AliceInPhysics Publications The Principles Of Energy
E=mc²
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
As the issue of the principles of energy has come to the fore, I hereby republish my work on E=mc², in the form I published it in Alice Law Version 5. It has been retranslated with the aim of achieving a better language.
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E=mc²
Animated Figure 1 – Let’s think of a plate mounted on a wagon and a ball lying on it. If the plate is in parallel with the ground, the ball lies on the ball as long as the train stays inert, whereas it falls down if the train moves.
Here, with reference to the examples above, I will explain you what E=mc² means.
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Let’s start by writing the forces affecting the ball:
We are employing the Principle of Forces.
Here, VP or VG is the the size of the potential energy which belong to gravitational force. |
The second force affecting the ball is the repulsive force of the locomotive on X axis direction. Now, let’s write down the potential energy born by this force. The size of the potential energy stemming from the repulsive force is calculated in a similar way. In compliance with the Principle of Forces, we define the repulsive force of the locomotive both as
a and as g. If we interpret the pushing force of the locomotive as repulsive force, our arrow will be
VP, whereas if we interpret it as gravitational force, it becomes
VG. Similar to above, VP or VG is the size of the potential energy which belong to repulsive force of the locomotive. |
On the left, we can see the potential energies belonging to both forces (gravitational force and the repulsive force of the locomotive).
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In our sample, as the size of the gravitational force does not change, the only variable force is the repulsive force of the locomotive. The man will be able to prevent the ball from falling off the plate, as long as he manages to keep the direction of the resultant force perpendicular to the plate. For each value of the repulsive force of the locomotive, there is a certain standing angle of the plate.
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Let’s write the kinetic energies of the ball.
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Now, we need to write down the kinetic energy on Y axis. Let’s see if the ball has kinetic energy on Y axis or not by asking a question to ourselves.
If the Earth, on which we live, disappeared in a moment, would we stay in our places, or would we be scattered in space?
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This way, we have defined the kinetic energies and the potential energies of the ball in both directions. The blue arrows in the figure demonstrate the kinetic energies, while yellow and green arrows show the potential energies. The total energy of the ball is determined by the vector sum of the resultant vectors belonging to the potential and kinetic energies. (Animated Figure 8).
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In the animation above, we have seen that the resultant vectors belonging to the kinetic and potential energies increase as we try to keep the ball on the plate. The sizes of the resultant vectors belonging to the potential and kinetic energies of an object having E=mc² energy have reached c value and both vectors point at the same direction. |
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With the aim of making a suggestion to you, I would like to show you under what kind of an effect an object carrying E=mc² energy is. As you already know, the size of the gravitational acceleration affecting us on the Earth is g=9,81 m/sn².
Now, please think of a gravitational force with an enormous size. Let’s calculate the potential energy of an object having E=mc² energy. The gravitational force affecting the object will constitute the potential energy of that object.
The energy of an object on a celestial body having such an enormous gravitational force is E=mc².
The reason for that is Alice moves upwards at c speed together with the celestial body. Therefore, the kinetic energy of Alice is Ek=½mc². At the same time, Alice is exposed to repulsive force as well. Therefore, her potential energy is Ep=½mc². Alice’s total energy is the sum of both energies. As both energies are in the same direction, Alice’s energy is E=mc².
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