel E =... 

The second term in this force is flie apparent force. One encounters such... 

Hendlik Lorentz indicated fliat the Galilean transformation represents only one possibility of making the apparent forces vanish (i.e., assuring that A = D). Both constants need not equal 1. As it happens, such a generalization was found by an intriguing experiment performed in 1887. 

Thus, we obtain the full Lorentz transformation, which on one hand assures no apparent forces and on the other, assures the same speed of light in both systems ... 

If experiments are to be described in the same way in two laboratories that move with respect to the partner laboratory with constant velocities v and —v. respectively, then the apparent forces have to vanish. The same event is described in the two laboratories (by two observers) in the corresponding coordinate system (in one, the event happens at coordinate x and time r, and in the second, at x and t ). A sufficient condition that makes the forces vanish is based on linear dependence x = Ax + Bt and r = Cat -b Dt, where A, B, C, D denote some constants. 

By adsorption on certain surfaces it is possible so to adsorb pseudoisocyanin from solutions, in which no association is possible, that the association band makes its appearance. This phenomenon occurs especially on mica, while glass and quartz are also suitable (see Skerlak ). The previous considerations make it already possible for us to see what conditions such a surface must satisfy naturally there must be negatively charged spots at which the positive dye ions will be attached. This adsorption does not succeed with polystyrene for example and this must be due to the non-polar character of this substance. Such an adsorption on mica apparently forces the molecules of the dye into a particular position so that the structure of the adsorbed layer becomes similar to that of the micelles. Not exactly so, since the spectral band is somewhat displaced on most adsorbents. Skerlak s investigation on the adsorption of pseudoisocyanin on mica gives a beautiful confirmation of this hypothesis. The molecules of the dye stand perpendicular to the adsorbiiig surface. 

Coriolis force Apparent force on moving particles caused by the Earth s rotation. 

Coriolis force An apparent force, due to the rotation of the Earth, that acts at right angles to the velocity vector of moving objects it is directed to the right of the direction of motion in the Northern Hemisphere, and to the left in the Southern Hemisphere. 

Coriolis force Apparent force acting on a moving object due to the rotation of the coordinate system in which the object s velocity is measured. It is directed perpendicular to the velocity (toward the right in the northern hemisphere and toward the left in the southern) with... 

The concept of apparent forces now follows. Newton s second law is valid in an inertial reference frame and therefore says... 

Thus the acceleration in the rotating frame equals the siun of the net force per unit mass that would be present in an inertial system and the two apparent forces due to the rotation of the coordinate system. When Newton s law is expressed in a rotating coordinate system, the Coriolis and centripetal accelerations are seen as additional forces per unit mass. 

The two capacitive energies are coupled when charge and distance are not independent and when the apparent force, given by the partial derivative of the total capacitive energy (maintaining constant all other independent basic quantities), is equal to zero ... 

One can also define, on the same scheme as the definition of an electrochemical potential (see case study J2), a resulting force, which is an apparent force given by the sum... 

---