Subtle Concepts of Work and Energy


By Robert Hazen, Ph.D., George Mason University

Energy is a subtle concept, its characteristics neither intuitive nor obvious. What are the different kinds of energy we encounter in our everyday life and what are its subtle forms?

Infographic of a cyclist going uphill reaching to the top then going downhill
The obvious forms of energy include kinetic energy and potential energy. (Image: udaix/Shutterstock)

Concept of Work

Work has a very specific scientific meaning. Work is expended whenever a force acts over a distance, and the formal definition of work is force times the distance. To cite an example, if your car runs out of gas, as long as you’re pushing it and it’s moving, you’re doing work. But, if despite the pushing, the car doesn’t move, you are not doing any work.

Work is only done if the force is exerted in the same direction as the object’s motion. So, the Earth does no work on the Moon because the Moon’s movement is always at right angles to the gravitational force. The unit of work is a joule, which in other words is a newton-meter.

Learn more about the ordered universe.

Defining Energy

Energy is defined as the ability to do work, which means it is the ability to exert a force over a distance. So, any physical system or a phenomenon that allows you to exert a force over a distance is a kind of energy.

The concept of energy was poorly defined until the middle of the 19th century. Energy is difficult to recognize and describe in part because it can adopt so many different forms in our surroundings.

Different Types of Energy

There are three common kinds of energy recognized for their ability to exert a force over a distance in our everyday life. Kinetic energy, potential energy and wave energy are all obvious ways of exerting a force over a distance. Once scientists understood the definition of energy, they also began to see some other subtle kinds namely heat, light, and mass.

Learn more about the first law of thermodynamics.

Kinetic Energy

Perhaps the most intuitively obvious form of energy is that carried by objects in motion, kinetic energy. The simple example being when you throw a ball, the ball goes through a window and can break things, meaning it exerts a force over a distance.

The kinetic energy of any object can be calculated from its mass and velocity. The formula for kinetic energy F = (½) (mv2) is derived from Newton’s second law of motion [F=m×a], distance equals one-half acceleration times time squared [d= (½)(a´t2)] and velocity equals acceleration times time, [v=a×t].

KE = F×d

F = m×a and d= (½) (a´×t2)

Substituting these two equations in the equation for KE,

KE = m×a (½) (a´×t2)

KE = (½) m (at)2

We know velocity, v=a×t

Hence, KE = (½)mv2

From the above equation, we know that kinetic energy is proportional to velocity squared, hence slight increments in velocity can greatly increase energy and that has consequences.

The first consequence being, suppose you go faster and faster in a car, you’re going to consume more gasoline because you have to put the energy into the car to get that kinetic energy. Your gas consumption, your miles per gallon, is going to start dropping off dramatically as you go to very high speeds.

The second thing is the danger if you get into an accident, as when you get into an accident, all your kinetic energy gets converted into other kinds of energy, the smashing of your car. At higher velocities there’s much more energy that has to be converted into the damage of the car and, therefore, high-speed crashes are proportionately much more damaging than low speed crashes.

This is a transcript from the video series The Joy of Science. Watch it now, on Wondrium.

Potential Energy

Many natural systems store energy, which is waiting to be used and exert a force over a distance. Their varied forms are called potential energy. The most obvious form of potential energy in everyday experience is due to gravity, such as the energy of water behind a dam.

This energy exists by virtue of a mass’s position within the Earth’s gravitational field. At a higher level, the water is waiting to drop and release energy, converting gravitational potential energy into kinetic energy.

Diagrammatic representation of a triangle with formula for gravitational potential energy
Formula for gravitational potential energy. (Image: Nasky/Shutterstock)

Deriving the Equation

To raise the mass, m, to a height, h, takes work.

We know, Work = Fxd (force times distance)

By the simple definition, we know Energy = Work

Force of gravity on an object = mass times gravitational acceleration times height

Hence, Energy contained by an object = (m×g)×h

There are many other kinds of potential energy common in our day-to-day life. There is chemical potential energy stored in food, in matches used to light a candle and in batteries. In refrigerator magnets, there is energy that can exert a force over a distance by picking up objects. There is also elastic potential energy in a stretched rubber band.

Learn more about entropy.

Wave Energy

Waves represent a very efficient kind of kinetic energy in which energy can be moved long distances without actually having to move lots of mass from one place to another. There are two kinds of waves that accomplish this feat in slightly different ways; transverse waves and compressional waves.

Characteristics of Waves

Waves have velocity; this can be demonstrated using a telephone cord. The chord itself does not have to move from one place to another, but the motion of the wave from one end to another can be seen by slightly flipping it and sending a wave going through.

Waves can travel through water, atmosphere and solid materials. Earthquakes are waves that can transfer tremendous amounts of energy through solid Earth.

Learn more about magnetism and static electricity.

Subtle Forms of Energy

Labeled power usage types collection scheme.
The light energy from the Sun is the principal source of energy on the Earth’s surface. (Image: VectorMine/Shutterstock)

Heat is actually a form of kinetic energy at the atomic level and represents the motion of individual atoms.

Light energy is another subtle form of energy. The light energy from the Sun is the principal source of energy on the Earth’s surface. Sunlight travels at a speed of 186,000 miles per second or 300,000 kilometers per second through all sorts of medium, including vacuum.

And finally, mass as a form of energy, one of Albert Einstein’s defining discoveries of the modern age of science. This is according to the very familiar equation E=mc2, where c is the speed of light. The implication being that the quantity of energy in everyday objects is unimaginable. While most of this energy is forever locked up in the mass around us, scientists have discovered special circumstances where they can convert mass to energy.

Common Questions about Subtle Concepts of Work and Energy

Q: What are the different examples of gravitational potential energy from everyday experience?

The stored energy of water behind a dam and the weight of a pendulum are examples of gravitational potential energy.

Q: What are the two different types of waves?

Transverse waves and compressional waves are the two different types of waves.

Q: Does wave energy transfer through various mediums?

Yes, wave energy transfers through various mediums such as solids, liquids, and gases.

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