Understanding Energy – Potential, Kinetic, and Visualization on a “Surface”

In order to work with a lot of physical concepts across disciplines, some level of understanding must be present regarding “energy.” On an instinctive level, people tend to have a foundational understanding of “energy” just by doing and observing everyday tasks; I aim to illuminate these moments and shed some further detail on what energy is, and why understanding it is so pivotal in science (and other disciplines!).

NOTE: this is aimed at those who have not explored physics courses, and not at those in fields that use these concepts regularly. I am not discussing anything to do with thermodynamic relations (at least not directly), statistical or quantum mechanical energy phenomena, etc… but those are also vital to application in upper-level research applications.

To begin, like many physics textbooks regularly do, I’m going to break apart energy into two easier concepts to grasp: potential and kinetic energies. We will grapple these one by one, linking the two together as we go!

Part 1: Understanding Potential Energy

To really grasp the idea of potential energy, think about jumping into a backyard swimming pool (cannonball style, and let’s say an in-ground pool).

Timmy and George, similar heights and weights, jump in one after the other. However, Timmy is a thrill-seeker, and jumps into the pool from the roof of the house (yes, it is close enough; yes, it is still a bad idea). George just hops in from pool-deck level.

Who makes the bigger splash?

Well, assuming Timmy doesn’t just miss the pool entirely, Timmy would make the bigger splash. Why? Because he “stored” a greater potential energy then George did by climbing up on the roof, and having to come back down (in the direction of gravity) to ground level until all that stored energy was “released” (arriving back at ground level). As this energy is transferred to the pool water, we get the splash effect.

Part 2: Understanding Kinetic Energy

To put it simply, kinetic energy is the “in motion” energy definition. As Timmy jumps from the roof into the pool, his potential energy begins being converted into kinetic energy – by the time he reaches the pool floor (ground level), all energy has been turned into kinetic energy!

Kinetic energy is further useful in other discussions, but for now, simply recognize it as potential energy’s complementary pair – as one goes up, the other goes down, and vice versa.

Part 3: Visualizing Potential Energy on a Surface

A potential energy surface is a map of two (or more) variables in a system (e.g. Timmy or George’s height, or distance from the ground), against the energy. It illustrates where a particular object or system is more “relaxed” or stable (a divet or valley), and where the object or system is more “uncomfortable” or strained (a peak or hill).

Key concept – “relaxed” is good, and usually implies a form of equilibrium. In other words, there is no further preference to change the situation. So, when Timmy reaches the bottom of the pool, he stops, and is not instead thrust back up onto the roof, or in some other direction.

Terrain maps for geographical work are a great potential energy surface (PES) analogy:

shadedsurface_polyhedron_ginosurf
Ginosurf Program 3D Shaded Surfaces – useful for generating topological contour maps (https://www.polyhedron.com/ginosurf)

Hills and mountains are the aforementioned peaks (i.e. maxima), and valleys are the wells (i.e. minima) in the PES. To remember which type of region (hills or valleys; peaks or wells) are more “favorable,” think about which direction it is easier to walk: uphill, or downhill? Alternatively, think of a runaway bowling ball, and where it is likely to end up on such a surface.

Summary:

Uphill = difficult to walk, requires work –> less favorable –> Peaks = Maxima

Downhill = easy to walk, no work (just fall) –> more favorable –> Wells = Minima

For example, with a water molecule, if I assume the hydrogen-oxygen bond lengths are the same and do not change (i.e. are frozen), but I flex the bond angle between H-O-H and calculate the potential energy along the way, you get a curve similar to this:

Water_1D_PES
Rough 1D PES (a.k.a. potential energy curve) of Water against H-O-H angle axis. Minima at 104.5 degrees for a bent geometry (optimal).

Completing the connection of a “backyard and pool” analogy to a PES, the bottom of the pool is the lowest possible point either Timmy or George can reach (without a shovel or something, and removing the fact that the yard may be slanted, have holes, or whatnot… work with me here). On the PES, that’s at 104.5 degrees between the two hydrogen atoms. That point is a (local) minimum in the backyard (or on the PES). The (local) maximum is the roof of the house (barring a flagpole or something), and would be nearly equivalent to either side of the parabola in the PES above.

Any situation meant to store “ability” or energy is an increase in potential energy: drawing back a bow and arrow, crouching in preparation for a jump, going to the top of a snowy hill to be able to ride a sled…

Once this energy is “released” into action or motion, it is called kinetic energy, and is able to be applied to other systems and impact THEIR energy! Think of water running downhill, and how we can generate energy from that by letting it flow through turbines, which essentially collect the kinetic energy of the running water, and move large gizmos and gadgets around to make a new kind of stored potential (electrical potential).

**NOTE 2: we discussed kinetic energy here, but it is not directly visualized on a PES!**

 

If this discussion has peaked your scientific interest at all, check out these further readings:

Introduction level

1) Potential and Kinetic Energy Discussion at Math Is Fun

2) PES w/ some Temperature Discussion at Chemistry LibreTexts

Advanced/Applications of PES

1) J. Chowdhary and T. Keyes. Thermodynamics and Dynamics for a Model Potential Energy Landscape. J. Phys. Chem. B, 2004, 108 (51), pp 19786–19798
DOI: 10.1021/jp047615t

2) David Wales. Energy Landscapes
: Applications to Clusters, Biomolecules and Glasses. Cambridge University Press, 2003.

Electric Potential & Work

1) Definition on Britannica of Electric Potential

2) Khan Academy Electric Potential Videos & Related Material

3 thoughts on “Understanding Energy – Potential, Kinetic, and Visualization on a “Surface”

  1. Pingback: Convergence Problems – Computer Defenestration Prevention – Len's Landing

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s