Kinetic Energy

Susie and I were married in our teens, and by the beginning of our third year at the university we were broke — flat busted and living on ramen and bean burritos (love can only cover so much). I finally took a year off and got full-time employment as a carpenter; framing apartments and tract homes. As a rookie my aim left much to be desired (this was before nail guns), and I ended up with bloody fingers on nearly a daily basis (fortunately, it was not before Band Aids). She’d do her best in the evenings with tears and kisses where it hurt, but the repeated impacts continued to plague me for the duration.

At the time it just hurt, but now I better understand the physics involved.

The Rules of Reality tell us that it takes energy to pick something up and move it (like my arm swinging the hammer). But they also tell us that the moving object has energy of its own, and is capable of doing work because of it.

We’re talking about kinetic energy here — the energy that any mass will have, just because it’s in motion: like the hammer flashing through the air and hitting the nail (and hopefully not my finger), or gravity pulling water downhill and giving its power to the river. Sounds like magic to me and it probably is, but there you go.

Kinetic energy has seemingly infinite application. From the midwife’s gentle slap that jumpstarts a newborn to a tornado jumpstarting your house, E_k is what gets things done. In just one of its many real-world contributions, E_k is where moving water gets the muscle it needs to transport the earth’s weathered and eroded continents to the ocean.

This may be a generally underappreciated task, but imagine how cluttered the planet’s skin would be if water and kinetic energy weren’t around to clear away the detritus of earthtime.

The formula may not appear simple (E_k = ½mv²), but there’s really nothing to it: the amount of kinetic energy available to do something (like bounce a piece of the Grand Canyon downstream) is equal to the mass of the moving object (how much water is in the Colorado River) times the square of its velocity (how fast it’s going).

Don’t sweat the ½ multiplier — it may look scary, but all it does is reduce the calculated value by half, so it doesn’t really affect how the equation works. Things that never change — things that are constant — have a predicable effect, and, once you get used to them and make the necessary adjustments, can be pretty much ignored.

Anyway… what we’re left with is mass in motion. Consider the energies involved when a dump truck full of rocks hits a cinderblock wall, as opposed to a kid on a tricycle — and then start playing around with how fast they’re going — and you’ll get the general idea.

The mass part of the equation is easy: double the amount of water in a river and you double the kinetic energy (and yes, this also doubles how much work can be accomplished). Triple the mass and the energy triples. And so on… Mass and kinetic energy: they have an uncomplicated, linear relationship.

But in our formula the velocity is squared. That little superscripted ‘2’ is an exponent, and means that the velocity value is multiplied by itself (not merely doubled—that would be written 2v). This is a not a linear change.

Oh sure, it starts off innocent enough: if the water is going twice as fast (v = 2), the energy doubles as expected (v² = 2 X 2 = 4). So far so good. But triple the velocity and the kinetic energy suddenly goes up by a factor of nine (v² is now 3X 3). Fourple it and the energy jumps by sixteen (4X 4). A fipple (5 X 5) takes it to twenty-five.

This is an exponential increase that gets real big, real fast. Increase the velocity of a river or stream by fifty — as can happen during episodes of major discharge — and the kinetic energy is now twenty-five hundred times greater (not to mention the increased mass from the additional water). Ramp it up by one hundred and the energy increases by ten thousand!

That the overwhelming majority of sediment transport and streambed erosion take place during times of flood is a true no-brainer. (As an aside: If the earth were the size of a beach ball, the asteroid that killed T-Rex would have been a speck of dust. It wasn’t that it was all that big, it was just moving really fast when it hit.)

This relationship between velocity and energy can be useful for another reason. Consider a drainage basin: trickles and hustling creeks and mature streams and sluggish rivers. But isn’t it weird how nearly all streams join at the same elevation, no matter how different their relative discharge? We see this so regularly that we don’t even recognize how impossible it should be.

Again it’s simple. Moving water will tweak how fast it’s going to equalize the overall energy, and, because the velocity is squared, even a minor adjustment can have a profound effect. The short version is that smaller streams flow faster and mighty rivers slower, and so they end up with the same energy where they meet and downcut into their beds at a comparable rate. Pretty slick… but kinda sad if you like waterfalls.

(BTW: Because of this, many of the best waterfalls are associated with alpine glaciers. They move so slowly that the velocity part of the energy equation doesn’t really come into play. All they have to work with is the mass, so a smaller tributary glacier just can’t cut as deep as a larger river of ice. When the ice melts, what is left behind is called a hanging valley. But more on this in a later post…)