Bumper cars obtain their initial forward momenta from the floor.
Like ordinary cars, bumper cars have powered wheels.
And they use frictional forces between those wheels in the floor to propel
themselves forward. As the floor pushes the bumper car
forward, the car gradually accumulates forward momentum.
The impulse that it's experiencing as it picks up speed involves a relatively weak
frictional force from the floor exerted for a long period of time.
During collisions however, things happen so fast that there's very little momentum
transfer to the floor. The frictional force between the wheels
and the floor are just too weak. And there isn't enough time for any
significant impulses. So, when two bumper cars collide, they're
pretty much on their own during that collision.
As though there, there's nothing else in the universe.
And for the sake of simplicity, I'm going to assume that they're completely
on their own. Ignore the floor.
Since momentum is conserved quantity, the collision can redistribute their
momentum, their total momentum, but it can't change that total.
Their total momentum before, and after the collision has to be the same.
The same is true for energy. The collision between two bumper cars can
redistribute their total energy, but it can't change that total.
Unfortunately, the collision between bumper cars can and does grind up some of
their ordered energy into thermal energy. So that we don't see it after the
collision. But that wasted energy is relatively
small for bumper cars and so for simplicity, I'm going to ignore it.
For the experts, perfect collisions, ones that waste no energy.
Are known as elastic collisions. Those that do waste energy, are said to
be inelastic. Elastic collisions are some what simpler
to understand then inelastic collisions. So pretending the bumper cars bounce
perfectly and waste no energy. We'll make our lives a little easier,
without really changing the story. So, a collision between two bumper cars
has two important constraints: their total momentum can't change, and their
total energy can't change before and after the collision.
So together, those two constraints determine how the cars bounce from one
another. The simplest case is two identical bumper
cars, and that's what I have here. These bumper cars have the same mass,
they're basically indistinguishable. And the need for them to have the same
total momentum and total energy after the collision as before the collision really
constrains how they bounce. And you get these very interesting
effects, like, if they have head-on collisions, that is collisions that are
entirely along one line, they exchange motion.
So if I have one of them at rest and I slam the second one into it, they trade,
they trade their motion. The second one continues on as though it
were the first one. And the first one continues on as though
it was the second one. So it works like that.
It works like that. It works if I slam the both in like that.
All of these variations. They trade places in effect in their
motions. If they hit off center, if they're not
riding this rail into each other and apart, then you get more complicated
motions, but still they're all related. Very highly constrained bounces and this
is how bumper cars the bumper car arena will behave if they have identical
masses. Actually, you don't even need bumper cars
to see some of these effects. Any objects that are identical and that
bounce almost perfectly off one another will work.
For example, coins. Here are a bunch of US quarters.
And if I bump one of them into another quarter head on, perfect shot, they'll
trade motion. The first one stops, the second one
continues on as though it were the first one.
Actually you can line a whole series of these quarters up and if I hit the first
one head on, the last one will go on as though it were the first one.
It's all about conserving momentum and energy during a very complicated
collision. That causes the first one to stop and the
last one to continue on. Actually, people have made toys that use
this principle and their called either Newton's cradle or the executive toy,
which doesn't say much about executives but that's the name under which it goes.
This has a set of very elastic balls. They're made of steel and they bounce
almost perfectly off one another and if I take the first one and I make it smack
into the entire row of, of balls the last will come off.
It's a series of collisions in which energy and momentum have to be conserved,
and the only way that can work is if the motion propagates through the entire row
of balls and the last one continues on as though it were continuing the work of the
first one. [SOUND] It's time for the full glory of
bumper cars, and that means having bumper cars with different masses.
So, I brought the little bumper car arena.
And first I can show you things you've already seen before.
I can take two bumper cars that have identical masses.
They differ in color, but otherwise, they're identical.
And if I smack the green one into the red one, the red one continues on with the
green one's motion. They exchange motion.
So, so, so far, so good. But the real interesting stuff starts
showing up when I bump different bumper cars into each other.
That is, ones with substantially different masses like this green one and
this little red one. When these collide, different things
happen. I'm going to make the green one hit the
red one. [SOUND] It just swats the red one out of
the way, and the green one continues on. Watch that again.
Why did that happen? Well, the physics isn't too hard to
understand. When the green one collides with the
motionless red one, it begins to transfer to.
Conserve physical quantities to the right one is transferring momentum by way of an
impulse and it is transferring energy by way of work.
It's using the same force to make both transfers but the impulse involves force
times time while the work involves force times distance.
