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Collisions
One dimensional collisions between two objects can be studied using a linear air track (shown below).  
The mobiles "float" on a cushion of air to eliminate the force of friction.  
The mass of a mobile can be changed by adding an extra piece of metal.  
The two mobiles have the same mass, m.  
   
Below is a brief description of experiments in which two bodies experience a collision and their velocities (speeds) before and after the collision are measured; first for elastic collisions and then for non-elastic collisions.  
 
Elastic Collisions  
An elastic collision is one in which kinetic energy is conserved.  
In other words, the total KE after the collision is equal to the total KE before the collision.  
   
The springs on the mobiles ensure that the collisions are (very nearly) elastic.  
 
Different collisions were observed but, for practical simplicity, in all the collisions, mobile B was initially stationary and mobile A was pushed (gently, by hand) towards it.  
   
The table below gives a summary of the observations made before and after the collisions.  
   
      Observations after collision
Collision 1  mass of A=mass of B A stops
B moves with the same speed as A had before the collision
Collision 2  mass of A>mass of B A slows down but continues to move in the same sense
B moves to the right but faster than A was moving before the collision
Collision 3  mass of A<mass of B A moves to the left
B moves slowly to the right
 
   
These observations should not be surprising if we remember Newton's Second and Third laws of motion.  
   
In elastic collisions like these, in which one body is stationary before the collision, it is fairly obvious from our observations here that the relative velocity of approach (before the collision) is equal in magnitude to the relative velocity of separation (after collision).  
   
It can easily be shown that this is also true for the case in which both bodies are moving before they collide.  
See here for proof.  
 
Non-Elastic Collisions  
In non-elastic collisions, KE is not conserved. During a non-elastic collision, some KE is converted to other forms (usually thermal energy and/or sound)  
   
A totally non-elastic collision is one in which the velocity of separation is zero (that is, the bodies do not separate, they stick together).  
   
Imagine dropping first a ping pong ball on a hard surface: it bounces.  
This is a very nearly elastic collision.  
Compare this with dropping a piece of plasticene (or similar) on a hard surface... totally "unbouncy" collision... totally non-elastic.  
   
Detailed study of non-elastic collisions is slightly easier, in practice because there is only one velocity to be measured after the collision.  
With the modification shown in the diagram below, we can obtain measurements of velocities before and after a non-elastic collision.  
 
Again, for simplicity, we made collisions in which mobile B was stationary before the collision.  
mass of A mass of B mass of (A + B) speed of A before speed after
m m 2m u u/2
2m m 3m u 2u/3
m 2m 3m u u/3
 
These (idealized!) results suggest that the quantity mass speed has the same value before and after the collision.  
   
Experiments involving interactions in which bodies are free to move in two (or three) dimensions show that, in fact, it is the quantity mass velocity which is the useful quantity.  
   
This quantity is called the linear momentum of the body, given the symbol, p (as usual, a "bold" letter as this is a vector quantity).  
 
the units of linear momentum are kgms-1  
   
The results of our experiments above therefore lead us to the principle of conservation of linear momentum, usually stated as follows:  
   
During any interaction in which no external forces act, the total linear momentum is conserved.  
   
See also Conservation of momentum and Newton's Laws  
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