﻿ The value and total quantity of forces acting on a particle must be assessed in each particular case.

# The value and total quantity of forces acting on a particle must be assessed in each particular case.

In that case, if a number of forces acting on the particle is greater than two, we should do the same as in the case of bodies. We need to build the parallelogram for two forces. Then we will make the next parallelogram, using the resulting vector and the next of forces. And so on, until it will be account all of Forces.

The angle between the vectors of forces acting on a particle is very important to clarify the magnitude and direction of the resultant force.

A) The angle between vectors of Forces is from 0˚ to 90˚.

In this case there is some kind of summation of the Forces acting on the particle. Of course, the resultant Force will not be exactly equal to the sum of two Forces acting on the particle. But in any case it will be more than any of two forces, on whose vectors we build the parallelogram. You can see this in magnitude of the diagonal of the parallelogram. And the sharper the angle, the bigger the value of the resultant Force.

An extreme case of acute angle is 0˚, i.e. absence of corner. Force vectors are on the one line and their direction is the same. In this case, it is impossible to construct the parallelogram. Instead of it - the straight. We postpone two segments on it, each of which is equal to one of the operating Forces. At 0˚ occurs the total summing of Force vectors.

B) The angle between vectors of Forces is more than 90˚.

In this case there is a kind of subtraction of the Forces. The resultant Force is always more than the smallest from two Forces and less than the biggest one. Confirmation of this is the magnitude of the diagonal. And the greater the angle, the smaller the resultant force.

An extreme case of obtuse angle is 180˚. Force vectors are collinear. However, unlike the angle equal to 0˚, the vectors are in opposite directions. In this extreme case there is just subtraction the vector of the less force out of the vector of greater force. The difference is exactly corresponds to the magnitude of the resultant force.

In any case, for any magnitude of the angle, the vector of resultant Force is always largely shifted to the larger of two Forces. That is, the biggest Force makes the particle to be displaced in its own direction more than other.

3) Finally, we present information about how the Rule of Parallelogram depends on the type of Forces acting on a particle.

A) Even though sources of all types of forces are different, and their effect on a particle can be compared, since each force seeks to cause the particles to move. And so, even if the forces acting on a particle are of different types, you can build the Parallelogram of Forces on the vectors, and its diagonal will be showing the direction in which the particle will move.

The magnitude of the Force vector is greater, the greater is the force. The Force is greater, the greater is the velocity, with which the particle would be displaced in this direction if another Force did not act on it (or other Forces).

The length of the vector of the resultant Force – the diagonal - corresponds to the rate at which the particle will be displaced by the action of two Forces applied to it.

B) We have established earlier that there are only four main types of forces. When Galileo deduced the Rule of Parallelogram, it is obvious that he has done in relation to the Forces, with which some bodies put pressure on others or drag them, forcing to move. This type of Force is called in this book the Force of Pressure of the Particle Surface. We have heard a little about that the Rule of Parallelogram is used for Gravity Force. Especially, this limit applies to the Repulsive Force and the Force of Inertia, the first of which is almost not recognized by science, and the second is not known at all.

But anyway, this rule is universal and can be used for any type of forces - Pressure of the Particle Surface, Attraction, Repulsion and Inertia. However unchanged it can be applied only to the Force of Pressure of the Particle Surface, i.e. for the same case, which is described by Galileo for bodies.

Two bodies affect on the body from both sides - either put pressure on it or pull. In our case, two particles press on the particle (they can’t mechanically drag the particle).

Taken separately a free particle will never cause the long-term pressure on other particle, if only the Force of Attraction doesn’t act on it from the side of another particle. Or if the particles are included into bodies and they squeeze each other and any particle is located between them. Therefore, in our case it is one-stage pressure on the particle of two particles as a result of collision with it. When two particles collide with a particle, it starts to move by inertia, exactly in accordance with the Rule of Parallelogram. The diagonal (resultant Force vector) shows the direction in which the particle will move. Duration of inertial motion of the particle depends on the rate at which the particles were moving at the time of collision with it, on the angle between the vectors of Forces and also on the quality of the particle itself.

C) The only difficulty, with which we face in the construction of Parallelogram of Forces is related to Attraction and Repulsion Forces. More likely it is not difficult but unaccustomed. The sources of forces of attraction or repulsion are located from the particle on one or another distance. However, the particle feels effect of these forces directly. This is not surprising, because gravitational interaction or anti-gravitational propagates instantaneously. This instantaneous dissemination is explained by the fact that the ethereal "cloth" – it is a kind of monolith that homogeneously fills the entire universe. And the appearance in this cloth of any excess or deficiency of Ether is immediately felt at any distance.

In this case, when the types of Forces acting on a particle are different, the vector of Forces must indicate the direction in which the Force strives to displace the particle. For example, if the Force of Attraction acts on a particle, so the vector will be directed to the object, the source of this force, and not away from it. But in the case of Repulsive Force all is the opposite. The vector will be directed from the source of the Force.

As for the Force of Pressure of the Particle Surface, everything is the same as in mechanics of bodies. In this case, the source of Force is in direct contact with the particle - collides with it. And vector of this Force is directed in the same direction as the motion vector of a particle whose surface exerts pressure.

And finally, there is last of Forces – Force of Inertia. We can talk about the presence of this force only in the case if the particle is moving by inertia. If the particle is not moving by inertia, there is no Force of Inertia. The vector of Inertial Force always coincides with the vector of motion of the particle at this moment. The vector of Inertial Force - this is the Ether emitted by the rear Hemisphere of the particle.

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