Lesson 1: Basic Terminology and Concepts


  1. Definition and Mathematics of Work
  2. Calculating the Work Done by Forces

Potential Energy

Kinetic Energy

Mechanical Energy



Lesson 2: The Work Energy Theorem

Internal vs. External Forces

The Work-Energy Connection:

  1. Situations Involving External Forces
  2. Situations in Which Energy is Conserved
  3. Application and Practice

Bar Chart Illustrations


Lesson 2: The Work-Energy Theorem

Internal vs. External Forces

There are a variety of ways to categorize all the types of forces. In a previous unit, it was mentioned that all the types of forces can be categorized as contact forces or as action-at-a-distance forces. Whether a force was categorized as an action-at-a-distance force was dependent upon whether or not that type of force could exist even when the objects were not physically touching. The force of gravity, electrical forces, and magnetic forces were classic examples of forces which could exist between two objects even when they are not physically touching. In this lesson, we will learn how to categorize forces based upon whether or not their presence is capable of changing an object's total mechanical energy. We will learn that there are certain types of forces, which when present and when involved in doing work on objects will change the total mechanical energy of the object. And there are other types of forces which can never change the total mechanical energy of an object, but rather can only transform the energy of an object from potential energy to kinetic energy (or vice versa). The two categories of forces are internal versus external forces.

Forces can be categorized as internal forces or external forces. There are many sophisticated and worthy ways of explaining and distinguishing between internal and external forces. Many of these ways are commonly discussed at great length in physics textbooks. For our purposes, we will merely say that external forces include applied forces, normal forces, tensional forces, friction forces, and air resistance forces. For our purposes, internal forces include gravitational forces, magnetic forces, electrical forces, and spring forces.

Internal Forces

External Forces









The significance of categorizing a force as internal or external is related to the ability of that type of force to change an object's total mechanical energy when it does work upon an object. When work is done upon an object by an external force, the total mechanical energy (KE + PE) of that object is changed. If the work is "positive work", then the object will gain energy. If the work is "negative work", then the object will lose energy. The gain or loss in energy can be in the form of potential energy, kinetic energy, or both. Under such circumstances, the work which is done will be equal to the change in mechanical energy of the object; this principle will be discussed in great detail later in this lesson.

When work is done upon an object by an internal force (for example, gravitational and spring forces), the total mechanical energy (KE + PE) of that object remains constant. In such cases, the object's energy changes form. For example, as an object is "forced" from a high elevation to a lower elevation by gravity, some of the potential energy of that object is transformed into kinetic energy. Yet, the sum of the kinetic and potential energies remain constant. This is referred to as energy conservation and will be discussed in detail later in this lesson. When the only forces doing work are internal forces, energy changes forms - from kinetic to potential (or vice versa); yet the total amount of mechanical is conserved.


In the following descriptions, the only forces doing work upon the objects are internal forces - gravitational and spring forces. Thus, energy is transformed from KE to PE (or vice versa); however, the total mechanical energy is conserved. Read each description and indicate whether energy is transformed from KE to PE or from PE to KE. Depress the mouse on the "pop-up menu" to check your answers.


of Motion

KE to PE or PE to KE?


A ball falls from a height of 2 meters in the absence of air resistance.


A skier glides from location A to location B across the friction free ice.


A baseball is traveling upward towards a man in the bleachers.


A bungee chord begins to exert an upward force upon a falling bungee jumper.


The spring of a dart gun exerts a force on a dart as it is launched from an initial rest position.

NOTE: Perhaps at this time you might find it useful to review the lessons on kinetic energy and potential energy.


When work is done by external forces, the total mechanical energy of the object is altered. The work that is done can be "+ work" or "- work" depending on whether the force doing the work is directed opposite the object's displacement or in the same direction as the object's displacement. If the force and the displacement are in the same direction, then "+ work" is done on the object; the object subsequently gains mechanical energy. If the force and the displacement are in the opposite direction, then "- work" is done on the object; the object subsequently loses mechanical energy.

The following descriptions involve external forces (frictional, applied, normal, and tensional forces) acting upon an object. Read the description and indicate whether the object gained energy ("+ work") or lost energy ("- work"). (NOTE: If this is part is difficult, review the section on work.) Then, indicate whether the gain or loss of energy resulted in a change in the object's kinetic energy, potential energy, or both. Depress the mouse on the "pop-up menu" to view answers.


+ or - Work?

Change PE or

KE or Both?

Megan drops the ball and hits an awesome forehand. The racket is moving horizontally as the strings apply a horizontal force while in contact with the ball.
A baseball player hits the ball into the outfield bleachers. During the contact time between ball and bat, the bat is moving at a 10 degree angle to the horizontal.

Rusty Nales pounds a nail into a block of wood. The hammer head is moving horizontally when it applies force to the nail.
The frictional force between highway and tires pushes backwards on the tires of a skidding car.
A diver experiences a horizontal reaction force exerted by the blocks upon her feet at start of the race.
A weightlifter applies a force to lift a barbell above his head at constant speed.


Note that in the five situations described above, a horizontal force can never change the potential energy of an object. Horizontal forces cannot cause vertical displacements. The only means by which an external force can contribute to a potential energy change is if the force has a vertical component. Potential energy changes are the result of height changes and only a force with a vertical component can cause a height change.

Link to Animation


Lesson 2: The Work-Energy Theorem

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