In colloquial use, “energy” is a vaguely defined term, used in different ways by different groups.

Some people say that the universe is made of “matter” and of “energy”,  and if this were true, then energy would be some sort of thing that exists on it’s own, like matter.

Other people say that our bodies contain “energy fields”.

In our class we are going to use a precise, scientific definition of energy.


New Age Energy, an analysis

Your Body’s Alleged Energy Fields

1. Energy is a property of a system that enables change to occur.

2. Energy has no independent existence.

3. You can’t ask “What is energy made of?”, just like you can’t ask “what is length made of?” The question has no meaning:

4. Energy is the way a system is set up, such that it can do work on another system.

For example, a ball on a crane can be set up, so that when it is released, it does work by smashing into a building. We say that energy is put into the wrecking ball when we lift it, energy is put into the pieces of the building when it is smashed, etc.  But the “energy” is not actually a thing. It is a way to keep track of how one part of the system affects another part.

Potential energy and Kinetic energy

gravitational potential energy = PE = energy an object has due to its height
we’ll usually just call this potential energy

translational kinetic energy = KE = energy of a moving object
we’ll usually just call this kinetic energy

In math, “translation” means moving a shape (or object) without rotating it.

kinetic energy (KE)

The energy of an object in motion

KE = ½·m·v2

What happens if an object doubles it speed?

KE  =  ½·m·(2v)2 = ½·m∙4v2 = 4∙(½·m·v2)

We see that its KE is quadrupled

potential energy

You do work on a marble when you lift it up.

This gives the marble PE.

Letting go of the marble: Marble loses PE, but it gains KE.

PE = mass  x  gravity  x  height = mgh   g = 10 m/s 2

Consider these 3 cases:

Work is done lifting the ball, gives it gravitational PE.

The same net work is done to lift it, in all 3 cases.

Ball ramp Potential energy

What about in this case?

Ball Block ramp PE

Both blocks reach the same h (height)
Both blocks acquire the same PE
The same work is done on each block.
What matters is the final elevation, not the path followed.

Transforming PE into KE

The skier starts with lots of PE and no KE.

W represents the (positive) work done by the skier, as she compacts the unpacked snow.

W also represents the (negative) work done by the snow on the skier, which slows her down.

TME = total mechanical energy

TME = KE + PE + W

We start with W = 0  (no work done on the snow)

As time goes by, she loses PE, but gains kinetic energy (KE)

KE PE Work Skier

Elastic potential energy

Gravitational PE is the energy that an object up high has, if it falls.

Elastic PE is the energy that a stretched object has, that’s released when we let go of the elastic


archer elastic PE

One can think of experiments which reveal how to release the potential energy in a stretched rubber band 😉

Nonetheless, “Don’t Start None, Won’t Be None” 😉

Spring potential energy

= energy stored in a stretched spring

Gravity pulls the mass down, adding PE into the spring
When we release the mass, the spring zips right back up!

hooke-law-illustration Spring scale

We need to put a force on the red ball, to pull it sideways

Since we did work to move it a distance, we’ve put potential energy into it.

PE energy spring

Chemical potential energy

is stored in molecules.

this chemical PE holds the atoms together as a molecule.

breaking a molecular bond can release the chemical PE

propane oxygen CO2 water energy

Vibrational kinetic energy

Since molecules vibrate, each atom has motion

So each atom has it’s own translational KE

atoms can vibrate in many different ways

CO2 vibration 2 CO2 vibration 1

Atoms in a CH2 group, commonly found in organic compounds, vibrate in different ways:

Scissoring (Bending)
Symmetrical stretching.gif Asymmetrical stretching.gif Scissoring.gif
Rocking Wagging Twisting
Modo rotacao.gif Wagging.gif Twisting.gif


Shown below is the thermal motion of protein alpha helix.

Molecules have various internal vibrational and rotational degrees of freedom.

Heat energy is stored in molecules’ internal motions …

Even though these motions are called “internal,” the external portions of molecules still move— like the jiggling of a water balloon.

ATP in Biology

Your cells store energy in a molecules called ATP

When your cells need energy, a chemical bond is broken, releasing the chemical PE in this molecule,

atp molecule
atp molecule energy

Solar energy

Sunlight contains energy which can be converted into heat (thermal energy)
Here a set of mirrors focuses sunlight onto a block of solid steel

The melting point of stainless steel is 1363  C,   2550 F

James May's Big Ideas Melt Steel Solar

Nuclear potential energy

Within every atom there is a nucleus made of protons and neutrons.

Under normal, everyday conditions, we never notice the immense energy stored in an atom

However, under certain conditions, this energy can be released:

e.g. nuclear fusion.

Example of hydrogen atoms undergoing nuclear fusion.





The work-energy theorem

How much work does it take to bring a moving object to a stop?

How much work does it take to bring a stopped object up to a certain velocity?

We can relate “work” and “energy”

Whenever work is done an object, it’s energy change

Work = ΔKE

F·d = ½·m·v2

Animations: work and energy


Roller coaster physics

Consider a marble rollercoaster:

We do work on the marble, lifting it up to put it on top.

marble now has gravitational PE.

Release the marble. Gravity accelerates it downwards… then it’s inertia allows it to continue up…. then it goes down again.

As the marble loses grav PE, it gains KE.

When it goes back up, it loses some KE but gains back some grav PE.

Back down again, loses more grav PE, but gains more KE.

CPO Physics

CPO Physics

KE is lowest at the coaster’s high points.

PE is highest at the coaster’s high points.

What does this tell us about the relationship between kinetic and potential energy?

Energy Transformation on a Roller Coaster: PhysicsClassroom.com

Amusement Park Physics: Learner.Org

Roller coaster physics: Wikipedia

Roller coaster physics: Real world physics problems

Video of roller coaster physics: PBS video


How about this clever relationship?

Convert PE into KE

Galileo discovered that the work done in lifting the mass gave the mass gravitational potential energy.

Potential energy then becomes kinetic energy.

Kinetic energy then does work to push stake into the ground.

also see Elastic-and-inelastic-collisions: KaiserScience

Scientists have never found a system where energy is not conserved.

Falling guy converts PE into KE

How was the law of conservation of energy discovered? See Discovery of conservation-of-energy

How does the law of conservation of energy, and thermodynamics, tie into biology and evolution? See Evolution and the 2nd law of thermodynamics

KPCOFGS Kingdom Phylum Class order Family examples Linnaean

How does the law of conservation of energy, and thermodynamics, tie into the Big bang (origin of the universe)?

The big bang theory and conservation-of-energy

The big bang theory and the second law of thermodynamics


Learning standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS3-1. Use algebraic expressions and the principle of energy conservation to calculate the change in energy of one component of a system when the change in energy of the other component(s) of the system, as well as the total energy of the system including any energy entering or leaving the system, is known.

Disciplinary Core Idea Progression Matrix

PS3.A and 3.B:  The total energy within a physical system is conserved. Energy transfer within and between systems can be described and predicted in terms of energy associated with the motion or configuration of particles (objects)

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