Conservation of Energy - Easy Examples Explained

Students often learn the statement “energy cannot be created or destroyed” and then feel stuck. What does that sentence actually mean when you solve a physics problem, design a device, or read news about energy-saving technology? Why do so many exam answers lose marks even when the calculations look right?

If you treat the law of conservation of energy as a memorized sentence instead of a tool, you miss key steps: identifying the system, tracking all forms of energy (not just the mechanical ones), and accounting for energy transformed into heat, sound, or chemical forms. That leads to mistakes on test questions, wrong intuition in labs, and poor engineering decisions-like expecting a machine to “lose” energy rather than transform it, or underestimating how much energy can actually be recovered in systems such as electric vehicles or hydro plants.

In this post I’ll treat conservation of energy as a method. I’ll define it rigorously, show how to apply it step-by-step, and then walk through realistic examples and case studies (with numbers and references). By the end you’ll have a repeatable checklist to use on problems, lab work, and real-world reasoning.

1. What the law actually says (short, precise)

At its core: in a closed system the total energy remains constant - energy may change form (mechanical ↔ thermal ↔ chemical ↔ electrical, etc.), but the sum of all forms does not change. This principle is the conservation of energy (the first law of thermodynamics in its general form). (Encyclopedia Britannica)

Key words: closed system, all forms of energy, transformation.

2. A practical, step-by-step method for solving energy problems

Whenever you face a problem or a real system, follow these steps:

Define the system and boundary. What is inside the “box”? Is the environment (air, ground, friction) inside or outside?
List initial and final forms of energy. Include mechanical (KE, PE), thermal (internal energy), chemical, electrical, magnetic, and energy stored in fields.
Write the energy balance. In a simple form:
- Initial total energy + Energy in (work/heat) = Final total energy + Energy out (work/heat)
- For closed, adiabatic systems: Initial total = Final total.
Identify non-mechanical sinks or sources. Friction → thermal; sound → acoustic energy; chemical reactions → heat + products. Don’t drop them.
Use formulas to compute numeric values. Common formulas:
- Kinetic energy: K = 1/2mv²
- Gravitational potential energy: U = mgh
- Electrical energy (in circuits): E=Pt , E = P t or E=Vq.
Check units and conserve energy numerically. If energy “disappears,” track where it went (usually into thermal/internal energy).
State assumptions and approximations. Frictionless? Perfectly elastic? If not, include loss.

Use that method every time. Now let’s apply it to concrete, real-life examples.

3. Example 1 - The pendulum (classroom experiment)

A pendulum is an ideal starting point to see energy transform back and forth.

At the highest point: nearly all energy is gravitational potential U = mgh.
At the lowest point: nearly all is kinetic K = 1/2mv²
With air resistance and friction at the pivot, mechanical energy is gradually converted to thermal energy in the air and the pivot. The energy is not destroyed - it appears as slightly warmer air and tiny sound. This is why amplitude decays.

What to write in an answer: define the system (mass + string + Earth for g), list energies at start and end, and explicitly add a term for energy lost to non-conservative forces (friction/air drag). Reference texts and educational resources describe this standard account. (Encyclopedia Britannica)

4. Example 2 - Roller coaster (mechanical → mechanical + heat + sound)

A roller coaster illustrates large exchanges between potential and kinetic energy.

When the train climbs the first hill, its energy is stored as potential mghmgh.
As it descends, this potential becomes kinetic.
Braking and friction convert some mechanical energy into thermal energy and sound.

Problem approach: compute initial UU, compute KK at a point using energy conservation minus estimated losses. If the initial potential energy is 500 kJ and measured mechanical energy later is 460 kJ, the 40 kJ difference is heating the wheels/track and the air (and producing sound).
This approach trains you to look for where energy goes rather than saying “energy lost.”

5. Real-world case: regenerative braking in electric vehicles (quantified)

Regenerative braking converts some braking kinetic energy into stored electrical energy in the battery. It’s a practical application of conservation: kinetic → electrical (then chemical in the battery).
Quantified findings from recent studies: in urban driving conditions, recovered braking energy can account for around 20% of the total trip energy or more, depending on driving pattern and system design. Some studies report even higher recovery rates in favorable conditions; others show wide variation depending on braking intensity and traffic. (MDPI)

Worked numeric example (step-by-step arithmetic):
A 1000 kg electric car is traveling at 20 m/s and comes to rest. How much kinetic energy is available to recover?

The formula for kinetic energy is : KE = 1/2mv²

Where:

m = 1000 kg
v = 20 m/s

KE = 12 × 1000 × (20)²

First calculate 20^2:

20² = 400

Now multiply:

1000 × 400 = 400,000

Take half:

400,000/2 = 200,000 J

The kinetic energy available to recover is 200,000 J (200 kJ).

6. Real-world case: hydropower turbines (high conversion efficiency)

Hydropower converts water’s potential energy into electrical energy via turbines and generators. Large hydropower turbines are very efficient: turbine mechanical efficiencies are typically very high (often above 90% for well-designed units), meaning most of the water’s potential energy ends up as mechanical energy and then electrical energy after the generator stage. (OSTI, The Department of Energy's Energy.gov)

Worked numeric example (step-by-step arithmetic):

One cubic meter of water has mass m=1,000kg. If it drops h=10 meters:

where :

Mass: m=1000 kg
Height: h=10 m
Gravity: g=9.8 m/s²

Potential energy

PE = mgh
PE=1000 × 9.8 × 10
PE = 98,000 J

Answer: One cubic meter of water dropping 10 meters has 98,000 J (≈ 98 kJ) of potential energy available.

7. Biological example: photosynthesis (light -> chemical energy) - efficiency numbers

Photosynthesis converts solar energy into chemical energy. But the conversion efficiency (solar energy → plant biomass) is low in most crops. Meta-analyses and reviews report field-level seasonal efficiencies typically only a few percent or less for many crops; C4 plants and specially bred or biofuel plants can show efficiencies in the range of a few percent (e.g., up to ~3–6% for some biofuel crops under good conditions), while many common C3 crops have lower figures. That limited efficiency is why there’s intense research into improving photosynthetic conversion. (PMC, Wikipedia)

Why this matters: conservation still holds - sunlight energy is accounted for as reflected light, heat, chemical energy in biomass, and losses. Knowing the efficiency numbers helps when comparing land use, crop yields, and the potential of bioenergy.

8. Everyday energy conservation: lighting and building retrofits

A practical application of energy conservation is in reducing energy input needed for the same useful output. For example, LED bulbs produce the same light with much less electrical energy than incandescent bulbs. Government and industry data show residential LEDs use at least 75% less energy (and in many cases up to ~90% less) than incandescent bulbs, and they last far longer. That’s energy conservation through improved conversion/efficiency - you still obey conservation of energy, but you require less input energy to get the same useful light (less energy wasted as heat). (The Department of Energy's Energy.gov)

Practical classroom note: when you calculate savings, always compare useful output (lumens) rather than wattage, and account for lifetime and disposal too.

9. Common student mistakes and how to fix them (actionable checklist)

Ignoring non-mechanical energy. Fix: always ask “What becomes heat/sound/chemical?” and write terms for those.
Forgetting the system boundary. Fix: redraw the system and explicitly include environment terms if necessary.
Using KE/PE but not accounting for work done by friction. Fix: include a Wfric term in the energy balance (negative when energy leaves mechanical form).
Treating “energy lost” as destruction. Fix: use the phrase “energy transformed into [thermal/sound/etc.]” and, where possible, quantify it.
Unit errors. Fix: check SI units (mass in kg, distance in m, velocity in m/s, g = 9.81 m/s²), and show the unit alongside your final numeric answer.

10. Short solved problem (step by step)

Problem: A 2.0 kg block slides down a frictional 2 m high incline and reaches the bottom with speed 4 m/s. How much mechanical energy was converted to heat by friction?

Solution:

1. Gravitational potential energy at the top

PE = mgh

Where

m = 2.0 kg
g = 9.8 m/s²
h = 2.0 m

PE = 2.0 × 9.8 × 2.0 = 39.2 J

2. Kinetic energy at the bottom

KE = 1/2mv²

Where v = 4.0 m/s

KE = 1/2 × 2.0 × (4.0)²
KE = 1.0×16 = 16J

3. Energy lost to friction

The difference between initial potential energy and final kinetic energy:

E_friction = PE−KE
E_friction = 39.2−16 = 23.2J

Answer: The block lost 23.2 J of mechanical energy as heat due to friction..

11. Experiments you can do (simple, instructive)

Damped pendulum: measure amplitude decay and feel the air warming slightly near the pivot. Save the data and compute mechanical energy vs time.
Rolling down ramps: measure velocities and compare to predicted values from energy conservation; include a friction loss term and estimate coefficient of friction from energy loss.
Regenerative braking demo (if available): with a motor/generator kit, capture voltage produced during braking and compute recovered energy. Compare to theoretical kinetic energy.
These experiments teach accounting: energy is transformed and can be tracked with careful measurement.

12. Final tips for tests and real projects

Always begin with system definition and list of energies.
Label units and compute arithmetic carefully (show steps).
When asked “where did the energy go?” provide a narrative answer: “converted into heat at the pivot and air (≈ xx J) and acoustic energy (small).”
For engineering problems, use published efficiency figures (e.g., turbine efficiencies, regenerative braking recovery rates, LED savings) when doing systems-level calculations. (OSTI, MDPI, The Department of Energy's Energy.gov)

13. Summary (quick checklist)

Conservation of energy: total energy in a closed system remains constant; energy transforms, it doesn’t vanish.
Use a consistent 7-step method: define system -> list energies -> write balance -> include non-mechanical sinks -> do the math -> check units -> state assumptions.
Real systems: regenerative braking (kinetic -> electrical, real recovery ≈20% in urban trips), hydropower (very high conversion efficiency, often >90%), photosynthesis (field efficiencies of a few percent), and LEDs (use 75 - 90% less energy than incandescent bulbs).

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