Imagine you are playing a video game where you pull back a slingshot to launch a bird at a tower (yes, kind of like Angry Birds 🐦). Before you let go, nothing is moving, but you know something powerful is about to happen. Where is that “hidden power” stored? That hidden power is potential energy, and it depends on how things are arranged in the system.
In this lesson, you learn how to develop and use simple models to show that when the arrangement of objects interacting at a distance changes, the amount of potential energy stored in the system also changes. You focus on three types of interactions between only two objects at a time: gravitational, electric, and magnetic.
Energy is the ability to cause change. There are two big types you will keep seeing:
A useful idea: systems can have the same total energy but different amounts of kinetic and potential energy. For example, a book on a shelf has more gravitational potential energy and no kinetic energy. When it falls, potential energy decreases and kinetic energy increases, but the total stays (almost) the same, ignoring air resistance.
[Figure 1] shows kinetic and potential energy in a simple situation where a ball is dropped from a height.
You might be used to seeing forces when things touch: you push a door, you kick a ball, you squeeze a spring. But some forces act without touching. These are called non-contact forces or interactions at a distance. In this lesson, you focus on three:
Whenever two objects interact at a distance, there is a field around them (gravitational, electric, or magnetic) that allows them to affect each other. A system of just two objects plus the field can store potential energy.
The arrangement of objects means how they are positioned relative to each other:
When you change the arrangement, you change how strong the interaction is, and that changes the amount of potential energy stored in the system. Often you can feel this as how hard or easy it is to move the objects to a new arrangement.
Developing a model means creating a simple representation—like a diagram, graph, or explanation—that shows how the arrangement is linked to the potential energy of the system.
The gravitational interaction happens between any two objects with mass. For you, the most noticeable gravitational interaction is with the Earth. When you lift something, like a backpack, higher above the ground, you are changing its arrangement with respect to Earth and increasing gravitational potential energy.
For moderate heights near Earth’s surface, scientists often use the formula for gravitational potential energy:
\(PE_g = mgh\)
Here, \(PE_g\) is gravitational potential energy, \(m\) is mass in kilograms, \(g\) is gravitational field strength (about \(9.8 \textrm{ m/s}^2\) on Earth), and \(h\) is height above a reference level in meters.
Numeric example: Suppose you lift a 2 kilogram textbook onto a shelf 1.5 meters high. The gravitational potential energy is \(PE_g = mgh = 2 \times 9.8 \textrm{ m/s}^2 \times 1.5 \textrm{ m} = 29.4 \textrm{ J}\). You have stored about 29.4 joules of energy in the Earth–book system by changing the arrangement (increasing the height).
Modeling the gravitational system:
On a graph of height vs. gravitational potential energy, the line goes up as height increases. You can model this visually by drawing objects at different heights with bigger “energy bars” for greater potential energy, as shown in [Figure 1].
When the object falls, arrangement changes again: the distance decreases, gravitational potential energy goes down, and kinetic energy goes up.
Magnets have two poles: north (N) and south (S). The rules for magnetic interaction between two magnets are:
The potential energy in a two-magnet system depends on both how far apart the magnets are and which poles face each other.
[Figure 2] illustrates several arrangements of two bar magnets and shows how potential energy changes with distance and pole orientation.
Attracting poles (N–S):
Repelling poles (N–N or S–S):
Simple conceptual model for magnet potential energy:
You do not need an exact formula here. Instead, your model can be a diagram, arrows showing forces, and energy bars showing relative amounts of potential energy, as in [Figure 2].
Electric charges come in two types: positive (+) and negative (−). Their interaction is similar to magnets:
Just like with magnets, the electric potential energy in a system of two charges depends on:
Attracting charges (+ and −):
Repelling charges (+ and +, or − and −):
Just like with magnets, you can model this with simple diagrams of charges, arrows for forces, and bars for more or less potential energy. You do not need to use the full electric potential energy formula at this level.
For all three interactions—gravitational, magnetic, and electric—the key pattern is the same when looking at two objects:
All of these involve a system of two interacting objects plus the field between them.
When you “develop a model” for these situations, you are creating a clear way to show how arrangement affects potential energy. Your model should include:
[Figure 3] shows a sample model using energy bar charts for a falling object and for two repelling magnets.
Imagine you hold a basketball above the floor and then drop it:
As the ball falls:
Just before the ball hits the floor, the system has low potential energy and high kinetic energy, similar to the lower position in [Figure 1]. When it bounces, some of that energy turns into sound and a bit of thermal (heat) energy, and some becomes potential energy as the ball rises again.
Your model: a diagram of the ball at different heights with energy bars showing that potential energy goes down while kinetic energy goes up.
Picture two carts on a low-friction track, each with a magnet facing the other so that like poles are facing (N–N). You push them close together and hold them with your hands, feeling them push apart.
When you release them, the magnets push the carts apart:
Your model can match Panel B in [Figure 3], where the potential energy bar is tall when magnets are close and shorter when they are far apart, while the kinetic energy bar grows.
You rub a balloon on your hair or a sweater. Some charges move, and the balloon becomes charged. Now you bring the balloon near a small piece of paper.
When the balloon is far, there is more electric potential energy but weaker attraction, so the paper might not move much. When the balloon is brought closer, electric potential energy decreases as the paper jumps up, gaining kinetic energy and sticking to the balloon.
Your model: draw the balloon and the paper at two different distances, with electric field lines or arrows showing attraction, and energy bars showing higher potential energy when they are apart and lower when they are together.
One big science idea is that energy is conserved—it is not created or destroyed, only transferred or transformed. In the systems you have seen:
In real life, some of the energy also becomes thermal energy (heating surfaces) or sound, but the total energy of the closed system stays the same.
When you develop a model, it is helpful to:
1. Roller Coasters
At the top of a hill, a roller coaster car has a large amount of gravitational potential energy because it is high above the ground. As it rushes down, potential energy decreases and kinetic energy increases. Designers use these energy changes to make rides thrilling but safe.
2. Maglev Trains
Some trains use powerful magnets to float above the tracks. The magnetic interaction between magnets on the train and on the track allows the train to “levitate.” The arrangement of these magnets and the changing magnetic fields control how potential and kinetic energy trade places, allowing smooth, fast motion with little friction.
3. Electric Power and Lightning
In storms, huge electric charges build up in clouds and between clouds and the ground. That means the cloud–ground system can have a large amount of electric potential energy. When a lightning bolt strikes, that potential energy rapidly transforms into light, sound, heat, and kinetic energy of the air.
4. Everyday Magnets on a Fridge
When you stick a magnet to a refrigerator door, you are changing the arrangement of the magnet and the metal door. As the magnet moves toward the door, magnetic potential energy decreases and a tiny amount of kinetic energy appears as the magnet “snaps” into place.
Potential energy is stored energy that depends on the arrangement of objects interacting at a distance. In a system of two objects:
When the arrangement changes (like changing distance or orientation), the amount of potential energy in the system changes. That energy often transforms into kinetic energy as objects speed up or slow down, while the total energy of the system is conserved. By building clear models—using diagrams, graphs, and energy bars—you can describe and predict how changing the arrangement of objects at a distance changes the potential energy stored in the system. 🔬
