# Work, Energy and Power VII

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COLLISION
Collision between the two bodies is defined as mutual interaction of the bodies for a short interval of time due to which the energy and the momentum of the interacting bodies change.

Types of Collision
There are basically three types of collisions :
i) Elastic Collision : That is the collision between perfectly elastic bodies. In this type of collision, since only conservative forces are operating between the interacting bodies, both kinetic energy and momentum of the system remains constant.
ii) Inelastic Collision : That is the collision between perfectly inelastic or plastic bodies. After collision bodies stick together and move with some common velocity. In this type of collision only momentum is conserved. Kinetic energy is not conserved due to the presence of non-conservative forces between the interacting bodies.
iii) Partially Elastic or Partially Inelastic Collision : That is the collision between the partially elastic bodies. In this type of collision bodies do separate from each other after collision but due to the involvement of non-conservative inelastic forces kinetic energy of the system is not conserved and only momentum is conserved.

Collision In One Dimension – Analytical Treatment
Consider two bodies of masses m1 and mwith their center of masses moving along the same straight line in same direction with initial velocities uand uwith mafter mCondition necessary for the collision is u> udue to which bodies start approaching towards each other with the velocity of approach u1 - u. Collision starts as soon as the bodies come in contact. Due to its greater velocity and inertia mcontinues to push min the forward direction whereas mdue to its small velocity and inertia pushes min the backward direction. Due to this pushing force involved between the two colliding bodies they get deformed at the point of contact and a part of their kinetic energy gets consumed in the deformation of the bodies. Also m being pushed opposite to the direction of the motion goes on decreasing its velocity and mbeing pushed in the direction of motion continues increasing its velocity. This process continues until both the bodies acquire the same common velocity v. Up to this stage there is maximum deformation in the bodies maximum part of their kinetic energy gets consumed in their deformation.

Elastic collision

In case of elastic collision bodies are perfectly elastic. Hence after their maximum deformation they have tendency to regain their original shapes, due to which they start pushing each other. Since mis being pushed in the direction of motion its velocity goes on increasing and mbeing pushed opposite to the direction of motion its velocity goes on decreasing. Thus condition necessary for separation i.e. v> v1 is attained and the bodies get separated with velocity of separation v2 - v1.
In such collision the part of kinetic energy of the bodies which has been consumed in the deformation of the bodies is again returned back to the system when the bodies regain their original shapes. Hence in such collision energy conservation can also be applied along with the momentum conservation.

Hence in perfectly elastic collision between two bodies of same mass, the velocities interchange. ie. If a moving body elastically collides with a similar body at rest. Then the moving body comes at rest and the body at rest starts moving with the velocity of the moving body.

Hence if a huge body elastically collides with a small body then there is almost no change in the velocity of the huge body but if the small body is initially at rest it gets thrown away with twice the velocity of the huge moving body. eg. collision of truck with a drum.

Case 3 : If a small body elastically collides with a huge body,

Hence if a small body elastically collides with a huge body at rest then there is almost no change in the velocity of the huge body but if the huge body is initially at rest small body rebounds back with the same speed.eg. collision of a ball with a wall.

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