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.

I published my study named ďPotential EnergyĒ within Alice Law Version 5 software in 2005 for the first time. I rewrote it so that it will be easier to read on the web. Although I added some minor stuff, the overall content of the essay did not change. Now, I am publishing it in a better-translated form.


The logic behind the setup of my work is as follows:

There are two identical cars; one of them accelerates, and the other one has a uniform linear movement. The only difference between these two cars is their colors. 


The red car, which is initially inert, starts moving and accelerates gradually. Meanwhile, the green car follows it with a fixed speed. The green car catches the red one and is aligned with it for a moment. At this very moment, the speed values of both cars are equal. However, as the red car continues accelerates, the green car immediately falls behind. Animated Figure 1.



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. Letís imagine that the red car accelerates by being pulled with a rope, and letís 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.

Letís first write the kinetic energy of the green car at the moment when the rope is cut. We employ the kinetic energy equation which we already know. As the equality between the speed values is a prerequisite, the kinetic energy of the red car will be similar.



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.


Letís refer to our knowledge of Classical Mechanics:

The arrival of a car moving under force from point A to point B is investigated below. Let the speed value of the car at point A be VA, and its speed value at point B be VB. The increase in the speed of the car will be as written in the equation below. In the equation, a stands for acceleration, while x stands for the distance between points A and B.





In this equation of speed, letís 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:
In order not to cause any confusion, I deliberately use colors while writing.




Letís 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.

Animated Figure 3, which is given below, shows us how the equation of energy above would change if we employ a shorter or longer measurement unit. Letís observe the change in the equation by scrolling the slider placed below the animation.


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.



Letís 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:



Letís 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 black-colored V positioned at the left of the equation must be bigger than the blue-colored V placed at the right of the equation.






Letís 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 red-colored V value in addition to the blue-colored V value in order to achieve equality with the side where the black-colored V is positioned. We must find the red-colored V because V values represent SPEED. As the speed values of both cars are equal and as the black-colored SPEED value is bigger than the blue-colored SPEED value, there must be a red-colored SPEED value maintaining the equality between.


We shall obtain the red-colored 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. Letís name these energies which all refer to something different.


  • Kinetic Energy: It is the motion energy which the object has previously obtained.

  • Potential Energy: It is the motion energy which the object obtains at the moment in question.

  • Motion Energy: It is the sum of the potential and kinetic energies of the object. We can call this energy as ďTotal EnergyĒ as well. This is the energy which determines the speed of the object. (In Alice Law Version 5, I named this energy as ďRelativistic Energy,Ē I hereby correct it.)

The Conclusions of Potential Energy Chapter:

Potential Energy chapter results in significant outcomes with respect to the fact that it presents the correspondent of acceleration in terms of energy. The equations below show how to calculate the energy which is involved in a system at ZERO TIME.



These equations can be used not only for classical forces (pushing-pulling), but also for gravitational force (on the right).

The equations point out that if there is a force affecting the object, the speed of that object cannot be zero.

The equations demonstrate the relationship between acceleration and energy in the way the nature utilizes it.


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=mc≤ equation next. 

You can suspect what I have written or the methods I have adopted here. They may be right or wrong, valuable or worthless, worth-reading or not; it is all about the destiny of what is written.
What matters is to speak out the things you believe in, with the way you deem fair.
If you ask me if I still have any questions about this chapterÖ Of course I do, and you wouldnít believe how many they are. One day, we will perhaps be discussing them as well.

In the study, the Principle of Forces has been utilized for the reasoning process undergone for the moment when the rope is cut.





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