An introduction to physics in the context of everyday objects.
How is Momentum Transferred From One Bumper Car to Another?
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Del curso dictado por University of Virginia
How Things Work: An Introduction to Physics
864 calificaciones
De la lección
Bumper Cars
Professor Bloomfield examines the physics concepts of momentum, impulse, angular momentum, angular impulse, and the relationship between potential energy and force using bumper cars.
Conoce a los instructores
Louis A. BloomfieldProfessor of Physics
How is momentum transferred from one bumper car to another?
The answer to that question is that the first bumper car does an impulse on the
second bumper car. Just as you can transfer energy by doing
work. You can transfer momentum by doing an
impulse. So what exactly is an impulse?
And impulse is a force exerted for a time.
For example, I do an impulse on this bumper car by pushing on it as time
passes. The product of my force on the bumper
car. Times the duration of that force.
Is the impulse. And correspondence to the amount of
momentum I transfer to the bumper car. Since an impulse transfers a vector
quantity. Namely momentum.
That impulse is also a vector quanity An impulse points in the same direction as
the force responsible for it. So, for example, if I push the bumper car
to the right. The impulse points to the right.
And transfers rightward momentum to the bumper car.
If I push the bumper car to the left. My force points to the left, the impulse
points to the left and I transfer a leftward momentum to the bumper car.
Of course, at an amusement park, people don't usually transfer momentum to bumper
cars. Bumper cars transform momentum to bumper
cars. So, here's one bumper car.
[SOUND] And it's going to do an impulse on a second bumper car and I'm going to
make it so that this bumper car is going to hit that one, like this and it's
going to do a rightward impulse on a second bumper car.
Here we go. Ready.
So, this guy transferred momentum to that guy.
But actually, there were two impulses occurring during that collision.
We've seen one. This one did impulse on that one, it
exerted a force on that one over a period of time.
But simultaneously, the second bumper car did an impulse back on the first bumper
car in the opposite direction. It had to, this is Newton's third law.
As this one pushes on that one, that one pushes back on this one equally hard in
the opposite direction. So there were two impulses occurring
simultaneously. That bumper car did a rightward impulse
on the second bumper car, but at the same time, the second bumper car did a
leftward impulse on the first bumper car. Well, that means that the second bumper
car transferred leftward momentum to the first bumper car.
But leftward momentum is the same as a negative amount of rightward momentum.
So as this bumper car was transferring rightward momentum to that bumper car,
the second bumper car was taking away rightward momentum from the first bumper
car. That's how the transfer works.
The bumper car over here transfers right where momentum the second bumper car and
gives it up. It comes out of this one into that one.
And you can see that where the collision occurs.
The original bumper car basically has lost its rightward momentum, and the
second bumper car carries it away. You can see, this one almost stops, and
the second bumper car carries away the rightward momentum that had started in
the first bumper car. The transfers of momentum that are
occurring as these two bumper cars collide have to be perfect, because
momentum is a conserved quantity. Whatever momentum the second bumper car
receives, the first bumper car has to loose.
Well, let's return to the fact that an impulse is proportional to both the force
that, that's responsible for it and the time of which it adds.
That's a rather interesting result. I'm going to go back to pushing a single
bumper car by hand. Now, of coarse, I can increase the amount
of momentum I transfer into that bumper car.
Either by pushing harder or by pushing for longer duration, but that's not
surprising. What is somewhat remarkable is that I can
transfer the same amount of momentum to the bumper car with different pairings of
my force and its duration. As long as the product of my force times
the duration doesn't change, I'd do the same impulse and transfer the same amount
of momentum to the bumper car. For example, I can start by exerting a
medium force for a medium amount of time. Here we go.
I pushed it medium hard for a medium amount of time and off it goes.
But I can do the same impulse by pushing hard for a short amount of time.
Same thing, or I can go back and transfer the same amount of momentum by using a
gentler force for a longer duration. I have some choices here.
Are there any consequences to changing those pairings of force and duration?
Oh, yeah. The faster the momentum transfer occurs,
the shorter its duration and the larger the force must be.
Big forces can break things. For example, here is a hammer.
And I'm going to invest some downward momentum in that hammer.
[SOUND]. Before it encounters a nail on a piece of
wood. And when the hammer reaches the nail,
it's going to transfer all of its downward momentum to the nail by way of
an impulse. The hammer will exert what is known as an
impact force on the nail as it transfers its momentum to the nail.
And that transfer is going to occur in the blink of an eye, short duration, so
the force has to be huge. The hammer exerts such a large force on
the nail. That it pounds the nail right into the
wood. I'm going to try that again, but this
time, I'm going to tape a rubber stopper on to the tip of the hammer before I hit
the nail. Now, there we go.
I'll pull the nail back out. Now, I'm going to try to pound in the
nail again. [SOUND].
Doesn't work. [SOUND].
I'm giving the hammer plenty of downward momentum before it strikes the nail.
The hammer is still. Transferring all of its downward momentum
to the nail, but somehow that doesn't cause the nail to enter the wood.
The problem is that the impulse that's occuring when the hammer hits the nail
involves a much longer time now. The softness of that rubber stopper
prolongs the impact. So, there's a long impact.
Consequently, there has to be a smaller force, and so there is.
The force [SOUND] that develops, the impact force of this rubber hammer
hitting the nail is too small to push the nail into the wood.
I occasionally insert what I call public service announcements into my how things
work course and here's one of them. This type of baseball is used in
professional sports and that I've mounted here on a handle so that it looks like a
hammer is extremely hard. It's so hard that it transfers its
momentum to whatever it hits extremely fast.
Because the duration of that impulse is so short the force of the impulse can be
huge. You could pound a nail in [SOUND] with
this kind of baseball. In contrast, a somewhat softer ball, so
this ball has the same mass, carries the same momentum, with the same velocity as
a professional ball, but it's got a somewhat softer surface.
And it takes a little longer to transfer it's momentum.
With a longer duration for its impulse. The force of that impulse is smaller.
So these softer balls are soft strike, or reduced impact force balls, because the
longer impulse involves a smaller force. A smaller impact force.
This type of ball. [SOUND].
Can't pound in a nail. In fact, you can hit your own hand with
it. Don't try that with, with a professional
sports ball. My advice is this.
Be careful with the professional hard balls.
Or consider switching to a softer ball. A fast-moving hard ball is effectively a
loose hammer, and it can cause serious injury or worse if it hits you in the
wrong place. So the trade-off between forces and
durations is also important with bumper cars.
So you've seen these bumper cars with their rubber bumpers, they're called
bumper cars. Because they have bumpers on them.
Without those bumpers, the steel frames of the cars would hit and they would
transfer momentum way too fast. I can show that because the bumpers come
off these guys, and I've already removed the bumpers from this pair of bumper
cars. So, if I turn them on And bump them into
each other. [SOUND] This kind of bumper car, like,
bumperless bumper cars, wouldn't be very fun.
The transfers of momentum are so fast, involve such big forces, that the cars
will get damaged by them. And you, as a rider in one of these cars,
will also experience unpleasantly large forces in rapid accelerations.
It's not going to be good. So, if you have the option of going and
riding bumperless bumper cars. Or, I guess, just bumperless cars, skip
it. Go for the bumper cars.
It's time for a question. We've seen that it's entirely possible to
use a hammer to pound a nail into the floor.
So the question is this, can you use a hammer to pound a nail into the ceiling?
You'll have no trouble driving a nail into the ceiling with a hammer.
That's because the impact between hammer and nail occurs over a very short period
of time. And transfers the hammer's momentum, the
upper momentum, to the nail so quickly that it involves an enormous force.
A force that's capable of pushing the nail right into the ceiling.
You might worry about gravity during this upside down hammering process, but the
force of gravity is so small compared to the force of the hammer on the nail
during the impact that it just doesn't amount to anything.
You can pretty much ignore gravity when it comes to hammering.
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.
The little red one moves easily during the impact.
It's being pushed on, and it's accelerating, and picking up speed, and
beginning to move so the green one is able to do a lot of work on it.
It's travelling in the direction of the force.
So, the green one's doing work on it and it turns out that the green one is able
to do enough work on the little red one. To, to set it off in the distance before
the green one has had time to transfer all of the green one's momentum.
So, the green one keeps on going it only gives some of it's momentum to the little
red one. The little red one runs away to soon and
heads off in the distance. The reverse is also interesting.
Let me let the little red one collide with the stationary green one.
Watch what happens there. The little red one bounces backwards.
I'll do it again. How did that happen?
Well, when the little red one arrives at the green one it's again trying to
transfer to conserve quantities to the green one.
Momentum and energy. Momentum by way of an impulse.
Energy by way of work. So the red one begins to push on the
green one. That force is going to transfer both of
these conserved quantities. But the green one won't move, not very
well any way. It's massive.
It's very hard for the, to get that green one moving.
So it doesn't travel very much distance during a collision, therefore the red one
is barely able to give the green one any energy.
Can't do much work on that almost immobile green one.
But there's the right one tries and tries and tries, so a lot of time goes by
during the impact. And the right one manages to transfer all
of it's momentum and it transfers more momentum, even than it had.
So it was heading to the right, it gives all it's rightward momentum to the green
one an extra. And it ends up with a deficit of
rightward momentum. Which was we know is leftward momentum.
And it heads backwards. It tried to give the green one all its
energy and momentum. And it didn't manage to give the green
one much energy. But it gave it a lot of momentum and off
it goes backward. So all of these impacts, then, are making
use of these transfers, energy and momentum, trying to get everything to
work out right, because those two quantities have to be conserved.
So this explains then a lot of wht you see or experience in bumper cars.
The really massive cars, the ones carrying a lot of heavy ha, high mass
occupants riding in them, they pretty much swap the other cars out of the way
when they hit them. They transfer a lot of energy to those
cars, but not all of their momentum. And so they, so these big, these big
massive cars just keep on going. They, they still have momentum after the
impact. In the same direction they had before the
impact. The little cars, on the other hand,
bounce off the other cars when they hit them.
Because they don't manage to transfer much energy to those other cars, but they
transfer a lot of momentum and they bounce back.
The things that I've said about bumper car collisions apply to many other
collisions. So let me ask you a question.
To successfully catch a ball, why do you have to let your hands move with the ball
as it collides with your hands? By letting your hands move with the ball
as it collides with your hands, you're letting the ball do work on you and
transfer its energy to you. In the process, it transfers its energy
and its momentum and comes to rest, and that's how you catch things.
If you hold your hands rigidly in place as the ball hits them, it's going to be
able to transfer momentum to you, but no energy.
And it will actually bounce off you like, like the little bumper cars bouncing off
the big bumper cars. [SOUND] They bounce backwards.
[SOUND] So that's it for translational motion in bumper cars.
We see how momentum moves from car to car during the collisions, as they, as they
do impulses on one another. But not all of the motion in bumper cars
is in straight lines moving from here to there.
Bumper cars can also spin. They exhibit rotational motion.
So the next video is about the rotational motion of bumper cars.
And the associated conserve quantity known as angular momentum .
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