Lies Your Physics Teachers Told You

Originally posted on Quora in response to the question What are some high school physics misconceptions?

Here are two misconceptions that persist far beyond high school. They surprise even physicists and engineers!

Attach a ball to a bungee cord and swing it in a horizontal circle over your head. What path will the ball take if you release the cord?

We’ve all been taught that it will continue in a straight line^* tangent to the circle. That’s wrong!

Why? Because all good physics students perform experiments in an ideal^† world: there’s no friction; gravity vectors and distant light rays are all parallel; and all solids are perfectly rigid. But that’s not how the real world™ works.^‡ The object would indeed continue in a straight line if the cord were perfectly inelastic. But it’s not.

You may have seen what happens if you let a Slinky™ dangle from some height and then release it. While you’re holding onto it, it stretches under its own weight. The tension remains in the spring at the moment you release it, and then the top begins to fall. But the bottom doesn’t “know” you’ve released the top, because it’s still being held by the tension along the Slinky’s™ length. As the “tension wave” travels down the length, everything beneath it remains motionless until the wave reaches it, at which point it begins to fall.

That’s exactly the reason the ball will continue along its circular path for a brief time after you release the bungee cord. Like the Slinky™, the cord continues to pull the ball toward you until the tension wave catches up to it. It’s only at that point in time that the ball begins to move in a straight line.^§ You can see this in the video below. You can watch the tension wave, starting at about 13:45.

I still find both videos a little surprising each time I watch them, even though I already know the punch lines. Apparently the physics in my head still can’t overcome the intuition in my gut.

If you throw a ball to a friend, what’s the shape of the path it takes?

Hint: it’s not a parabola.

This is yet another case of physics lore that lies to us in an attempt to simplify things. A parabola is a close estimation of the path, but only because we can’t throw hard enough. Let’s try a thought experiment.

Imagine you were able to throw the ball much, much harder. So hard, in fact, that you could launch it into orbit. What would its trajectory be? If it’s still unclear, imagine a ball as large as a planet being hurled from space toward our solar system. What shape would that trajectory be?

If you remember learning about Johannes Kepler and his laws, you’ll recall that orbits are always elliptical. That’s true for any trajectory that’s governed by gravity, even if the object doesn’t make it into orbit. The reason is that gravity always pulls an object toward the center of the Earth, so the direction of the force changes as the object moves horizontally (or, more accurately, perpendicularly to the force). The change in direction generates an elliptical trajectory. On the other hand, if the force were always in the same direction, the trajectory would trace a parabola.

The reason we usually can’t tell the difference is that the amount of horizontal movement is negligibly small compared to the diameter of the Earth. So the change in the direction of gravity is also negligible, and we can estimate its direction as constant.

__________

^*As opposed to some other type of line?

^†Well, ideal for physics students, maybe. The rest of us would have a devil of a time with it.

^‡There’s a joke that high school teaches us how physics would work in a perfect world. College teaches us how to handle the “imperfections” using linear equations. And grad school reminds us that the world isn’t linear.

^§Let’s be good physics students and assume the bungee cord is weightless. In reality (and in the video) it pulls the ball away from the center of the circle.