When we began the study of Physics in Chapter 1 the statement was made that energy was the concept that unified all the various subfields of physics. We now have learned enough about the basic laws of physics to introduce the concept of energy and to use it to solve problems in mechanics. In many cases the problems could be solved using the techniques we developed in the first five chapters of this text, but we will find that an approach using the concept of energy often provides easier solutions.

We begin by defining work as the product of the component of the force that is along the line of motion of the object times the distance that an object moves under the influence of the force. The part about the component of the force along the line of motion sometimes provides difficulty for students. Actually it is not that complicated. What it does is to specify that a force only does work on an object when the motion is along the same direction as that of the force. If you push on a crate in a direction parallel to the floor as you slide the crate along the floor your force does work on the crate. If your pushing force is not parallel to the floor so that part of your force is directed downward, that portion of your force which is directed downward does no work on the crate. This definition of work is more specific than the several definitions of work that are used in ordinary conversation such as the definition of work as a paying job. If you were to stand outside your room holding a heavy suitcase while waiting for someone to open a door you might urge that person to hurry in opening the door because it was "hard work" holding the suitcase. According to the physics definition of work you would not be doing any work because there was no motion of the object. The definition of work in physics is more specific than that in ordinary conversation.

Work is calculated as a product of force and distance, so its units will be newtons times meters. Since work appears so often in physics we give this unit a name in honor of a famous physicist, Joule, and define 1 Joule as 1 Newton meter or 1 J = 1 N m.

In many cases the amount of work that is done by a force is not the only quantity of interest. Often we are also interested in the rate at which the work is performed. To describe the rate at which work is performed we define a new quantity called the power. Power is defined as the rate of doing work or P = W / t. This quantity also appears often in physics, so we give its unit a special name. Work is measured in Joules, and time is measured in seconds, so we define the unit of power as one Watt is equal to one Joule per second or 1 W = 1 J / s. In this equation the W stands for the unit Watt and not for the physical variable, Work. In general this will provide no difficulties because it will be clear whether the letter means a variable or a unit by whether it is used in an equation or at the end of an equation where we place the units.

Kinetic energy is defined as the energy of motion. The name, kinetic, should be a hint as to what it is all about. If you think of the meaning of the word you should be well on your way to identifying what kind of energy kinetic energy is. The "motion" part of the definition is expressed in the dependence of kinetic energy upon the square of the velocity, KE = 1 / 2 m v². As with work and eventually with all forms of energy the unit for kinetic energy is the Joule. The work done on an object is equal to the change in the kinetic energy of that object.

Potential energy represents some potential for doing work. It is energy that an object possesses by virtue of its position. Thus when a monkey carries a coconut to the top of a tree the coconut possesses potential energy by virtue of its position, and if the monkey releases the coconut, the force of gravity will do work on the coconut, and the coconut will experience an increase in its velocity. An increase in the velocity means an increase in the object's kinetic energy. The kinetic energy continues to increase until the ground does work on the coconut by splitting it open, the goal the monkey had in mind in the first place. In a sense the monkey has figured out how to convert energy from one form to another, from the gravitational potential energy at the top of a tree to kinetic energy and finally to work done on the coconut shell by the ground during the collision. Gravitational potential energy depends upon the mass, m, the acceleration of gravity, g, and the distance above some reference level, h, (generally chosen as the surface of the Earth) or PE_g = m g h.

We can also store energy with a potential for doing work by stretching or compressing a spring. Experimental investigations have shown that the force necessary to stretch or compress a spring is directly proportional to the amount of stretch. Actually this should conform to your experience. Perhaps you have observed that when you try to stretch a spring a greater distance, a greater force is required. The constant of proportionality is the spring constant, k. In equation form F_s = - k x where the negative sign tells us that the force of the spring is in the opposite direction of the force that we apply. The units for the spring constant are Newtons / meter.

When a spring is stretched or compressed, work is done on the spring, because the force acts along the same direction as the displacement. That work becomes stored energy or potential energy in the spring given by PE_s = 1 /2 k x². Note how the potential energy of a spring depends upon the square of the displacement of the spring. Because of this it is possible to store a large amount of energy in a spring even though a small displacement is involved.

As you progress through this course you will find that more types of energy will be introduced. They are all linked together by the principle of conservation of energy, which states that if there is no work done on the system (essentially if there is no input of energy from the outside) then the total energy remains constant. Actually, in this chapter we are considering only mechanical energy, but this statement provides an even more general expression of the principle of conservation of energy. This means that energy is not created nor destroyed; it is merely changed from one form to another. In some cases such as that of work done against friction the energy is converted to a form that is no longer accessible to you. Sometimes we state that such energy is lost when we really mean we have lost the ability to convert it to another form of energy.