>> Safety test crashes
are a good way to see
just how powerful
a collision can be.
When tons of metal collide
at high speeds the force
and momentum is incredible.
Well what are the physics
of this kind of event?
We'll find out in this segment
of "Physics In Motion",
as we look at collisions.
♪♪
So what makes a collision?
We all know one when we see one,
but in physics it's when
momentum or kinetic energy
is transferred from one object
to another.
Kinetic energy
you might remember
is the energy of motion
and momentum is the quantity
of that motion.
When objects hit each other
the collision falls into
one of two categories:
elastic or inelastic.
When two objects collide
and do not bounce away
from each other
that's an inelastic collision.
Momentum is conserved
but kinetic energy is not.
Some of the kinetic energy
is converted into heat, sound,
and deformation of the objects.
In a perfectly inelastic
collision, the objects
stick together
so their final velocities
are the same.
Think about the qualities
of our paintball collision.
Why is this inelastic?
Do the two objects stick
together when they collide?
Are they moving
with the same velocity
after they collide?
In both cases,
the answer is yes.
Now, let's do a problem
using our inelastic
paintball collision.
In our collision,
the system is the paintball
and the barrier,
so our problem asks:
What is the final velocity
of the two objects,
the paint and the barrier,
in this collision?
The paintball has a mass
of about 3 grams and velocity
of 90 meters per second,
so it has momentum.
The total momentum of our system
before the collision is the
momentum of the paintball
because the barrier,
which has a mass of 9 kilograms,
is initially at rest
and has no momentum.
Remember, an object's momentum
is equal to its mass
times its velocity.
We convert the mass
of the paintball from grams
to kilograms
and get 0.003 kilograms.
We then multiply this times
the 90 meters per second
velocity and end up with
a momentum of 0.270
kilograms meters per second.
When the paintball
and the barrier collide,
the momentum in the system
must be the same both before
and after the collision happens.
The paintball and the barrier
are moving together
after the collision,
so we add their masses
to get the total mass
of the system,
which is the mass of
the paintball, 0.003 kilograms,
plus the mass of the barrier,
9 kilograms, for a total
of 9.003 kilograms.
Then, we set the momentum
of our system, 0.270
kilograms meters per second,
equal to the combined mass
of the paintball
and the barrier,
9.003 kilograms,
times the final velocity
of the paintball
and barrier together.
In order to solve
for the final velocity
we must divide the momentum
by the total mass and we end up
with a final velocity of
0.03 meters per second.
Keep in mind that this velocity
only holds for the instant
after the collision.
Eventually, both the paintball
and the barrier slow down
until they're at rest
at 0 meters per second.
The second type of collision,
as we mentioned,
is an elastic collision.
That's when two objects
bounce apart when they collide.
Momentum and kinetic energy
are both conserved,
meaning the amount of momentum
and kinetic energy in the system
is the same after the collision
as it was before the collision.
Also in an elastic collision
no energy is lost due to sound,
heat, or deformation,
which is a change in the shape
or size of an object
due to force.
In other words,
dents, dings, and alike.
Let's do a problem
using an elastic collision
with the help of
Summer and Tom
and two rubber exercise balls.
Okay, let's stop the video
for a second while I give you
some information
about what's happening.
Tom has a mass of 75 kilograms
and is running at a velocity
of -1 meter per second
holding an exercise ball.
Summer has a mass of
50 kilograms and is running
at a velocity of 4 meters
per second also holding
an exercise ball.
Okay, play the video.
Now that's an elastic collision
if I ever saw one.
See how they bounced off
of each other?
If 50 kilogram Summer bounces
backward with a velocity
of -2 meters per second,
what is Tom's final velocity?
Remember that momentum
is conserved in all collisions
so we always start with that,
which is P sub I
equals P sub F.
Now, let's determine
the initial momentum
by adding up the momentum
of each person.
Plug in the equation
for an object's momentum,
which remember is
its mass times its velocity.
We do this for Summer
and for Tom.
Summer's mass is 50 kilograms
and her velocity
is 4 meters per second.
Tom's mass is 75 kilograms,
his velocity
is -1 meter per second.
We make his velocity negative
because he moves in the
opposite direction of Summer.
Multiply 50 kilograms
times 4 meters per second
and add it to 75 kilograms
times -1 meters per second.
Summer's initial momentum
is 200 kilograms meters
per second and Tom's initial
momentum is -75 kilograms
meters per second.
When we combine
those two together
we get a total momentum
of the system of 125 kilograms
meters per second
before the collision.
Our initial and final momentum
must be the same,
125 kilograms meters per second.
So, let's solve for the
final momentum in the system
for each of the two people.
We plug in the values
that we know,
the total momentum is equal
to 125 kilograms
meters per second,
which is equal to the sum of
the momentum of Tom and Summer.
Summer's mass is 50 kilograms
and her velocity
is -2 meters per second,
which we multiply together
to get her momentum.
The velocity is negative
because it is in
the opposite direction
of her initial velocity,
which we made positive.
We also plug in Tom's mass
of 75 kilograms
times his final velocity,
which is what we are
solving for.
We multiply 50 kilograms
times the -2 meters per second
to get Summer's momentum
after the collision.
We get -100 kilograms
meters per second.
We're solving for Tom's
final velocity
so we add 100 kilograms
meters per second
to both sides of the equation.
That's the first step
in getting Tom's
final velocity by itself.
We end up with 225 kilograms
meters per second on the left
hand side of the equation
and the expression
for Tom's momentum
on the right.
The final step is to divide
both sides by Tom's mass
of 75 kilograms,
which gives us
Tom's final velocity
of 3 meters per second.
The final velocity shows us
that they also bounce backward
and move in the direction
opposite to their original
motion because the sign
of the final velocity
is opposite the sign
of the initial velocity.
Got it?
Because this collision
was elastic kinetic energy
was conserved.
In this segment, we've learned
how the term collision
is defined in physics
and we've looked
at the differences between
the two types of collisions,
elastic and inelastic.
That's it for this segment
of "Physics In Motion"
and we'll see you next time.
>> For more practice problems,
lab activities,
and note-taking guides,
check out the
"Physics In Motion" tool kit.