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Final Velocities

Final Velocities In Elastic Collision

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Final Velocities

Response to question: Determination of the final velocities in an elastic collision given masses and initial velocities

An elastic collision refers to a collision that helps in conserving the kinetic energy. Internal kinetic energy on the other hand refers to the sum of all the kinetic energising system. Elastic collisions can be got through the subatomic particles including the striking of the nuclei by the electrons. Macroscopic collisions on the other hand are not completely elastic and kit also includes- kinetic energy that is converted into different energy forms such as the transfer of heat that is the result of friction and sound. An example of the macroscopic collision includes- placing steel blocks on ice. Another major example of the elastic collision includes- the collision of two carts with soring bumpers in an air track. The air tracks and icy surfaces are frictionless and allow elastic collision upon them. Therefore there can be problems with a one dimensional collision between the objects. In order to solve the same problem it is necessary to use the momentum conservation equation of the kinetic energy that is internal. The equation for the same includes-

m1v1+ m2v2= m1v`1+m2v`2(Fnet=0)

In the equation (`) represents the values after collision. Therefore the elastic collision helps in conserving the internal kinetic energy and therefore includes kinetic energy before the collision equals the sum after collision.

An elastic collision includes- the encounter between bodies where the kinetic energy of both the bodies after the encounter in the collision equals to kinetic energy before encounter. Therefore the elastic collision occurs when there is a lack of net conversion in different forms. It can hereafter be said that an elastic collision that is considered to be perfect is one where there is no loss of kinetic energy even during the collision. The observation of momentum conservation and kinetic energy conservation can be done in an elastic collision. There is a collision in case there are two elastic bodies with mass m1 and m2. There also takes place a collision when the above mentioned two bodies have an initial velocity of u1 and u2. The formula of the elastic collision includes- 
m1u1+ m2u2 = m1u1 + m2u2

Here, in this equation, m1 is equal to mass of the first body, m2 is equal to the mass of the second body, u1 is refers to the 1st bodies initial velocity and u2 includes- second bodies initial velocity. V1 is equal to first bodies final velocity, v2 includes the second bodies final velocity. 
In real life situations most of the collisions are not elastic in nature. Parts of colliding objects which includes the initial kinetic energy is converted into other forms of energy such as the heat energy, mechanical deformation energy related to objects, that occur during collision. These types of collision are actually considered as the inelastic collision. For example in case of an automobile accident the initial kinetic energy is converted into the mechanical energy as a result of deformation of the two vehicles. Some of the games in which the inelastic collision occurs includes- handball games, squash, racquetball games. This is so because in case of all the games, after playing with the balls for longer period of time it becomes warm. The kinetic energy arising because of collision between the walls of court gets converted into heat energy.

 Therefore it can be said that the characteristics of inelastic collision includes- velocities of both objects initially and the final velocity of at least one object has been given. There is also a special collision called the total inelastic collision that is characterised by the initial velocities of colliding objects. In case of the totally inelastic collision, two objects stick together. Therefore in case of elastic velocities, objects exchange velocities as they collide with each other. For instance if a second object is stationary and the first object strikes the same the first object halts and the second object starts moving with full velocity.  This same effect is seen in the pool game when the ball gets stroked in such a way that it starts sliding rather than rolling. 

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