Inelastic Collision

An inelastic collision is in contrast to an elastic collision is a collision in which the energy which is the kinetic energy is not conserved due to the action of internal friction. In collisions of bodies which are macroscopic bodies and some of the energy which is the kinetic energy is turned into vibrational energy of the atoms which cause a heating effect and the bodies are deformed.

At any one instant, we can simply say that the half the collisions are said to be inelastic to a varying extent that is the pair possesses less kinetic energy after the collision than before and we can also say that half could be described as “super-elastic” that is possessing more kinetic energy that too after the collision than before. The averaged which is across an entire sample is a  molecular collision that is said to be elastic.

Inelastic Collision Definition

Both kinetic energy and momentum are said to be of conserved quantities in elastic collisions.

Suppose, we can say that if there are two similar trolleys which are travelling towards each other with equal speed. After a period of time, they collide that too by bouncing off each other with no loss in speed. This collision which we have seen is said to be perfectly elastic because no energy has been lost.

In reality, we can say that the examples which are of perfectly elastic collisions are not part of our everyday experiences. Some of the collisions which are between atoms in gases are said to be examples of perfectly elastic collisions. However, we can say that there are some examples which are of collisions which are in mechanics where the energy lost can be negligible. These collisions which we have seen can be considered elastic and even though they are not perfectly elastic. The collisions which are of rigid billiard balls or the balls which are in Newton's cradle are said to be two such examples.

Given that no mechanics problem we can see is likely to encounter a perfectly elastic collision, it may seem that the concept which is of little practical use. However, we can say that in practice it is often very useful. This is because the requirement that the kinetic energy is conserved provides an additional constraint to our equations of motion. This allows us to very easily solve problems which were created in which we would otherwise have too many unknowns. Often we can see that the solution will be quite adequate because the collision is 'close enough' to being perfectly elastic.

Inelastic Collision in Two Dimension

An inelastic collision is a collision in which there is a loss of kinetic energy. While momentum that we are aware of is of the system is conserved in an inelastic collision so the energy which is the kinetic energy is not. This is said to be because some energy which is kinetic had been transferred to something else such as thermal energy, sound energy and even material deformation are likely outcomes.

Suppose we can say that there are two similar trolleys travelling towards each other. They collide but because the trolleys are equipped we can say that with magnetic couplers they join together in the collision and generally become one connected mass. This type of collision which we have just learnt is perfectly inelastic because the maximum possible kinetic energy has been lost. This does not at all mean that the final kinetic energy is necessarily zero or we can say that the momentum must still be conserved.

In the real world, we can notice that most of the collisions are somewhere in between perfectly elastic and perfectly inelastic. A ball dropped from a height h the above a surface typically is found to be bouncing back to some height which is less than h, and that is totally depending on how rigid the ball is. Such collisions are said to be simply known as inelastic collisions.

Inelastic Collision Kinetic Energy

The pendulum which is ballistic is said to be a practical device in which an inelastic collision takes place. We can say that until the advent of modern instrumentation, the ballistic pendulum was widely used to measure the speed of the projectiles.

In this device, we can say that a projectile is fired that too into a suspended heavy wooden block. The wooden block which we have taken is initially stationary. Following the collision that is the projectile generally becomes embedded in the block. Some of the kinetic energy that gets transformed into heat or sound and used to deform the block. However, we can say that the momentum must still be conserved. Consequently, we will notice that the block swings away at some speed. After the collision, the block which we have chosen behaves like a pendulum in which total mechanical energy is conserved. 

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This totally depends on what we are concerned about damaging the vehicle or the occupant.

Suppose we can see that a vehicle collides elastically with another object. The vehicle which will necessarily be in the process of rebound. The change which we can now see in the momentum as the vehicle rebounds is greater than in an equivalent that is the inelastic collision. The force that is on an occupant is said to be therefore greater and that is clearly worse for the occupant. On the other hand, we can say that this is because it is an elastic collision which with no energy will be dissipated in deforming the vehicle. Damage which occurs to the structure of the vehicle would therefore be said to be minimized.