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What is an elastic collision?
An elastic collision is a collision in which there is no net
loss in kinetic energy in the system as a result of the
collision. Both momentum and kinetic energy are
conserved quantities in elastic collisions. Suppose two
similar cars are traveling toward each other with equal
speed. They hit and bounce off each other with no loss
in speed. This collision is perfectly elastic because no
energy has been lost.
In reality, examples of perfectly elastic collisions are
not part of our everyday experience. Some collisions
between atoms in gases are examples of perfectly
elastic collisions. However, there are some examples of
collisions in mechanics where the energy lost can be
negligible. These collisions can be considered elastic,
even though they are not perfectly elastic. Collisions of
rigid billiard balls or the balls in a Newton's cradle are
two such examples.
The Law of Conservation of Momentum
The law of conservation of momentum states that for two
objects colliding in an isolated system, the total momentum
before and after the collision is equal. This is because the
momentum lost by one object is equal to the momentum gained
by the other
Conservation of momentum is derived from Newton's laws of
motion. Newton's third law states that every action has an
equal but opposite reaction; the force that one object A
exerts on object B is equal but opposite to the force that
object B exerts on object A. By Newton's second law, this
force is equal to the product of the mass and the acceleration
of the objects, so the product of the mass and acceleration of
object A is equal but opposite to the product between the
mass and acceleration of object B.
Acceleration is the change of velocity divided by the time.
Time is cancelled in the equation because in a collision, the
forces act within the same time frame. Thus, the product of
object A's mass and change in velocity is equal but opposite to
the product of object B's mass and change in velocity.
Momentum is defined as the product of mass and velocity, so
finally the change in object A's momentum is equal to the
opposite of the change in object B's momentum.
What is an inelastic collision?
An inelastic collision is a collision in which there is a
loss of kinetic energy. While momentum of the system
is conserved in an inelastic collision, kinetic energy is
not. This is because some kinetic energy had been
transferred to something else. Thermal energy, sound
energy, and material deformation are likely.
Suppose two similar cars are traveling towards each
other. They collide, but because the cars are equipped
with magnetic couplers they join together in the
collision and become one connected mass. This type of
collision is perfectly inelastic because the objects hit
and stick. This doesn't mean that the final kinetic
energy is necessarily zero; momentum must still be
conserved.