This week, Nathan from Europe wrote in:
I have a question about the theory that energy can neither be created nor destroyed.
If you have two waterfalls, and one has a turbine and the other doesn’t, yet the water eventually hits the ground with the same volume and force on both, have you not created energy with the turbine?
|Water tumbling from the highest falls in the world, Angel Falls in Venezuela.
Image Credit: Diego Delso, via Wikimedia. (CC BY 3.0)
Energy is a tricky subject—it can be hard to define exactly what it is, though we’ve got some pretty good clues: you find energy anywhere there’s a difference between the way things are and the most stable possible state that they could be in. When the surface of a pond is totally flat, that’s the most stable state it can be in—the state it’ll eventually return to if it’s left on its own. We call this state equilibrium, which makes sense: all the water is at an equal height. Throwing a rock into the pond adds energy to it, and for a little while there are ripples on the surface—some of the water is higher than at equilibrium, and some is lower. That’s energy—but so are the compressions of a sound wave in quiet air, and so is the “juice” in your phone’s battery. Energy is a term that can mean a million different things, but what makes it so amazingly useful is that the total amount of it always stays exactly the same, no matter how it transforms.
Let’s look at your question about the waterfalls—it’s a clever one, and the solution is subtle. We mentioned earlier that water at the top of the falls has potential energy, thanks to the fact that it’s starting out high up and gravity “wants” to pull it downward. The potential energy of an object is easy to calculate: it’s the object’s weight, multiplied by the height it’s at.
In the real world, though, that’s not quite true—which brings us to the other really wonderful thing about the idea that energy is never created or destroyed. The law is so universal, so consistent and reliable, that it’s a great way of telling how well we understand a system.
Imagine we go to an actual waterfall and start taking measurements: the height of the falls, the speed of the water as it reaches the ground—we’re going to find that things don’t quite add up: the water isn’t moving as fast as it ought to be. Has the law of conservation of energy been broken? Probably not. More likely, we’re forgetting something; somewhere, the energy is sneaking out. In this case, that’s probably air resistance: as water droplets move toward the ground, they push the air that’s in their way downwards and aside. If you could somehow measure the combined speed of all the air molecules that get pushed by the water, and add their kinetic energy to the kinetic energy of the water as it reaches the bottom of the falls, you’d find an answer a lot closer to the potential energy that the water started out with!
The tricky part of your question comes from the air, here—whether you meant to or not, you brought in a concept called terminal velocity: the maximum speed an object can fall. This speed limit varies for different objects, but it comes from a simple rule: the faster something is moving, the more energy it transfers to the air it moves through. That means that, once it’s falling at a certain speed, an object loses kinetic energy to the air just as fast as it converts potential energy into kinetic energy, and it doesn’t speed up any more.
You specified in your question that the water from both falls strikes the ground with the same speed and force. For that to happen, the falls have to be tall enough that the water has time to reach its terminal velocity again after hitting the turbine. That’s why it looks like energy is coming out of nowhere in your scenario—in the falls without the turbine, all that extra energy is just getting transferred to the air!
Thinking of things in terms of conservation of energy paints a beautiful picture of the world, as an interconnected web. The kinetic energy of a woman on her bicycle started as chemical energy in her body, in the form of sugar molecules that power the motion of her muscles when they’re broken down. Those sugars might have come from some rice she ate earlier that day, and the rice plant built them out of carbon dioxide and water. Turning those molecules into sugar takes energy too, though, which the plant gets by harnessing sunlight…so the woman on her bike is solar-powered, too!*
You can do a similar exercise with just about any kind of energy on Earth, and most of the time you’ll find it all leads back to the sun. That’s not always the case, though: the heat of Earth’s interior—which produces volcanic eruptions, hot springs, and geothermal energy—comes partly from radioactive decay, for example.
Where could you find a life form that doesn’t use solar energy? Where else can energy come from, and what other forms can it take?
*Before Einstein came along, the source of the sun’s light and heat were mysterious—but his most famous equation, E=mc2, tells us that mass is just another kind of energy! When four hydrogen atoms get smashed together in the sun’s hot interior, they form a helium atom. A helium atom has slightly less mass than four hydrogen atoms, so the difference comes out as kinetic and electromagnetic energy.