♪♪
Nice shot, Tom.
(sighs)
Ooh, mine, not so much.
Seems like the momentum of my ball got lost, or did it?
Pool is a game of real skill,
and it's also a way to look at
one of the most powerful laws of physics.
We'll find out how
in this segment of "Physics in Motion,"
as we look at the law of the conservation of momentum.
During this series,
we'll talk about a few conservation laws,
specifically for energy, momentum, charge, and mass.
These fundamental quantities
cannot be created or destroyed.
They can only be changed from one form to another,
or transferred from one object to another.
So, what do you think happens to the momentum
of billiard balls when they strike another ball?
If you figured that the momentum is conserved,
you're right.
The law of the conservation of momentum says that
in a collision between objects
in a closed and isolated system,
the total momentum of the objects in the system
before the collision is equal to the total momentum
of the objects in the system after the collision.
Just like the other laws of conservation,
momentum is not created or destroyed.
There's another law of physics that might sound familiar
when we talk about collisions.
Remember Newton's laws,
which predict the motion of most objects?
His third law of motion states
that for every action,
there is an equal and opposite reaction.
This means that objects exert equal forces
on one another when they interact.
One of the consequences of Newton's third law
is the law of conservation of momentum.
We can see it in action when you hit a straight shot,
like this, and it does this.
You exert a force on the cue ball,
which makes it gain momentum.
When you strike the ball,
that momentum is transferred to it.
When the ball collides with the other ball
and the first ball stops,
all the momentum has been transferred
from the first ball to the second ball.
But what about in this case?
This time, the cue ball hits the other ball at an angle,
and both balls are moving.
So, was the momentum conserved?
If you answered yes, you're right.
Remember that momentum, like velocity and direction,
is a vector quantity.
When the first ball travels in this direction,
it carries some of the momentum with it.
The rest is transferred to the second ball,
but not enough to reach the pocket.
However, none of the momentum was lost,
only transferred.
In equation form, we see that the total momentum, P,
before objects interact with one another,
is equal to the total momentum of all the objects
after they interact.
Now, ready to try solving a problem?
A pool player is about to use the cue ball
to make a direct hit on the eight ball,
which is at rest.
Each ball has a mass of 170.0 grams,
and the cue ball's initial speed
is 6.00 meters per second.
After the collision, the cue ball comes to a stop.
If no momentum is lost in the collision,
what is the total momentum of this system,
and how fast is the eight ball moving after the collision?
Remember, the momentum of an object
is equal to its mass times its velocity.
P equals M times V.
The unit for momentum is kilogram meters per second.
To be consistent, we'll convert the mass to kilograms.
The cue ball has a mass of 0.170 kilograms.
So, let's multiply that by the velocity
of 6.00 meters per second.
So, the momentum of the cue ball before the collision
is 1.02 kilograms meters per second.
Since objects at rest do not have momentum,
the eight ball begins with zero momentum.
So, the total momentum of the cue ball
and the eight ball together before the collision
is also 1.02 kilograms meters per second,
and because momentum is conserved,
1.02 kilograms meters per second
is the system's total momentum after the collision, too.
Now, what about the final velocity of the eight ball?
Since the collision brings the cue ball to rest,
the eight ball carries all the system's momentum.
That means we can divide 1.02 kilograms meters per second
by 0.170 kilograms, the eight ball's mass,
to find its velocity,
and that turns out to be 6.00 meters per second,
the same as the cue ball had at first.
See how the law of conservation of momentum
helped us solve this equation?
You apply the law of conservation of momentum
only when a collision happens in a closed,
isolated system.
That means matter and energy
do not enter or leave the system,
which means there are no net outside forces
acting on the system.
In our example, the two pool balls are the system.
They don't enter or leave, so the system is closed.
The only force we consider
is the force between the two balls when they collide.
We're not concerned about the initial force of the cue stick
or the friction between the balls and the table.
So we say that the system is isolated.
♪♪
Let's do one more where we can look at speed and direction,
but this time, we'll do it while roller skating.
We have two people facing each other.
Chirag is 60.0 kilograms, and Summer is 45.0 kilograms.
Both are at rest.
Okay, so, put your hands together.
Now, push.
Chirag is moving in one direction
at a speed of 2.00 meters per second.
What is Summer's speed and direction?
We're doing this mathematically, remember.
First, we establish their initial momentum.
That would be zero because they're at rest.
The final momentum of the system
will be the sum of the momentum values for Summer and Chirag,
which are equal to their mass times their final velocity.
If the total initial momentum of the system is zero,
the total final momentum of the system
must also be zero.
So, we know that Chirag and Summer must have equal
and opposite momenta.
Now, let's substitute the mass of Chirag and Summer
in our values and Chirag's final velocity
to determine Summer's final velocity.
We know that Summer's mass is 45.0 kilograms.
Chirag's mass is 60.0 kilograms,
and his final velocity is 2.00 meters per second.
The only other value in the equation
is Summer's final velocity,
which is what we're solving for.
We multiply Chirag's mass times his final velocity
to get a final momentum of 120.0 kilograms meters per second.
Remember, the sign indicates the direction of motion
of Chirag and Summer.
And because they're moving in opposite directions,
they should have opposite signs.
We divide both sides by 45.0 kilograms
to get Summer's final velocity,
and that turns out to be
negative 2.70 meters per second.
So, let's check.
Does this answer make sense?
Does the sign in front of Summer's velocity
represent the direction of her motion
compared to the direction of Chirag?
And secondly, does the value of Summer's speed
compare reasonably to the value of Chirag's speed?
The answer to both of these questions is yes.
Chirag's had a final velocity of positive
2.00 meters per second,
and Summer's was negative 2.70 meters per second.
The sign indicated the direction of motion,
and when they pushed off of one another,
they moved in opposite directions.
We see the conservation of momentum at work
all around us.
When you step onto a dock from a boat,
you push forward, and the boat moves backward.
When you shoot an arrow at a target,
the recoil of the bow has the opposite
and equal momentum of the arrow.
And when you launch a rocket,
the exhaust pushes it forward in equal and opposite measure,
sending it out of the earth's atmosphere
with power and precision.
Conservation laws,
including the conservation of momentum,
are vital in physics
because they make it possible to predict
how a system will behave
without having to consider every detail.
Once you know a few things about the initial condition,
you can say a lot about the final state of a system.
For more practice with momentum,
check out our Closer Look.
That's it for this segment of "Physics in Motion,"
and we'll see you guys next time.
For more practice problems,
lab activities, and note-taking guides,
check out the "Physics in Motion" toolkit.