An instance of one moving object or
person striking violently against another.

**Elastic collision:**

An elastic collision is
an encounter between two bodies in which the total kinetic energy of the two
bodies after the encounter is equal to their total kinetic energy before the
encounter. Elastic collisions occur only if there is no net
conversion of kinetic energy into other forms.

If
two bodies of masses

**m**and_{1}**m**, moving with speeds_{2}**u**and_{1}**u**with_{2}**u**the same straight line, collide with the each other, their respective speeds_{1}> u_{2}**v**and_{1}**v**after collision are given by_{2}
By the law of
conservation of momentum

**m**

_{1}u_{1}+ m_{2}u_{2 }= m_{1}v_{1}+ m_{2}v_{2}

_{}**m**… (1)

_{1 }(u_{1 }– v_{1}) = m_{2}(v_{2}– u_{2})

**m**

_{1}(u_{1}^{2}– v_{1}^{2}) = m_{2}(v_{2}^{2}– u_{2}^{2})

**m**… (2)

_{1}(u_{1}+ v_{1}) (u_{1}– v_{1}) = m_{2}(v_{2}+ u_{2}) (v_{2}– u_{2})

Divide the equation (2) by equation (1)

We get

**u**… (3)_{1}+ v_{1}= v_{2}+ u_{2}**V**

_{2}= u_{1}+ v_{1}– u_{2}

_{}
Substitute this in the equation (1) we get

**m**

_{1}(u_{1}– v_{1}) = m_{2}(u_{1}+ v_{1}– u_{2}– u_{2})

**m**

_{1}u_{1}– m_{2}u_{1}+ 2m_{2}u_{2}= m_{2}v_{1}+ m_{1}v_{1}

_{}

_{}

Now from
equation (3) we can write

**v**_{1}= u_{2}+ v_{2}–u_{1}

_{}
Substitute
this in the equation 1 and solve as done above then you will get the value of
as

**v**_{2}

**Inelastic collision:**

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

If two bodies of masses

**m**and_{1}**m**, moving with speeds_{2}**u**and_{1}**u**along the same straight line, collide and stick together, the speed_{2}**v**of the composite body is given by

The kinetic
energy of the system of bodies after collision is less than that before
collision. The loss in kinetic energy appears in the form of heat and sound
energy.

**The coefficient of restitution (e):**

The coefficient of restitution (COR)
is a measure of the "restitution"
of a collision between two objects: how much of the kinetic energy remains for
the objects to rebound from one another vs. how much is lost as heat, or work
done deforming the objects.

Suppose a body is dropped from a height

**h**and it strikes the ground with a speed_{0}**v**. Let, after the inelastic collision, the speed with which it rebounds be_{0}**v**and_{1}**h**the height to which it rises, then_{1}

If after

**n**collisions with the ground, the speed is**v**and the height to which the body rises is_{n}**h**_{n}_{,}then