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The term “energy” seems to be a very common word. Everyone has used
the word, but do you really know exactly what it means? If not, you’re
not alone. Even scientists aren’t sure exactly what energy is; they just
know what it does and how it works. Energy is often
defined as the ability or capacity for doing work. Remember that work is a force
moving an object a certain distance. Energy is used to do work. In fact, the
units for energy are the same as the units for work: Joules (Newtonmeters)
in the SI system and footpounds in the Imperial system.
Energy is the capacity for doing work; that means that energy doesn’t always have to be doing work on an object. It can also be stored in an object, ready to do work once released. These two forms of energy are called kinetic and potential energy. Kinetic energy is energy of motion. The more massive an object is or the faster it’s moving, the more kinetic energy it has. This may sound like momentum, which was defined as the mass of an object times its velocity. Kinetic energy has a slightly different formula, however.
KE = ½ m v^{2}
Kinetic Energy = ½ (mass) • (velocity)^{2}
Potential energy can be thought of as stored energy. When discussing work, we did an example in which the work required to lift a hovercraft onto workhorses was calculated. Energy was used to do that work. That energy is now stored in the hovercraft as gravitational potential energy. When sitting on the workhorses, the hovercraft is not moving, but it has the potential to move. If the workhorses were taken out from under it, the hovercraft would fall due to gravity. As the hovercraft began to move downwards, its potential energy would be converted into kinetic energy, or energy of motion. The following formula is used to calculate how much gravitational potential energy an object has.
PE = mgh
Potential Energy = (Mass) • (Acceleration due to Earth’s gravity)
• (Height)
Increasing the mass of an object, or raising the height of the object will increase its potential energy. Remember in the example of dropping a pebble and a bowling ball from the same height at the same time, both objects hit the ground at the same time. This is because the force of gravity tries to accelerate all objects by the same amount. The acceleration due to Earth’s gravity used in the formula above is equal to 32.15 ft/s^{2} [9.8 m/s^{2}]. Any object lifted above the ground has potential energy. When allowed to fall, the potential energy is then converted into kinetic energy.
Example
1: Solution: PE = mgh If the hovercraft has 9800 Joules of potential energy at the top of the hill, it will have 9800 Joules of kinetic energy at the bottom of the hill. Using the formula for kinetic energy, we can find the speed of the hovercraft. KE = ½ m v^{2} When the hovercraft reaches the bottom of the hill, it will be traveling 19.8 m/s, or 44.3 mph. 
Example
2: Solution: PE = mgh KE = ½ m v^{2} When the hovercraft is still 5 m from the bottom of the hill, it is
traveling at 17.1 m/s [38.4 mph]. PE_{(at 5 m)} = PE_{(at top)} – KE_{(at 5 m)} Just to make sure this is right, use the formula for potential energy to check the potential energy when the hovercraft is 5 m above the bottom of the hill. PE = mgh 
Not only did we find the potential energy 5 m up the hill in the last example, we just demonstrated an extremely important law of physics: Conservation of Energy.
Law of Conservation of Energy: Within a system, energy can never be created or destroyed.
This states that although energy can be converted from potential to kinetic and vice versa, the total amount of energy always stays the same. This is why we were able to simply subtract the two energies in Example #2. Potential energy was converted into kinetic energy, but the total amount of energy always stayed the same.
Potential energy is converted into kinetic energy as the hovercraft
travels down the drop
The hovercraft works best in the example because there is very
little friction between a hovercraft and the ground. If a car was used, the
calculations wouldn’t be accurate because friction would slow the car
down as it rolled down the hill. At first glance this seems to violate the law
of conservation of energy. Slowing the car means kinetic energy is lost, so
where does that energy go? Quickly rub your hands together for a while and notice
that they begin to warm up. Friction converts kinetic energy into heat, another
form of energy. Heat is actually a form of kinetic energy. The atoms and molecules
that make up all matter vibrate and move around very tiny distances. What we
measure as temperature is simply a measurement of how quickly the atoms and
molecules are moving about.
Besides gravitational potential energy, there are other forms of potential energy.
One is called elastic potential energy. This is observed
in springs or anything else that stretches and compresses. There is a certain
relaxed length that a spring wants to be at. If it is compressed or stretched
from this length, potential energy is added to the spring. Releasing it causes
the spring to bounce back to its relaxed length, releasing its potential energy
as kinetic energy.
Another form of energy is chemical potential energy.
This is potential energy located within the atomic bonds of molecules. This
form of energy is most commonly put to use in gasoline. When gas is burned,
its atomic bonds are broken, releasing its potential energy, usually in the
form of heat. Engines are designed to use this release of energy to do useful
work, such as powering a hovercraft fan or propeller.