PRIME FACIE EVIDENCE AS A REAL WORK DONE AND MATHEMATICAL DETERMINATION OF CENTRIFUGAL FORCE: A REAL FORCE OF THE NATURE

A REAL WORK DONE BY THE CENTRIFUGAL FORCE: A REAL FORCE OF THE NATURE

Arun Gathoria, India.

E-MAIL: astroarungathoria@rediffmail.com

This research work is fully based on following postulates :-

An effect follows the cause in lock step.
A real force performs a real work done.

Kind attention:

Centrifugal Force is a real force which gets generated to act upon particle in circular motion, out-words from the centre of circular path. Its magnitude is equal to the magnitude of centripetal force and its direction is opposite to the centripetal force.

In existing Physics centrifugal force has been established as a pseudo / imaginary / false force

Centrifugal force as a "real" force may be understood by an experiment in two parts:-

(i) Part-I - Two dimensional event Fig. 1 Work done by a variable force : Two – dimensional case.( see ref.1)

(ii) Part-II - Three dimensional event. Fig. 3 Swinging pendulum (conical Pendulum).

Part-I – Two Dimensional Event: In this part a horizontal force P acting on a particle "m" may vary in direction as well as in magnitude and the particle may move along a curved path.( see refer.1)

A small object of mass "m" is suspended from a string of length L. The object is pulled sideways by a force "P" that is always horizontal until the string finally makes angle q with the vertical. The displacement is accomplished so slowly that we may regard the system as being in equilibrium during the process.

In the free body diagram in fig. 2 the cord makes an angle q with the vertical and by applying the Newton's second law the vector analysis is as follows:

X Component T sin q – 'P' = 0 (Zero) ........................(1)

Y Component – T cos q – mg = 0 (Zero) ...................(2)

T = Tension (as a force)

Since force P acts only in horizontal direction therefore the work done by P is

Wp = mgh

By applying galileon concept of "cause & effect" we observe the following three effects by a horizontal force "P" as a cause –

(1) Formation of an angle “q”

(2) Displacement “d” of mass m in horizontal plane.

(3) Gain of work done "mgh" against gravity ( “m” gains the height “h”).

After observing above three effects, now horizontal force P is withdrawn from the system and mass “m” regains its initial vertically suspended position.

Part-II (Fig. three) Three Dimensional Event: (Swinging pendulum). Now object ‘m’ suspended vertically is allowed circular motion about a point. The force given to the circular motion is increased successively. As a result of this, an angle “q”, radius “r” and gain of work done "mgh" against gravity are observed in the system in equilibrium. These are the same effects which we have already observed in two dimensional events in Fig. 1 as effects of horizontal force "P". Therefore in three dimensional event of swinging pendulum, these three observations as effects confirms that the horizontal force "P" is existing naturally as a real force in this system and along the circular path this horizontal force "P" becomes radial one as a real centrifugal force acting on the object "m".

In three dimensional event of swinging pendulum, the vector analysis of the forces in free body diagram (see fig.2) is the same as has been given in

two dimensional event of part-I. Therefore free body diagrams of mass "m" of part-I and part-II are the same (Fig. 2).

In equilibrium in Part-II event, from the equation "1" in vector analysis diagram:

T sinq — P = 0 (Zero)

It confirms that in circular motion in swinging pendulum centripetal force " T sin q" equalizes real centrifugal force "P" and object remains at net force (0) (Zero) radially, in equilibrium (no force remains for circular motion). Then what force is responsible for circular motion that is a subject matter of angular mechanics and new laws of Motion discovered by the same author given on forth coming pages.

D'Alemburt Principle & Centrifugal Force: (see refer.2) Author claims this principle as very clever principles as it describe the real centrifugal force as a pseudo/imaginary/fictitious force. In D'Alemburt principle, no responsible factor has been considered for the formation of “q” angle, radius “r” and gain of "mgh" against gravity by the object “m” in circular motion in conical pendulum. Therefore, this principle does not have any option other than to consider the real centrifugal force as a pseudo/imaginary/fictitious force and to keep the centripetal force as a responsible factor for circular motion.

"Prediction based on the equation 1 and 2 in two dimensional even" in equilibrium – equation 1 and 2 predict that an analogy of geostationary satellite may be developed in a room by a object suspended in mid air at net force zero by applying a counter field force just against the direction of field force of the gravity (Fig. 4 on 6^th page) and the analogy has been successfully fruitful. Such object on the one hand remains at net force zero in static equilibrium while on the other it remains in circular motion along with the earth with same angular velocity (see fig.5)

Conclusion

1. It is clear from above text that following identical characters in Part I & II events conform the existence of centrifugal force as a real force in circular motion:-

(1) Formation of angle “q”

(2) Horizontal gain of displacement "d"/radius "r".

(3) Gain of work done "mgh" against gravity.

(4) Free body diagram of mass "m".

Indeed above four findings are the Prime facie evidences of centrifugal force in circular motion in a conical pendulum.

2 Centrifugal force as a real force has a magnitude equal to the magnitude of centripetal force and its direction is opposite to that of centripetal one.

3 In equilibrium the real centrifugal force equalizes the centripetal force therefore no specific equation of centrifugal force is required. Equation of centripetal force with minus (–) sign may be used as a equation of centrifugal force. e.g. –GMm/r² in case of determination of the weightlessness of the geostationary satellite. In Geostationary satellite the force of gravity + GMm/r² as a centripetal force is equalized by a real centrifugal force - GMm/r² , this equalization results in weightlessness, then what force is responsible for orbital motion of the satellite in the space that has been discovered by the same author in his further research papers.

4. Source of centrifugal force is a subject matter of angular mechanics and new laws of the motion discovered by the same author and is described in the fourth coming research paper of the same. This development calls for a total revision of total fundamental physics immediately.

References

Physics by Resnick, Haliday and Krane, Physics, vol. 1, V Edn., p.137/138, John Willey and Sons, Singapore (1994).
Engineering Mechanics by MERIUAM & KRAIGE 4^th Edn. P.246/247 John Willey and Sons, Singapore.

GSS

FIGURE 4

The Photograph of a magnetic disk levitating over a super Conducting Material.

(It is the analogy of Geostationary satellite, (GSS), magnetic disk is suspended in mid air at net force zero in static equilibrium. Gravitational force (+mg) acting on the magnetic disk., is equalized by repulsive magnetic field force (-mg).

Note: The previous paper on contradiction to Newton's First Law of Motion by primafacy evidence is just explanatory/complimentory one to this paper as in both the papers uniform circular motion takes place at net force zero (0) practically.

When we are whirled in a circle by a fairground ride, ‘centrifugal force’ makes us fly outwards. It is due to the centrifugal force as a real force only