L2. Kinetic and Potential Energy

Energy and Its Forms

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L2. Kinetic and Potential Energy: Swinging Between Speed and Height

Why does a playground swing feel fastest at the bottom and slowest at the top?

Connection: What you already know

In the previous lesson you learned that energy is what powers things and can appear in different ways. For this lesson we use a single, familiar scene — a person on a playground swing — to see two specific kinds of mechanical energy. You do not need any new math beyond multiplication and a simple square, but we will use a short formula to describe how speed and height affect energy.

Kinetic energy: energy of motion

Kinetic energy is the energy an object has because it is moving. On the swing, when the rider is moving fastest through the bottom, the swing has the most kinetic energy. Two key ideas help predict how much kinetic energy an object has: more mass makes more kinetic energy at the same speed, and a small change in speed makes a bigger change in kinetic energy. Scientists write kinetic energy as KE = 1/2 × mass × speed squared. That speed-squared part means doubling speed makes kinetic energy about four times larger. In everyday terms: a slow skateboard and a fast skateboard of the same weight have very different kinetic energy because the faster one’s speed is squared.

• Formula (simple): KE = 1/2 × m × v² (m = mass, v = speed). Practical note: speed matters more than mass because v² grows fast.

Potential energy: stored energy of position

Potential energy is stored energy based on an object’s position or condition. For the swing, gravitational potential energy depends on how high the rider is above the lowest point. A higher position stores more gravitational potential energy because gravity could pull the rider farther, allowing more motion later. Another everyday example is a stretched rubber band (elastic potential energy) that can snap and send something flying when released. For gravity near Earth’s surface, we use a simple relation: PE = mass × gravity × height (PE = m × g × h). If you lift an object twice as high, it gains twice the gravitational potential energy.

• Gravity formula: PE = m × g × h (g ≈ 9.8 m/s² on Earth). Types of potential energy students see: gravitational (height) and elastic (stretched or compressed).

Watching energy swap during motion

A swing makes it easy to watch energy change form. At the highest point the swing is moving slowly, so kinetic energy is small and potential energy (height) is large. As the swing falls toward the bottom, height drops and that stored potential energy turns into kinetic energy, so the swing gets faster. At the lowest point height is smallest and kinetic energy is largest; after passing the bottom it climbs the other side and kinetic energy becomes potential again. You can check these steps with a simple observation or stopwatch: measure how high the swing goes and how fast it is at the bottom to see the trade.

• Sequence on one side to the other: high (PE large, KE small) → fall (PE decreases, KE increases) → bottom (KE largest) → rise (KE decreases, PE increases). Quick investigation: mark a height, let the swing go, time a short pass through the bottom — faster passes mean more KE at that moment.

Big idea for your next steps

Kinetic and potential energy are two ways we measure mechanical energy: one depends on motion, the other on position or condition. Watching a swing or a skateboard ramp gives a clear, testable model for how energy moves between these forms.

Try a short experiment: mark the swing’s highest points, measure a drop in height and time passes through the bottom. Use observations to describe when KE or PE is larger — this builds the habit of linking numbers and formulas to real motion.