It's professor Dave, let's learn about collisions.
Whenever an object in motion comes into contact with
another object, we can call this event a
collision, and this concept applies to
balls on a pool table just as it does to
tiny molecules or huge celestial objects
like asteroids and planets. As we just
learned, in any collision there must be a
conservation of linear momentum, but this
can manifest itself in different ways
depending on the type of collision that
is occurring, so let's go over these
varieties now. First we will discuss
elastic collisions. These resemble
collisions between balls on a pool table
where the objects involved remained
separate after the collision occurs. With
elastic collisions, total kinetic energy
will be conserved as well as the total
momentum of the system, so the objects
will bounce off of one another with no
energy lost whatsoever as a result of
the collision. We approximate collisions
between atoms and molecules as being
elastic when we refer to an ideal gas
just the way we do with billiard balls.
There are many other examples of
collisions that aren't completely
elastic but we can treat them that way,
like when a soccer player kicks a ball
since the player's foot and the ball do
indeed remain completely separate after
the collision. We would refer to all of
these scenarios as examples of nearly
elastic collisions, since some kinetic
energy is lost to heat and sound in each
case. Perfectly inelastic collisions are
those in which two separate objects
collide, after which they move together
as one mass. Sometimes when celestial
bodies collide, like two asteroids, the
collision is inelastic and they fuse
together to form a larger body. In fact,
this is how all planets begin to form,
including the earth, over the course of
millions of such collisions. When we
examine perfectly inelastic collisions
it is easy to analyze momentum because
we can treat the two objects as a single object
after the collision, with a momentum
equal to the sum of the two individual
momenta. This is illustrated by the
following expression, where m1 v1 plus m2
v2 is equal to the sum of the masses
times v final, which will depend on the
magnitude and directions of the two
initial velocities. This approach can
also be used to model car collisions
whether the two cars were moving in the
same direction or opposite directions.
Adding the masses of the cars and
combining the velocity vectors will tell
us what will happen after the collision.
We should note that during inelastic
collisions like car crashes, total
momentum is conserved but total kinetic
energy is not conserved. Much of the
kinetic energy is converted into sound
energy, which we hear as the sound of the
crash, as well as heat energy, and the
internal energy of the new system, which
allows the bodies to deform as a result
of the collision.
That's why we call it an inelastic
collision, an elastic band always returns
to its original condition after being
stretched, but with an inelastic
collision things are very different
before and after the collision. The
amount of kinetic energy lost during an
inelastic collision will depend largely
on what the objects are and a variety of
other factors. In reality, no collision is
completely elastic or perfectly
inelastic, but is somewhere in between
which we can simply label inelastic,
implying that some kinetic energy is
lost due to the collision even if just a
little bit. But we can usually
approximate a collision as being one
of the two extremes, which will simplify
the math that must be done in order to
make predictions about systems that end
up being extremely accurate.
This concludes our study of linear
motion, which from kinematics and
dynamics, to harmonic motion and momentum
has been quite extensive, but before we
move on to circular motion, let's check comprehension
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