Elastic and Inelastic Collision
For an elastic collision it is characteristic that the
sum of the kinetic energies of the involved bodies
is constant
In an inelastic collision, however, both bodies have
the same velocity; the sum of their kinetic
energies is reduced, compared with the initial
value, because a part of it has changed into
internal energy
Inelastic collisions occur when the colliding bodies
deform or stick together
An inelastic collision is
one where the total
kinetic energy of the
colliding particles is
not the same after the
collision as it was
before
Have you ever smashed a toy car into a wall? Before the
collision, the car was moving fast and had lots of kinetic
energy - and afterward, it just sat there with zero
kinetic energy
Energy and momentum are conserved in elastic collisions. In the game of
billiards, elastic collisions occur between balls of equal mass. However,
elastic collisions can occur between objects of very different mass. This
difference in mass creates different outcomes for the collisions
Have you ever seen a basketball
bounce off a backboard? It comes
back with the same level of kinetic
energy as it had when it hit, which
means it was an elastic collision.
The total momentum of the involved bodies is conserved,
regardless whether the collision is elastic or inelastic
Momentum is conserved in inelastic
collisions, but one cannot track the
kinetic energy through the collision
since some of it is converted to other
forms of energy.
Collisions in ideal gases approach perfectly
elastic collisions, as do scattering interactions of
sub-atomic particles which are deflected by the
electromagnetic force. Some large-scale
interactions like the slingshot type gravitational
interactions between satellites and planets are
perfectly elastic.
Head-on Elastic Collisions
For a head-on collision
with a stationary object
of equal mass, the
projectile will come to
rest and the target will
move off with equal
velocity, like a head-on
shot with the cue ball on
a pool table. This may be
generalized to say that
for a head-on elastic
collision of equal masses,
the velocities will always
exchange.
In a head-on elastic collision where the projectile is much more massive
than the target, the velocity of the target particle after the collision will
be about twice that of the projectile and the projectile velocity will be
essentially unchanged.
For a non-head-on elastic collision between equal masses, the angle
between the velocities after the collision will always be 90 degrees.
The spot on a pool table is placed so that a collision with a ball on the
spot which sends it to a corner pocket will send the cue ball to the
other corner pocket.
For non-head-on collisions, the angle between
projectile and target is always less than 90 degrees.
This was important in the analysis of the original
Rutherford scattering experiment.
This case implies that a train moving at 60 miles/hr which hits a small
rock on the track could send that rock forward at 120 miles/hr if the
collision were head-on and perfectly elastic. It also implies that if the
speed of the head of your golf club is 110 miles/hr, the limiting speed
on the golf ball off the tee is 220 miles/hr in the ideal case. That is,
the limiting speed of the ball depends strictly on the clubhead speed,
and not on how much muscle power you put into the swing.
In a head-on elastic collision between a small projectile
and a much more massive target, the projectile will bounce
back with essentially the same speed and the massive
target will be given a very small velocity. One example is a
ball bouncing back from the Earth when we throw it down.
In the case of a non-head on elastic collision, the angle of the
projectiles path after the collision will be more than 90
degrees away from the targets motion.
Inelastic Collision Examples
Most ordinary collisions are classified as inelastic collisions because
some of their kinetic energy is converted to other forms such as
internal energy. Links to some examples are provided.
Example of Force on Car
Inelastic Collisions
Perfectly elastic collisions are those in which no kinetic
energy is lost in the collision. Macroscopic collisions are
generally inelastic and do not conserve kinetic energy, though
of course the total energy is conserved. The extreme inelastic
collision is one in which the colliding objects stick together
after the collision, and this case may be analyzed in general
terms:
K.E. Lost in Inelastic Collision
Non-Stretching Seatbelt
Stretching Seatbelt
Airplane and Duck
Ballistic Pendulum
The ballistic pendulum is a
classic example of a dissipative
collision in which conservation
of momentum can be used for
analysis, but conservation of
energy during the collision
cannot be invoked because the
energy goes into inaccessible
forms such as internal energy.
After the collision,
conservation of energy can be
used in the swing of the
combined masses upward, since
the gravitational potential
energy is conservative.
The Air Track
http://www.walter-fendt.de/ph11e/collision.htm
http://hyperphysics.phy-astr.gsu.edu/hbase/colcon.html#c1