Alice In Physics Publications The Principles Of Energy
Potential Energy
Han
Erim August 30 ,2011 Copyright © 2011 Han Erim All Rights Reserved.
(First release is in the Alice Law Version 5 physics program, November 2005 ) Reprinted for web
Potential Energy
Does acceleration have a correspondence in terms of energy? This research which I have carried out with the aim of answering this question has always been important for me.
The logic behind the setup of my work is as follows:

What we would like to investigate is the energies of both cars when they are in alignment and have the same speed.

Animated Figure 2. Let’s imagine that the red car accelerates by being pulled with a rope, and let’s assume that this rope is cut when the two cars are aligned and have the same speed. In this case, both cars will continue travelling at the speed values they have achieved. As the speed values of both cars are equal at the moment when the rope is cut, they will keep the alignment with each other.
However, there is a force affecting the red car at the moment when the rope is cut, and the kinetic energy equation we have employed above does not show us this detail.
In this equation of speed, let’s imagine that x distance is one meter. In this case, x is omitted from the equation and the equation will have the form shown below. We will have changed the equation into an equation of energy, if we multiply each sides of it with (m/2). (The m value is the mass of the car)
This equation tells us the following:
Let’s follow an interesting way now:
As we already know, choosing meter as our measurement unit is completely arbitrary. The length of standard meter could have been longer or shorter.
Regardless of the length of the measurement unit, the energy that the car has when it reaches point B, namely the left side of the equation, will never change. On the other hand, the right side, which consists of two sections, is variable. In order to maintain the equality in the equation, the kinetic energy on point A will decrease as the measurement unit extends, whereas the force will increase. If the measurement unit is chosen to be shorter, the kinetic energy on point A will increase, whereas the force will be reduced.
Another thing that the figure suggests us is: Due to the fact that the car moves under the effect of force, even if the measurement unit equals to zero, the force value positioned at the right side of the equation (m.a), will never be zero.

Let’s change the length of the measurement unit and reduce it to zero by using the slider in the Animated Figure 3. Let points A and B overlap each other. In this case, the equation we have described above will have the following form:
Let’s write this outcome in the form of an equation of energy:
As
it is obviously seen, since m.a, namely the
force, is not zero in the equation, achieving the equality is possible only in
one way. The blackcolored V positioned at the left of the equation must
be bigger than the bluecolored V placed at
the right of the equation.
Let’s
combine the outcome we have reached with the sample of two cars we had in the
beginning. We shall write the kinetic energies of both cars next to them.
We see that we need a redcolored V value in addition to the bluecolored V value in order to achieve equality with the side where the blackcolored V is positioned. We must find the redcolored V because V values represent SPEED. As the speed values of both cars are equal and as the blackcolored SPEED value is bigger than the bluecolored SPEED value, there must be a redcolored SPEED value maintaining the equality between.
We shall obtain the redcolored V value by writing the correspondent of m.a force value in terms of kinetic energy.
We achieve the result this way. The speed of the red car is determined by the Blue V and the Red V together. All of these energies, which we have defined with different colors, are all kinetic energies; however, all of them have different meanings. Let’s name these energies which all refer to something different.
The Conclusions of Potential Energy Chapter:
These equations can be used not only for classical forces (pushingpulling), but also for gravitational force (on the right).
The research of Potential Energy is a genuine one. There may be similar publications previously written by others, I am not sure about that. To tell the truth, I have not investigated if there are any. All in all, I have been researching something that I need an answer for, the correspondent of acceleration in terms of energy. This is what only mattered for me, because when I achieve it, I knew that it will be the E=mc² equation next.

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