Use energy representations to track energy before and after...

SECTION 1

Why Do Scientists Track Energy?

Have you ever wondered where the energy goes when a ball bounces? Or why a hot cup of cocoa cools down? For hundreds of years, scientists have asked the same questions. They discovered that energy (the ability to make things move, change, or heat up) never just appears or disappears. It always goes somewhere. Tracking energy is how we make sense of every interaction in the universe.

1686

Leibniz and "Living Force"

Gottfried Leibniz proposed that moving objects carry a quantity he called vis viva, or living force. This was an early version of what we now call kinetic energy.

1843

Joule Measures Heat from Motion

James Joule showed that stirring water with a paddle made the water warmer. He proved that mechanical energy could turn into thermal energy. The unit of energy, the joule (J), is named after him.

1850

Law of Conservation of Energy

Scientists like Rudolf Clausius and William Thomson established that energy is never created or destroyed. It only changes form. This became known as the law of conservation of energy.

1960s

Energy Bar Charts in Education

Teachers and scientists began using bar chart diagrams to help students visualize how energy transfers and transforms. These representations made the invisible flow of energy much easier to understand.

The big question scientists kept asking was: If energy cannot be created or destroyed, how can we keep track of it? The answer is energy representations—diagrams and bar charts that show every type of energy before and after something happens. In this lesson, you will learn to build and read these powerful tools.

SECTION 2

Core Principles of Energy Tracking

Before we draw any diagrams, we need to understand a few big ideas. These principles are the rules that every energy representation must follow.

Conservation of Energy

Energy cannot be created or destroyed. The total energy before an interaction must equal the total energy after the interaction. Energy only transfers (moves between objects) or transforms (changes type).

Types of Energy

Kinetic energy (KE) is the energy of motion. Potential energy (PE) is stored energy, like a stretched rubber band or a ball held high. Thermal energy is the energy of vibrating particles, often felt as heat.

System and Surroundings

A system is the set of objects you are studying. Everything outside the system is the surroundings. Energy can move between the system and surroundings.

Energy Representations

An energy bar chart uses bars to show the amount of each energy type. A "before" set and an "after" set sit side by side so you can compare them.

✦ KEY TAKEAWAY

Think of energy like money in different pockets. You might move a dollar from your left pocket (kinetic energy) to your right pocket (thermal energy). The total money never changes—you just rearranged it. Energy bar charts are like checking all your pockets before and after to make sure everything adds up.

SECTION 3

The Energy Bar Chart: A Visual Tool

Let's look at a real scenario. Imagine you hold a ball above the ground and drop it. At the top, the ball is not moving, so it has gravitational potential energy (PE) but zero kinetic energy (KE). As the ball falls, PE transforms into KE. Just before hitting the ground, nearly all the energy is KE. The diagram below shows this with an energy bar chart.

This energy bar chart shows a ball dropped from a height. Before the drop (left side), all 100 J of energy is stored as gravitational PE. After the drop (right side), most energy has transformed into KE (94 J), and a small amount became thermal energy (6 J) from air resistance. Notice that the totals on both sides equal 100 J—energy is conserved!

Look at the diagram above. Each bar represents one type of energy. The height of the bar shows the amount in joules. On the left (before), the PE bar is tall and the KE bar is zero. On the right (after), the KE bar is tall and the PE bar is zero. A tiny thermal energy bar appeared because some energy was lost to friction with the air. The dashed line in the middle represents the interaction—the moment the ball falls.

🎢 Anchoring Phenomenon

Think about a roller coaster. At the very top of the first hill, the car is slow and high up (lots of PE, little KE). At the bottom of the hill, the car is fast and low (lots of KE, little PE). An energy bar chart helps you see this swap at every point on the track!

SECTION 4

The Math Behind Energy Tracking

Energy bar charts are based on a simple math rule. The total energy before an interaction must equal the total energy after. Let's write that as an equation.

CONSERVATION OF ENERGY

Total Energy (before) = Total Energy (after)

This means if you add up every type of energy before the interaction, the sum must match the total of every type of energy after the interaction.

EXPANDED FORM

KE₁ + PE₁ = KE₂ + PE₂ + Thermal

KE₁ = kinetic energy before, PE₁ = potential energy before, KE₂ = kinetic energy after, PE₂ = potential energy after, Thermal = energy that became heat (from friction, air resistance, etc.).

KINETIC ENERGY FORMULA

KE = ½ × m × v²

m = mass in kilograms (kg), v = speed in meters per second (m/s). The answer comes out in joules (J).

GRAVITATIONAL POTENTIAL ENERGY FORMULA

PE = m × g × h

m = mass in kilograms, g = 10 m/s² (approximate gravitational acceleration on Earth), h = height in meters above a reference point.

When you draw an energy bar chart, you calculate each type of energy using these formulas. Then you draw bars whose heights match the values. The bars on the "before" side should add up to the same total as the bars on the "after" side.

SECTION 5

Identifying Energy Types in Different Interactions

Energy bar charts work for all kinds of interactions, not just dropping a ball. The key is to identify every type of energy in your system. Here is a reference table of common energy types you will see in middle school science.

Common energy types encountered in middle school physical science

Energy Type	What It Is	Example
Kinetic (KE)	Energy of an object in motion	A soccer ball rolling across a field
Gravitational PE	Stored energy due to height above the ground	A book sitting on a high shelf
Elastic PE	Stored energy in a stretched or compressed object	A pulled-back rubber band
Thermal	Energy from the random motion of particles (heat)	Warm brakes on a bicycle after stopping
Sound	Energy carried by vibrations through air or another medium	The crack of a bat hitting a baseball

This second energy bar chart shows a rubber band being launched. Before release, all 50 J is elastic PE. After release, the energy has transformed into kinetic energy (44 J), thermal energy (4 J), and sound energy (2 J). The total remains 50 J.

In this rubber band example, the elastic potential energy transforms into three different forms: kinetic, thermal, and sound. No energy was lost. It just spread out into different types. When you draw your own bar charts, remember to check: do the "before" bars add up to the same total as the "after" bars?

SECTION 6

Worked Example: A Skateboarder on a Ramp

A 40 kg skateboarder stands at the top of a 3-meter-high ramp. She is not moving yet. She then rolls to the bottom of the ramp. Let's track her energy before and after.

Skateboarder Energy Bar Chart

Step 1 — Define the SystemOur system is the skateboarder and the Earth. The interaction is her rolling from the top to the bottom of the ramp.

Step 2 — Calculate PE BeforeShe is at the top of a 3 m ramp and not moving. Use PE = m × g × h. PE = 40 kg × 10 m/s² × 3 m

PE = 1,200 J

Step 3 — Calculate KE BeforeShe is standing still, so her speed is 0 m/s. KE = ½ × m × v² = ½ × 40 × 0² = 0 J.

KE = 0 J

Step 4 — Draw the BEFORE BarsDraw a tall PE bar at 1,200 J. Draw a KE bar at 0 J. Draw a Thermal bar at 0 J. The total before = 1,200 J.

Step 5 — Identify Energy AfterAt the bottom, her height is 0 m, so PE = 0 J. If friction took away 100 J as thermal energy, then by conservation: KE = Total − PE − Thermal = 1,200 − 0 − 100.

KE = 1,100 J

Step 6 — Draw the AFTER Bars and CheckDraw a PE bar at 0 J. Draw a KE bar at 1,100 J. Draw a Thermal bar at 100 J. The total after = 0 + 1,100 + 100 = 1,200 J. This matches the total before, so energy is conserved. ✓

Total Before (1,200 J) = Total After (1,200 J) ✓

🔬 SEP Spotlight: Developing and Using Models

When you draw an energy bar chart, you are building a model. Scientists and engineers use models to explain how things work. Your bar chart is a model that makes the invisible flow of energy visible!

SECTION 7

Strengths and Limitations of Energy Representations

Energy bar charts are powerful, but like any tool, they have strengths and limitations. Understanding both helps you use them wisely.

Comparing the strengths and limitations of energy bar charts

Strengths	Limitations
Clearly show how much of each energy type exists before and after	Cannot show what happens during the interaction (only snapshots)
Make conservation of energy easy to check (totals must match)	Do not show the direction energy flows between objects
Work for any type of interaction—mechanical, thermal, chemical	Require you to know or estimate the energy values first
Help identify where "missing" energy went (often thermal or sound)	Can become complex when many energy types are involved

✦ KEY TAKEAWAY

Think of an energy bar chart like a scoreboard at halftime and after the final buzzer. It tells you the score at two moments, but it does not replay every pass and goal. If you need to understand the play-by-play of energy flow, you would combine a bar chart with an energy flow diagram that uses arrows to show direction.

SECTION 8

Connecting to Bigger Ideas in Science

Energy bar charts are your first step into a larger world of energy analysis. In high school and beyond, you will encounter more detailed tools. Here is a quick preview of how middle school energy tracking connects to advanced science.

How middle school energy concepts connect to advanced physics

What You Learn Now	What Comes Next
Energy bar charts with PE, KE, and thermal energy	Energy pie charts, Sankey diagrams, and detailed system models
Conservation of energy: totals before = totals after	First Law of Thermodynamics: ΔU = Q − W (change in internal energy equals heat minus work)
Identifying thermal energy from friction	Second Law of Thermodynamics: energy spreads out and becomes less useful over time (entropy)
Using KE = ½ × m × v² and PE = m × g × h	Work-energy theorem, spring potential energy (½kx²), and power calculations

The crosscutting concept of Energy and Matter runs through all of science. Biologists track energy through food webs. Earth scientists track energy from the Sun as it heats land and water. Chemists track energy released or absorbed in reactions. The bar chart skills you learn now will help you in all of these areas.

🔗 CCC Connection: Energy and Matter

The crosscutting concept of Energy and Matter reminds us that within a system, energy flows in, out, and between objects. Tracking this flow with representations is a skill used in every branch of science.

SECTION 9

Practice Problems

PROBLEM 1 — CONCEPTUAL

A ball is held at the top of a hill and then released. It rolls to the bottom. Which statement best describes the energy transformation? A) Kinetic energy transforms into potential energy. B) Potential energy transforms into kinetic energy and some thermal energy. C) Thermal energy transforms into kinetic energy. D) Energy is created as the ball speeds up.

PROBLEM 2 — BASIC CALCULATION

A 2 kg book sits on a shelf that is 5 meters high. What is its gravitational potential energy? (Use g = 10 m/s²) A) 10 J B) 50 J C) 100 J D) 200 J

PROBLEM 3 — INTERMEDIATE

A 2 kg book falls from a 5 m shelf to the floor. Its PE at the top was 100 J. At the bottom, it has 90 J of kinetic energy. How much thermal energy was produced by air resistance? A) 0 J B) 5 J C) 10 J D) 190 J

PROBLEM 4 — APPLIED

A student launches a toy car using a compressed spring. Before the launch, the spring has 80 J of elastic potential energy and the car is not moving. After the launch, the car has 68 J of kinetic energy and the spring is relaxed. The student draws an energy bar chart but cannot figure out where the remaining energy went. What is the best explanation? A) Energy was destroyed during the launch. B) 12 J was converted to thermal and sound energy from friction and vibration. C) The car gained more energy than the spring had. D) The spring still has 12 J of elastic PE after launching.

PROBLEM 5 — CRITICAL THINKING

Two students draw energy bar charts for the same event: a bouncing ball hitting the floor and bouncing back up. Student A shows the ball reaching the same height after the bounce. Student B shows the ball reaching a lower height after the bounce. Which student's bar chart is more realistic, and why? A) Student A, because energy is always conserved so the ball must return to the same height. B) Student B, because some kinetic energy is destroyed when the ball hits the floor. C) Student B, because some energy transforms into thermal and sound energy during the bounce, leaving less PE for height. D) Student A, because gravity gives the ball extra energy on the way back up.

SUMMARY

Lesson Summary

In this lesson, you learned to use energy bar charts to track energy before and after an interaction. You identified key energy types: kinetic energy (KE), gravitational potential energy (PE), elastic potential energy, and thermal energy. You used the formulas KE = ½ × m × v² and PE = m × g × h to calculate bar heights.

The most important rule is the law of conservation of energy: the total energy before an interaction always equals the total energy after. If energy seems to be "missing," it has transformed into thermal or sound energy. Drawing bar charts is a science and engineering practice called developing and using models. This skill helps you explain real-world phenomena—from roller coasters to bouncing balls—using evidence and the crosscutting concept of Energy and Matter.