Basic Terminology and Concepts
Potential Energy
An object can store energy as the result of its position. For example, the heavy ball of a demolition machine is storing energy when it is held at an elevated position. This stored energy of position is referred to as potential energy. Similarly, a drawn bow is able to store energy as the result of its position. When assuming its usual position (i.e., when not drawn), there is no energy stored in the bow. Yet when its position is altered from its usual equilibrium position, the bow is able to store energy by virtue of its position. This stored energy of position is referred to as potential energy. Potential energy is the stored energy of position possessed by an object.
Gravitational Potential Energy
The two examples above illustrate the two forms of
potential energy to be discussed in this course -
gravitational potential energy and elastic
potential energy. 
Gravitational
potential energy is the energy stored in an object as the
result of its vertical position or height. The energy is
stored as the result of the gravitational attraction of the
Earth for the object. The gravitational potential energy of
the massive ball of a demolition machine is dependent on two
variables - the mass of the ball and the height to which it
is raised. There is a direct relation between gravitational
potential energy and the mass of an object. More massive
objects have greater gravitational potential energy. There
is also a direct relation between gravitational potential
energy and the height of an object. The higher that an
object is elevated, the greater the gravitational potential
energy. These relationships are expressed by the following
equation:
PEgrav = mass •
g • height
PEgrav = m *• g
• h
In the above equation,
m represents the mass of
the object, h represents
the height of the object and
g represents the
gravitational field strength (9.8 N/kg on Earth) - sometimes referred to as the acceleration of gravity.
To determine the gravitational potential
energy of an object, a zero height position must
first
be arbitrarily assigned. Typically, the ground is considered
to be a position of zero height. But this is merely an
arbitrarily assigned position that most people agree upon.
Since many of our labs are done on tabletops, it is often
customary to assign the tabletop to be the zero height
position. Again this is merely arbitrary. If the tabletop is
the zero position, then the potential energy of an object is
based upon its height relative to the tabletop. For example,
a pendulum bob swinging to and from above the tabletop has
a potential energy that can be measured based on its height
above the tabletop. By measuring the mass of the bob and the
height of the bob above the tabletop, the potential energy
of the bob can be determined.
Since the gravitational potential energy of an object is directly proportional to its height above the zero position, a doubling of the height will result in a doubling of the gravitational potential energy. A tripling of the height will result in a tripling of the gravitational potential energy.
Use
this principle to determine the blanks in the following
diagram. Knowing that the potential energy at the top of the
tall platform is 50 J, what is the potential energy at the
other positions shown on the stair steps and the
incline?
Elastic Potential Energy
The
second form of potential energy that we will discuss is
elastic potential energy. Elastic
potential energy is the energy stored in elastic
materials as the result of their stretching or compressing.
Elastic potential energy can be stored in rubber bands,
bungee chords, trampolines, springs, an arrow drawn into a
bow, etc. The amount of elastic potential energy stored in
such a device is related to the amount of stretch of the
device - the more stretch, the more stored energy.
Springs are a special instance of a device that can store elastic potential energy due to either compression or stretching. A force is required to compress a spring; the more compression there is, the more force that is required to compress it further. For certain springs, the amount of force is directly proportional to the amount of stretch or compression (x); the constant of proportionality is known as the spring constant (k).
Such springs are said to follow Hooke's Law. If a spring is not stretched or compressed, then there is no elastic potential energy stored in it. The spring is said to be at its equilibrium position. The equilibrium position is the position that the spring naturally assumes when there is no force applied to it. In terms of potential energy, the equilibrium position could be called the zero-potential energy position. There is a special equation for springs that relates the amount of elastic potential energy to the amount of stretch (or compression) and the spring constant. The equation is
To summarize, potential energy is the energy that is stored in an object due to its position relative to some zero position. An object possesses gravitational potential energy if it is positioned at a height above (or below) the zero height. An object possesses elastic potential energy if it is at a position on an elastic medium other than the equilibrium position.
Check
Your Understanding
Check your understanding of the concept of potential energy by answering the following questions. When finished, click the button to view the answers.
1.
A cart is loaded with a brick and pulled at constant speed
along an inclined plane to the height of a seat-top. If the
mass of the loaded cart is 3.0 kg and the height of the seat
top is 0.45 meters, then what is the potential energy of the
loaded cart at the height of the seat-top?
2. If a force of 14.7 N is used to drag the loaded cart (from previous question) along the incline for a distance of 0.90 meters, then how much work is done on the loaded cart?
Note that the work done to lift the loaded cart up the inclined plane at constant speed is equal to the potential energy change of the cart. This is not coincidental! The reason for the relation between the potential energy change of the cart and the work done upon it is the subject of Lesson 2.