Apply energy conservation and transformations. - GED Science

SECTION 1

Historical Context & Motivation

For centuries, people observed that fires burned out, moving objects slowed down, and hot drinks cooled off. It seemed like something was being lost each time. Scientists spent hundreds of years trying to figure out what that "something" was and whether it truly vanished. The answer turned out to be one of the most powerful ideas in all of science: energy is never created or destroyed — it only changes form. This principle, called the law of conservation of energy, is central to the GED Science exam and to understanding how the physical world works.

1689 • Leibniz's "Living Force"

Gottfried Leibniz proposed that a moving object carries a quantity he called "vis viva" (living force), laying early groundwork for the concept of kinetic energy.

1843 • Joule's Paddle Wheel Experiment

James Prescott Joule showed that mechanical work could be precisely converted into heat, proving that mechanical energy and thermal energy are interchangeable. The unit of energy, the joule (J), is named after him.

1847 • Helmholtz Formalizes Conservation

Hermann von Helmholtz published a paper stating that the total energy of an isolated system remains constant — the first formal statement of the law of conservation of energy.

1905 • Einstein's Mass-Energy Equivalence

Albert Einstein's famous equation E = mc² showed that mass itself is a form of energy, extending the conservation law even further.

The central question these scientists answered is this: when energy seems to disappear — a ball stops bouncing, a car runs out of gas — where does it actually go? Understanding the answer allows you to analyze everything from roller coasters to power plants, and it is a key skill tested on the GED Science exam.

SECTION 2

Core Principles & Definitions

Before you can analyze energy conservation problems on the GED, you need to understand a few foundational ideas. Energy is the ability to do work or cause change. It exists in many forms, and these forms can convert into one another. The total amount of energy in a closed system always stays the same — that is the law of conservation of energy.

Kinetic Energy (KE)

The energy of motion. Any object that is moving has kinetic energy. A faster object or a heavier object has more kinetic energy.

Potential Energy (PE)

Stored energy due to position or condition. A book on a high shelf has gravitational PE; a stretched rubber band has elastic PE; chemicals in a battery have chemical PE.

Thermal Energy (Heat)

The total kinetic energy of all the tiny particles (atoms and molecules) vibrating inside an object. A hotter object has more thermal energy.

Energy Transformation

The process of energy changing from one form to another. For example, a light bulb transforms electrical energy into light and thermal energy.

Conservation of Energy

Energy cannot be created or destroyed. In any process, the total energy before equals the total energy after. Energy may change form or transfer to another object, but the total never changes.

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KEY TAKEAWAY

Think of energy like money in a bank account. You can move money between checking and savings, convert it to cash, or spend it on a purchase — but the total dollars don't vanish. They just end up somewhere else. In the same way, energy can change forms (kinetic, potential, thermal, chemical, electrical, sound, light), but the total amount in a closed system is always conserved.

SECTION 3

Visual Explanation — The Roller Coaster

A roller coaster is one of the best everyday examples of energy conservation. At the top of the first hill, the car has maximum gravitational potential energy and almost zero kinetic energy. As it rolls downhill, potential energy converts into kinetic energy, and the car speeds up. At the bottom, kinetic energy is at its peak. As the car climbs the next hill, kinetic energy converts back into potential energy, and the car slows down. The diagram below shows this exchange at different points along the track.

At point A (top of the first hill), potential energy is at its maximum and kinetic energy is near zero. At point B (first valley), potential energy is low and kinetic energy is high. At every point, PE + KE = the same total. Some energy is always lost to friction as thermal energy in real coasters, which is why each successive hill must be shorter.

Notice that the roller coaster never goes higher than its starting hill. That is because its total mechanical energy was set at the top of the first hill. Without an engine adding more energy, the car cannot climb higher than where it started. In real life, some energy is always transformed into thermal energy through friction and air resistance, which is why each hill on a real coaster must be shorter than the one before it. The energy isn't gone — it has just been transferred to the track and air as heat.

SECTION 4

Mathematical Framework

The GED Science exam rarely asks you to do heavy math, but understanding the key formulas helps you reason through problems and interpret data. Here are the most important energy equations you should know.

KINETIC ENERGY

KE = ½ × m × v²

KE = kinetic energy (joules, J); m = mass (kilograms, kg); v = velocity or speed (meters per second, m/s). This tells you that doubling the speed quadruples the kinetic energy.

GRAVITATIONAL POTENTIAL ENERGY

PE = m × g × h

PE = potential energy (J); m = mass (kg); g = acceleration due to gravity (9.8 m/s²); h = height above a reference point (meters, m). The higher or heavier the object, the more stored energy it has.

CONSERVATION OF MECHANICAL ENERGY

PE₁ + KE₁ = PE₂ + KE₂

The total mechanical energy at any point (1) equals the total mechanical energy at any other point (2), assuming no energy is lost to friction or other non-conservative forces. This is the core equation for solving roller coaster, pendulum, and falling-object problems.

GENERAL CONSERVATION LAW

Total Energy (before) = Total Energy (after)

This is the broadest form of conservation of energy. It includes all energy types — kinetic, potential, thermal, chemical, electrical, sound, light. Energy may change form, but the total never changes.

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GED Tip

On the GED, you are more likely to be asked to interpret a graph or describe an energy transformation in words than to plug numbers into a formula. However, knowing the formulas helps you understand WHY energy behaves as it does. For example, knowing KE = ½mv² helps you explain why a car at 60 mph has four times the kinetic energy of a car at 30 mph.

SECTION 5

Types of Energy Transformations

Energy transformations happen constantly all around you. Every machine, every living thing, and every natural process involves energy changing from one form to another. The GED frequently tests your ability to identify these transformations in everyday scenarios. The diagram below shows some of the most common energy transformation chains.

Five common energy transformation chains: Solar panels convert light to electrical energy. Car engines convert chemical energy (gasoline) to thermal, then kinetic energy, with waste heat and sound. Light bulbs convert electrical to light and thermal. Photosynthesis converts light to chemical energy. Hydroelectric dams convert gravitational potential energy to kinetic to electrical energy.

Everyday Scenario	Energy Input	Useful Energy Output	Waste Energy
Toaster	Electrical	Thermal (heat)	Light (glowing coils)
Person running	Chemical (food)	Kinetic (motion)	Thermal (body heat)
Campfire	Chemical (wood)	Thermal + Light	Sound (crackling)
Wind turbine	Kinetic (wind)	Electrical	Thermal + Sound

Common energy transformations in everyday life

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Important for the GED

In every energy transformation, some energy is always converted to thermal energy (heat) that spreads out into the surroundings. This is why no machine is 100% efficient. The energy is not destroyed — it is just transformed into a less useful form. This concept explains why perpetual motion machines are impossible.

SECTION 6

Worked Example

Let's work through a problem that combines energy conservation with a real-world scenario — the kind of stimulus-based reasoning the GED expects.

A Ball Dropped from a Building

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Step 1 — Read the Scenario

A 2 kg ball is held at rest at the top of a 20-meter building and then dropped. Ignoring air resistance, what is the ball's speed just before it hits the ground? We will use energy conservation to solve this.
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Step 2 — Identify the Energy at the Top

At the top, the ball is not moving, so KE = 0. All of its energy is gravitational potential energy. Using PE = m × g × h:

PE = 2 kg × 9.8 m/s² × 20 m = 392 J
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Step 3 — Identify the Energy at the Bottom

Just before hitting the ground, the height is 0, so PE = 0. All the energy has been converted to kinetic energy. By conservation of energy: KE at bottom = PE at top = 392 J.

KE at bottom = 392 J
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Step 4 — Solve for Speed

Now use KE = ½ × m × v² and solve for v. Rearranging: v² = 2 × KE / m = 2 × 392 / 2 = 392. Taking the square root: v = √392 ≈ 19.8 m/s.

v ≈ 19.8 m/s (about 44 mph)
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Step 5 — Check Your Reasoning

The ball started with 392 J of potential energy and ended with 392 J of kinetic energy. Total energy was conserved — 392 J throughout the fall. No energy was created or destroyed; it simply transformed from gravitational PE to KE.

Total energy at top = Total energy at bottom = 392 J ✓

SECTION 7

Efficiency & Energy "Loss"

In textbook problems, we often ignore friction and assume 100% of energy converts from one useful form to another. In the real world, though, every energy transformation wastes some energy as heat. The term efficiency describes what percentage of input energy is converted to the desired output. The GED may ask you to compare efficiencies or explain why energy is "lost" (remember, it's not actually lost — just converted to a less useful form like heat).

Device / Process	Approximate Efficiency	Where "Wasted" Energy Goes
LED light bulb	~80–90%	Small amount of heat
Incandescent bulb	~5–10%	Mostly heat (very hot to touch)
Gasoline car engine	~20–25%	Heat (radiator, exhaust), sound
Electric motor	~85–95%	Friction heat, sound
Human body (running)	~25%	Body heat (you sweat!)

Efficiency of common devices and processes

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KEY TAKEAWAY

When a question says energy is "lost" or "wasted," it does NOT mean the energy is destroyed. Think of it like a leaky garden hose: water (energy) enters the hose, some comes out the nozzle (useful work), and some leaks out along the way (waste heat). The total water in equals the total water out — it just doesn't all end up where you wanted it.

SECTION 8

Connection to Broader Science

Energy conservation is not just a physics topic — it connects to nearly every area of science you might encounter on the GED. In biology, it explains how food chains work: energy flows from the sun to plants to animals, transforming at each step. In Earth science, it explains weather patterns driven by solar energy absorbed and re-radiated by Earth. In chemistry, it explains why some reactions release heat (exothermic) and others absorb it (endothermic). The table below compares the basic GED-level understanding with more advanced concepts you may encounter.

GED-Level Concept	Advanced Extension
Energy is conserved in a closed system	First Law of Thermodynamics: the change in internal energy equals heat added minus work done
Some energy is always "wasted" as heat	Second Law of Thermodynamics: entropy (disorder) always increases; no process is 100% efficient
PE converts to KE as objects fall	Lagrangian and Hamiltonian mechanics describe energy transformations in complex systems
Food provides chemical energy for the body	ATP hydrolysis and cellular respiration involve detailed biochemical energy transfers

GED-level concepts and their advanced extensions

You do not need to know the advanced versions for the GED. However, understanding that conservation of energy is the foundation for these bigger ideas can help you feel confident when a GED question touches on thermodynamics, ecology, or chemistry. The core principle is always the same: energy in = energy out, always.

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

A student rubs her hands together vigorously on a cold day and notices they become warm. Which of the following best describes the energy transformation occurring?

A. Thermal energy is being created from nothing.
B. Chemical energy from the student's muscles is being converted into kinetic energy, which is then converted into thermal energy through friction.
C. Cold energy is being destroyed and replaced by heat energy.
D. Potential energy in the hands is being released as thermal energy.

Show answer (B)

B is correct. The student's muscles convert chemical energy (from food) into kinetic energy (the rubbing motion). Friction between the hands then transforms that kinetic energy into thermal energy (heat). A is wrong because energy cannot be created from nothing — this violates the law of conservation of energy. C is wrong because "cold energy" is not a real form of energy; cold is simply the absence of thermal energy. D is wrong because the energy source is chemical energy in the muscles, not potential energy stored in the hands.

Question 2: BASIC CALCULATION

A 5 kg rock is sitting on the edge of a cliff 10 meters above the ground. Using PE = m × g × h (where g = 9.8 m/s²), what is the gravitational potential energy of the rock?

A. 50 J
B. 98 J
C. 490 J
D. 980 J

Show answer (C)

C is correct. PE = m × g × h = 5 kg × 9.8 m/s² × 10 m = 490 J. A (50 J) results from using g = 1 instead of 9.8, likely from multiplying only m × h. B (98 J) results from forgetting to multiply by the height or using m = 1. D (980 J) results from doubling the correct answer, perhaps by multiplying by 20 instead of 10 for the height.

Question 3: INTERMEDIATE

A researcher measured the energy of a pendulum at three points in its swing. The data is shown below: Position 1 (top left): PE = 8 J, KE = 0 J Position 2 (bottom center): PE = 0 J, KE = ? Position 3 (top right): PE = 6 J, KE = ? Assuming some energy is lost to air resistance, what are the missing kinetic energy values at Positions 2 and 3?

A. Position 2: KE = 8 J; Position 3: KE = 2 J
B. Position 2: KE = 8 J; Position 3: KE = 0 J
C. Position 2: KE = 7 J; Position 3: KE = 0 J
D. Position 2: KE less than 8 J; Position 3: KE = 0 J

Show answer (D)

D is correct. At Position 1, the total mechanical energy is 8 J (all PE). As the pendulum swings, some energy is lost to air resistance (converted to thermal energy). So at Position 2, the total mechanical energy is less than 8 J, meaning KE must be less than 8 J (since PE = 0). At Position 3, the pendulum reaches its maximum height on the other side, where KE = 0 and all remaining mechanical energy is PE = 6 J. The 2 J difference (8 J − 6 J) was lost to thermal energy via air resistance. A is wrong because it assumes no energy was lost before Position 2. B is wrong because it assumes KE = 8 J at Position 2, which would mean no energy was lost to friction at all before that point, yet 2 J is clearly lost by Position 3. C gives a specific KE at Position 2 that we cannot determine exactly without more data — we only know it is less than 8 J.

Question 4: APPLIED

2 pts

A homeowner is deciding between two water heaters. Heater A uses natural gas (chemical energy) and is 60% efficient. Heater B is an electric heat pump that is 300% efficient (it moves existing thermal energy from outside air into the water). Both heaters need to deliver 1,000 J of thermal energy to the water. In 3–5 sentences, explain why Heater B requires less input energy than Heater A, and identify the energy transformations involved in each heater. Use the concept of energy conservation in your answer.

Show answer

Rubric (2 points): Point 1 (Energy input comparison): The student correctly explains that Heater A requires about 1,667 J of chemical energy input (1,000 ÷ 0.60) because 40% is wasted as exhaust heat, while Heater B requires only about 333 J of electrical energy input (1,000 ÷ 3.0) because it moves existing thermal energy from the outside air rather than creating all the heat from scratch. The student must use the concept of efficiency to explain why less input energy is needed. Point 2 (Energy transformations and conservation): The student correctly identifies that Heater A transforms chemical energy → thermal energy (with waste heat and exhaust gases), while Heater B transforms electrical energy → mechanical energy (compressor) → transferred thermal energy. The student must reference conservation of energy — in both cases, total energy is conserved; the difference is that Heater B harvests environmental thermal energy that already exists, so its electrical input does not need to account for all the output heat.

Question 5: CRITICAL THINKING

3 pts

A student conducts an experiment where she drops a 0.5 kg steel ball from different heights and measures the ball's speed just before it hits the ground. Her data is shown below: Trial 1: Height = 1 m, Speed = 4.2 m/s Trial 2: Height = 2 m, Speed = 5.8 m/s Trial 3: Height = 3 m, Speed = 7.0 m/s Trial 4: Height = 4 m, Speed = 8.5 m/s The theoretical speed (no air resistance) can be calculated from conservation of energy: v = √(2 × g × h), where g = 9.8 m/s². Analyze the data in 5–7 sentences. Calculate the theoretical speed for at least one trial and compare it to the measured speed. Explain any differences using the concept of energy conservation. Identify what this tells us about the experimental conditions.

Show answer

Rubric (3 points): Point 1 (Correct calculation): The student correctly calculates theoretical speed for at least one trial. For example, Trial 1: v = √(2 × 9.8 × 1) = √19.6 ≈ 4.43 m/s. Trial 4: v = √(2 × 9.8 × 4) = √78.4 ≈ 8.85 m/s. The student compares these to the measured values (4.2 and 8.5 m/s, respectively) and notes the measured values are consistently lower. Point 2 (Energy conservation explanation): The student explains that the measured speeds are lower than theoretical because some gravitational potential energy is converted to thermal energy through air resistance and possibly sound, rather than entirely becoming kinetic energy. Conservation of energy still holds — the total energy (KE + thermal + sound) equals the initial PE — but not all of it ends up as KE. Point 3 (Pattern analysis and experimental insight): The student identifies that the difference between theoretical and measured speeds increases with height (longer fall = more time for air resistance to act), OR correctly notes that the percentage of energy lost to air resistance increases with greater drop heights because the ball reaches higher speeds where air resistance is stronger. This tells us the experiment was NOT conducted in a vacuum and that air resistance is a measurable factor in the system.

SUMMARY

Lesson Summary

Summary

The law of conservation of energy states that energy cannot be created or destroyed — only transformed from one form to another. The key forms of energy include kinetic energy (energy of motion), potential energy (stored energy due to position or condition), thermal energy (heat), chemical energy, and electrical energy. Every machine and natural process involves energy transformations, and in every transformation, some energy is converted to thermal energy that disperses into the surroundings.

For the GED, remember these key equations: KE = ½mv² and PE = mgh. More importantly, be prepared to identify energy transformations in everyday scenarios (car engines, light bulbs, food chains), explain why measured values differ from theoretical predictions (friction and air resistance convert energy to heat), and use the principle that total energy before = total energy after to reason through data-based questions. The concept of efficiency tells us what fraction of input energy goes to useful output — no device is 100% efficient because some energy always becomes waste heat.