Potential and Kinetic Energy

All things in everyday life require energy to happen. Cars, planes, trains, and ships need energy to move on land, air, and sea. Lights, televisions, radios, and computers need energy to work. Even people, animals, and plants need energy for their cells to function properly. Each of these examples uses a different form of energy. Vehicles and people require chemical energy. Electronic equipment requires electrical energy and produces light and sound energy. Mechanical energy is necessary whenever something moves. In fact, humans, plants, and animals exist on Earth because the Sun provides heat and light energy to drive our climate and life processes.

There are two types of energy. Potential energy is energy that is not being used. It is often referred to as stored energy or inactive energy and is usually associated with objects at rest. A pencil on the edge of a table has potential energy due to its position. This is known as gravitational potential energy because the pencil has the possibility of moving toward the floor if it is pushed off the table. A battery has chemical potential energy because its energy is contained in the electrons of the chemicals inside it. A rubber band or muscle that is stretched has potential energy because it can contract and do work. When the pencil begins to fall from the table edge, or when the battery is connected to a circuit or the muscle and rubber band begin to contract, potential energy is converted to kinetic energy.

Kinetic energy is the energy of molecules and objects in motion. Molecules are particles that make up matter. Molecules transfer energy to one another through contact as they collide. Since we can’t see individual molecules with our unaided eyes, kinetic energy occurs in objects that we do not perceive as moving at all. However, we can indirectly “see” the kinetic energy of moving molecules by determining the temperature of an object. Hotter objects generally contain more kinetic energy than cooler objects. This type of kinetic energy is very important and we will learn more about it when we talk about thermal and heat energy. However, in this Investigation, we will focus on the potential and kinetic energy of larger objects that we see every day.

It is much easier to see kinetic energy in visible moving objects. When a pencil falls off the table, for example, its potential energy is transformed into kinetic energy as it moves closer to the floor. The molecules of the pencil are colliding with the air as they fall, transferring energy to the air molecules which then move away from the pencil. When the pencil hits the floor its molecules transfer their kinetic energy to the molecules of the floor. This energy transfer goes unnoticed by humans because the amount of energy involved in relation to the size of the floor is minute; nevertheless, an energy transfer does occur. In the illustration below, you can see that the kinetic energy of the falling pencil is converted to other forms of energy when it hits the floor. The impact may break the point, create a sound, and if your hand is placed close to the impact on the floor, you might very well feel a slight vibration as the pencil’s kinetic energy is transferred to the floor.

The Law of Conservation of Energy

The Law of Conservation of Energy states that energy can neither be created nor destroyed, it merely changes form. Each of the previous examples proves the Law of Conservation of Energy. Thus, the total energy of an object is the sum of its potential and kinetic energy. This relationship can be demonstrated mathematically as:

where TME = total mechanical energy, PE = potential energy, and KE = kinetic energy. The change from potential energy to kinetic energy is not instantaneous. As the pencil falls to the floor, its potential energy is constantly decreasing and its kinetic energy is constantly increasing. When the pencil is sitting on the edge of the table, 100% of its energy is potential energy. At the moment when the pencil impacts the floor, 100% of the energy is kinetic energy. But in between, the pencil has both potential and kinetic energy. For example, if the pencil has traveled half of the distance between the tabletop and the floor, 50% of the energy is in the form of potential energy, and 50% of the energy is in the form of kinetic energy.

In the PreLab for Investigation 1, students will discuss the cycling from potential to kinetic energy and back by analogy to a swing or pendulum. At the highest point of the swing of either a pendulum or swing, the object essentially comes to a stop in order to reverse direction. As we have discussed, an object at rest is 100% potential energy. As the swing or pendulum begins falling, it loses potential energy as it is converted into kinetic energy of motion. This principle is shown below for a pendulum. It is very important to notice that the conversion of potential into kinetic energy occurs smoothly percent by percent during a complete swing cycle. In the illustration below, kinetic energy is indicated by red and potential energy is represented by yellow. Look at how gradually the change occurs. At no time in the swing cycle does the amount of potential energy plus kinetic energy ever equal greater than or less than 100% total energy. That would break the Law of Conservation of Energy. That can’t happen!

Although the sum of the object’s energy is referred to as total mechanical energy, the relationship holds true regardless of the form the energy takes. Why? Energy is the capacity to do work. Therefore, all forms of energy ultimately end up being transformed into mechanical energy. Mechanical energy is the form of energy that performs work. In the pencil example, the pencil performs work on the floor, because the impact of the pencil causes the molecules of the floor to move. The naked eye does not notice this if the floor is concrete. However, if the floor is carpeted the work done by the pencil would be observed as a depression in the pile of the carpet, and the kinetic energy of the pencil was thus transferred to the carpet.

Energy is often referred to as “lost”, implying that it is destroyed and thus contradicting the Law of Conservation of Energy. In reality, while energy may no longer be useful in a particular system, the energy has not been destroyed. Instead, it is transferred to the next system or converted back to potential energy.

In Investigation One, students will explore the relationship between potential and kinetic energy by investigating how the potential energy of steel and plastic marbles can be converted into mechanical energy as they perform work on a flower pot at the end of an inclined plane.