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#### Internal Kinetic Energy in Dimensional Collision

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## Derive an Expression for Conservation of Internal Kinetic Energy in a One-Dimensional Collision.

The term kinetic energy refers to the possession of force within an object due to its movement or motion. If an object is gaining force or energy, and therefore speeds up, because of work being done upon it, then, that particular energy gained by that specific object is called Kinetic Energy.  Therefore, the Kinetic Energy can be regarded as the property of an object and it refers to the energy gained by motion only. The object or the body which has possessed the Kinetic Energy, tries to maintain the motion or the energy unless there is a change in the acceleration or the motion of the body. Therefore if the object starts to accelerate, then the amount of energy is restoring within the body also increases, and while decelerating, the amount of work done by the body is the same with the amount of kinetic energy it had gained.

Now, the Kinetic Energy can be explained from two perspective, Newtonian Kinetic Energy, and the Relativistic Kinetic Energy. The Newtonian concept or the classical mechanics explain that the kinetic energy of a point object or a non- rotating object can be determined by the mass of the object and the velocity of the same. Thus, the formula of Kinetic Energy, in classical mechanics is,

Ek = ½ mv2

On the other hand, the Relativistic Kinetic energy refers to the energy of the object in motion is essentially to be determined by the speed of the light. Therefore, the equation of the linear momentum of the object is modified as according to the Relativistic Theory of Kinetic Energy, and thus, the formula of the expression is also modified, where the mass of the object, the velocity of the same, and the speed of the light, and the linear momentum, all are included. Therefore, the expression is,

p = mv, where  = 1/ 1- v2/ c2

Now, considering the question, it is important to understand the concept of internal kinetic energy or internal energy. The internal kinetic energy or the internal energy refers to the random motion of the molecules. The scientists have claimed that the external work which contributes in the generation of the kinetic energy, within an object, also, influences the molecules which consists the object as a whole. Therefore, the internal kinetic energy and the change of the same can only be determined on a microscopic level, and it includes all the translational kinetic energy, potential kinetic energy and the vibrational kinetic energy.

The laws of physics discusses upon the laws of conservation of energy. Which states that the total energy of an isolated system remains constant. This refers, that, the energy of an object, cannot be created or destroyed, rather it can only be transformed or transferred, from one body or form to the other. For example, the explosion of the dynamite refers to the transformation of the chemical energy into kinetic energy. The Newtonian physics states that the conservation of energy does not consider the conservation of mass, however, the Relativity showed that during the conservation of energy, the mass of the object is also conserved. The special theory of relativity shows that the conservation of mass is related to the conservation of energy, and vice versa. The relativity theory has explained this by exemplifying the Big Bang theory, and theoretically it states that an object, along with its mass can be compete converted into pure energy and the big bang theory and the creation of the galaxy is the example of the same.

Now, in case of a one dimensional explosion it is obvious that the laws of conservation of energy will take place and it can be expressed as the following.

In case of a static collision,

E = U1 – U2/ V1 - V2 = 1
Therefore, U1 = V1 – V2 + U2 …… (i)

Conservation of Linear Momentum,

M1U1 + M2U2 = M1V1 + M2V2
M1 (V1 – V2 + U2) + M2U2 = M1V1 + M2V2
M1V1 – M1V2 + M1U2 + M2U2 = M1V1 + M2V2
- (M1 + M2) V2 = - (M1 + M2) V2
U2 = V2

Therefore, it is proved that the changes in the mass will consequently refer to the changes in the energy and vice versa.

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