A Ferrari Yanking Carpet From Under People Is Hilarious *and* Educational

 wired.com  6/20/2017 2:30:00 PM 

The internet may never forget, but people sure do, which explains the renewed popularity of this three-year-old video of a Ferrari. You can see why people find it funny: an expensive car tries to stop on a carpeted stage, knocking over four people.

Now, I'm sure you find yourself wondering, "What kind of physics are at play here?" I've heard a few explanations, including the idea that for every action, there is an equal and opposite reaction." This is not wrong, but it does not give the full story.

You know I can't watch something like this and not break it down. I'll do this by examining the three objects in the event: the people, the car, and the carpet.

The Momentum Principle

I'll start with the big idea: the momentum principle. Momentum is the product of an object's mass and velocity. You almost always see it represented with the the letter p because m represents mass. Oh, you ought to know that momentum is a vector, which means that the direction of the velocity matters.

The momentum principle states that the total force on an object is equal to the rate of change of momentum. As an equation, it looks like this:

If the total force on an object is zero (the zero vector), then the momentum remains the same. That object could be moving in a straight line or just sitting there. In either case, there is no change in momentum. With a net force of anything but zero, the momentum changes in some way—it speeds up, slows down, or changes direction

Something else you need to know about forces: They are an interaction between two objects. This means that if the carpet pushes on the Ferrari, the Ferrari pushes back on the carpet with the same magnitude of force. Some people call this Newton's Third Law. I am not one of those people.

The Humans

OK. Now to the video. It shows a vintage Ferrari rolling across a carpeted stage, then stopping. At this point, just three forces act on the people. Gravitational force pushes down as the floor pushes up. These forces are boring, because they essentially cancel each other out and keep the people upright. The third force comes from the carpet pushing horizontally on their feet. Technically, this is a frictional force, but it's still from the carpet. It looks like this:

The horizontal force on the human changes the horizontal momentum. The human, once at rest, now speeds up to the right. But wait! Because the force is applied to the human's feet and not the center of mass, the human also rotates. Before long, the gravitational rotation is no longer directly over the feet, and the human tips over.

The Car

Of course, the car must slow down. How? With frictional force in the opposite direction of the car's motion. Here. I drew a force diagram:

Notice that both the human and the car both have a force from the carpet. These are different interactions. The carpet interacts with the humans and the car.

The Carpet

Here is the cool part. The carpet changes motion because a non-zero total force acts on it. I drew a diagram to explain:

There is a lot happening here, so you can see why I saved it for last. Of course, gravitational force pulls down on the carpet even as the the stage pushes up. That's boring. It's the other forces here that are fun.

Let me start with the Ferrari. Since the carpet pushes on the car to slow it down, the car pushes back on the carpet with the same magnitude force. Notice that the carpet pushes on both the car and the humans, which means the humans also push on the carpet. However, the force from the car pushing to the right exceeds the forces pushing to the left. This means the total force on the carpet is not zero, and the carpet will increase in speed to the right.

But wait! If the stage exerts a frictional force on the carpet, does that mean the carpet pushes on the floor? Absolutely. Does that mean the floor also changes its momentum? Technically, yes—even though the floor is connected to Earth. Let's go back to the momentum principle. Suppose I include all of the objects that are interacting in this event—even the earth. In that case, for every interaction you see two balancing forces. Overall, the net force would be zero such that the change in momentum for the whole system must also be zero. But clearly the car stops. Where does its momentum go? In order to conserve momentum of a stopping car, the Earth must increase in momentum.

It gets even crazier. The change in momentum of the car has the same magnitude as the change in momentum of the earth. And this isn't a problem because the mass of Earth is huge (about 6 x 1024 kg). Given this giant mass, Earth needs only the very tiniest change in velocity to experience the same change in momentum as that Ferrari. So, technically, you can make the earth move simply by pushing on it.

So, back to the question I posed at the beginning. How do you easily explain the physics at play here? It's obviously not a simple question, but I will go with "forces change the momentum of stuff."

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