Citizen Science No. 17 by Jamie Zvirzdin

Energy Demystified: Bounce Back This Summer with Elastic Potential Energy

What do ballpoint pens, Slinkies, your muscles and tendons, and my dog’s running leash have in common? Last month we talked about potential energy (PE for short). It’s a beautiful, invisible physics quantity that stores energy based on where something is placed, like a book on a high shelf. The book now has the potential to fall, but it hasn’t fallen yet. While that book on the shelf is an example of “gravitational potential energy, there’s another type of PE that you can store in pens, Slinkies, muscles, tendons, and certain kinds of leashes: elastic potential energy.

When you compress a spring, like the one in the click mechanism of a ballpoint pen, you’re using the force (the physics version, F = -kx, not the “Star Wars” version, sorry) to push the spring in, and this force, exerted over a distance, gives you work—which, as we covered in February, is measured in the same units as energy: joules. The work you did squishing the spring inside the pen now lies in wait as elastic potential energy, ready to . . . well, spring out again and return to its original form when you are done with the pen and release its pent-up spring.

Pull the spring instead of push, like we used to do with metal Slinkies—stretch the coils out until your sister yells at you—and you’re doing the same thing, putting work into stretching the spring, giving it the potential to snap back to its original form. (Fun fact: plastic Slinkies were marketed in the 1970s as being safer than the metal ones, since apparently some kids were sticking them into electrical outlets. We’ll talk about electric potential energy next time!)

I’m well aware that a lot of people have the same jump-reaction to physics equations as they do to toys like the jack-in-the-box, the snake-in-a-can, and spring-loaded spiders (the last being another kind of spring, a torsion spring), but like exposure therapy, a little bit here and there can ease the trauma that so many—too many!—people seem to have around physics.

So below is the equation for elastic potential energy. We represent the distance you push or pull the spring with the letter x and measure that distance in meters (which you can, if you like, later convert into feet, or furlongs, or sheppeys, the distance at which sheep remain picturesque; see Wikipedia, “List of humorous units of measurement,” for more entertaining units).

PEelastic = 1/2 kx^2

So if x is the distance you’ve forced the spring to move, what is k? It’s called the spring constant (why it’s “k” is a mystery to me), and it tells us how stiff or stretchy a spring is. A high k means a stiff spring, like the suspension system of a car; a low k means a stretchy spring (like a Slinky). Every kind of material has its own spring constant. Hooke’s Law, the aforementioned F = -kx (negative if you push, positive if you pull) also uses that same spring constant k to help us calculate the force needed to stretch or compress a spring. Because we measure k in “Newtons per meter,” (N/m, or kilograms per second squared, kg/sec2), we will end up with the right units for the elastic potential energy, joules.

Even though it all seems abstract, with a lot of physics jargon, we can actually measure and use this energy to our advantage . . . in fact, it can literally help us bounce back. Last week, after consuming a lot of chocolate during my quantum mechanics course at Johns Hopkins this past semester (totally a coping mechanism, but I did earn an A+!), I decided to improve my fitness this summer over the course of 10 weeks.

I’m not a great runner, and I unfortunately don’t like running even though it’s an amazing, efficient way to improve both heart and health. Nevertheless, I managed to convince myself last week to run a mile, timing myself and tracking my heart rate to create a baseline measurement of fitness that I can improve on over the summer.

I enlisted the help of my enthusiastic Australian shepherd, Zoe, to get me out the door and into the nearby park, and then we sprang into action. The elastic band in her running leash, attached to my waist, stretched enough to give my wildly energetic dog room to run in front of me but remained stiff enough to allow her to pull me along when she wanted to go faster. Yes, I cheated a little.

When we run, our muscles and tendons continuously stretch and contract, converting stored elastic potential energy into kinetic energy, the energy of motion. One study in 1975 said that animals hopping from place to place can conserve up to 70 percent of their energy by transferring the kinetic energy from the hop into their muscles and tendons, which they then use for the next bounce. The spring–mass model, as it’s called, helps us understand how animals—and humans who harness themselves to animals—efficiently conserve and recycle energy during physical activities.

Alas, my plan was foiled. When I hit 7/8 of a mile (1.4 kilometers, the same distance as a sheppey), Zoe stopped abruptly to do her business in the bushes, and since I was tethered to her, I had to stop abruptly too. My perfectly timed run was ruined, which is the price I pay for trying to cheat. I ultimately clocked in 12 minutes and 31 seconds for my efforts, admittedly with the aid and obstruction of elastic potential energy.

Elastic potential energy is all around us, in trampolines, car suspension systems, and even in the springs inside pens. Harnessing this energy—sometimes literally—can enhance our athletic performance, make toys more fun for you but not your sister, keep pen ink from leaking in your shirt pocket, and even improve our understanding of how the world works.

Jamie Zvirzdin researches cosmic rays with the Telescope Array Project, teaches science writing at Johns Hopkins University and is the author of “Subatomic Writing.”