Energy: In motion and at rest

Archer 01

The string has potential energy when pulled back like in this photo; its energy is transferred as kinetic energy to the arrow when she releases the string. (Photo credit: Wikipedia)

My youngest sister is in elementary school, and last week I was excited when she told me they were learning about energy in her science class.  I thought it would be fun for us to talk about what she was learning and come up with different examples for the concepts – we often do this when talking about what she’s learning in school.  Needless to say, I was a little surprised when only one of the terms on her page was a real form of energy as defined by scientific standards.  My other sister, (she’s trained as a bioengineer) and I couldn’t even figure out what one of the terms (“uniform energy”) was supposed to describe.  I’m not sure I want to go into my feelings about teaching science, since that’s not what this blog is for, and I’m not an educator or even that informed about the issues and debates in science teaching; however, there’s no reason concepts taught at any age should have to be unlearned or relearned at a later age.  Here’s what I would have talked about if I were her teacher.

There are lots of different types of energy.  I touched on one type a couple of weeks ago when talking about heating curves: heat is a common form of energy.  Other forms of energy include nuclear energy, electrical energy, magnetic energy, and gravity.   These energies can be broadly described according to two classes of energy: kinetic energy and potential energy.

Simplistically, potential energy describes the energy of a body at rest, and kinetic energy describes the energy of a body in motion.  It’s easier to understand kinetic energy – in order to be moving, a body must have some sort of energy.  Potential energy is a little bit trickier.  The amount of potential energy something has is dependent on its location in space.  The easiest way to conceptualize this is to think about holding a ball above your head, about six feet in the air.  The potential energy of this ball depends on its distance from the ground – it has more energy if you’re holding it at six feet than if you were holding it at three feet from the ground.  If you let go of the ball, it begins to move – now its potential energy is converted into kinetic energy since it is moving.

There are plenty of good examples of potential and kinetic energy, but my favorite is a roller coaster.  At the top of a peak, the roller coaster (let’s imagine it’s at a standstill) has only potential energy; as it begins to move faster and faster down the hill, it gains kinetic energy until at the bottom (ground level) its energy is largely kinetic and minimally potential.  It then loses kinetic energy as it slows going up the next incline, until it once again has potential energy proportional to its height when it reaches the top of the next peak.


At the top of the hill, the roller coaster has all potential energy, and then its energy is converted to kinetic energy as it speeds down the hill. At the bottom, it has mostly kinetic and very little potential energy. (I apologize for my complete lack of computer graphics skills.)

But how did it initially move from the ground to the top of the first hill?  Something did work in order to propel the roller coaster to the top.  If the roller coaster runs on electricity, then electrical energy was put into the roller coaster in order to move it from the loading area to the top of the hill; or if it runs on gasoline then chemical energy was used.  Either way, some sort of energy had to be expended to get the roller coaster to the top.  This is another way to think about potential energy – how much work (energy) did it take to get it to the place where it is when you’re measuring its potential energy?  The value of this “work” energy is equal to the value of the potential energy of the body.

A better example of this relationship between the energy required to move a body and its resulting potential energy is to think about archery.  (Thanks to the movie Brave, my youngest sister is currently really into archery.  She even has her own pink bow and arrow that we could’ve used for talking about this.)  In order to shoot the arrow, you have to pull back the bowstring.  Pulling back the bowstring requires you to use energy, since the bowstring won’t just move back of its own accord.  Once you’ve used energy to pull it back, its potential energy is directly equal to the amount of energy you used to get it to that position.  When you let go of the string, it snaps back into its original position, and its potential energy is converted to kinetic energy while it’s in motion.

One final thing about kinetic energy fits perfectly into the archery example.  Kinetic energy can be transferred from one body to another.  So when you let go of the string, its energy is transferred to the arrow, which uses that kinetic energy to fly through the air and (hopefully) connect with the bull’s-eye on your target.

Post-script: I noticed only after the fact that the examples I used are also used on the Wikipedia pages for kinetic and potential energy.  They’re the most common examples used in class…so I guess that shouldn’t be surprising.

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