Chapter 8
Potential Energy and Energy Conservation
8.0 Potential Energy
Potential energy is the potential to do work. It is also the energy an object posses by virtue of its position. The definition of potential energy (PE) is equal to the weight of an object times it height above the some reference point, e.g., ground. This is represented by:
(potential energy)
(8.1)
where m is the mass of the object, g is the acceleration due to gravity, and h is the height. Alternatively potential energy can be defined as work done against the gravity. The units of PE are the same as the units for work (joules). Because gravity (and therefore acceleration) is in the definition of PE, Eq. (8.1), it follows that we must have some sort of acceleration for work to be done. If an object is already in motion, it takes no force for it to keep moving (Newton’s 1st law). It takes force to speed it up or slow it down, giving us acceleration, and therefore, work is being done.
When a diver jumps off a high board into a swimming pool, she hits the water moving pretty fast, with a lot of kinetic energy.
Where does the work come from?
The answer is that the gravitational force (her weight) does work on the diver as she falls. The divers kinetic energy, (the energy associated with motion), increases by an amount equal to the work done.
However, there is a very useful alternative way to think about work and kinetic energy. This approach is based on the concept of Potential energy, which is energy associated with the position rather than motion.
8.1 Energy transformation
In this approach the potential energy is the gravitational potential energy, which is associated with a body’s weight and its height above the ground. Hence, the potential energy is present even while the diver is standing on the diving board. Energy is not added to the earth-diver system as the diver falls, but rather a storehouse of energy is transformed from one form of energy (potential energy) to another (kinetic energy) as she falls.
In this Chapter we will see how this energy transformation can be understood from the work-energy theorem. We will prove that in some cases the sum of kinetic energy and potential energy, called the total mechanical energy of the system, is constant during the motion of the system. This will lead us to the general statement of the law of conservation of energy, one of the most fundamental and far-reaching principles in all of sciences.
