DiscoverHover CURRICULUM GUIDE #14
KINETIC AND POTENTIAL ENERGY
© 2004 World Hovercraft Organization
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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 (Newton-meters) in the SI system and foot-pounds 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 v2
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/s2 [9.8 m/s2]. Any object lifted above the ground has potential energy. When allowed to fall, the potential energy is then converted into kinetic energy.

Example 1:
A 50 kg hovercraft is hovering at the top of a steep hill that is 20 m high. Without using the propeller to produce any forward thrust, the hovercraft is nudged so that it begins to slip down the hill. How fast will it be going when it reaches the bottom of the hill?

Solution:
In order to find the speed of the hovercraft at the bottom of the hill, we need to find its kinetic energy at that point. Remember that the gravitational potential energy of the hovercraft at the top of the hill will be converted to kinetic energy as the hovercraft slips down the hill, so begin by calculating the potential energy at the top of the hill.

PE = mgh
PE = (50 kg) (9.8 m/s2) (20 m)
PE = 9800 J

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 v2
9800 J = ½ (50 kg) v2
v2 = 392 m2/s2
v = 19.8 m/s

When the hovercraft reaches the bottom of the hill, it will be traveling 19.8 m/s, or 44.3 mph.

Example 2:
How fast will the hovercraft be traveling when it is ¾ of the way down the hill? How much potential energy will the hovercraft still have at this point?

Solution:
The method for solving this problem is the same as the first example. When the hovercraft is ¾ of the way down the hill, however, the hovercraft has both potential and kinetic energy. It still has potential energy because it is 5 m above the bottom of the hill, and it has kinetic energy because it has slid down 15 m. First calculate how much potential energy was converted to kinetic energy when the hovercraft slid down 15 m.

PE = mgh
PE = (50 kg) (9.8 m/s2) (15 m)
PE = 7350 J

KE = ½ m v2
7350 J = ½ (50 kg) v2
v2 = 294 m2/s2
v = 17.1 m/s

When the hovercraft is still 5 m from the bottom of the hill, it is traveling at 17.1 m/s [38.4 mph].
To find out how much potential energy the hovercraft still has, it would make sense to simply subtract how much energy was converted to kinetic energy from the total amount of potential energy it originally had.

PE(at 5 m) = PE(at top) – KE(at 5 m)
PE(at 5 m) = 9800 J – 7350 J
PE(at 5 m) = 2450 J

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
PE = (50 kg) (9.8 m/s2) (5 m)
PE = 2450 J

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.