Kinetic Energy and Potential Energy

Roller Coaster in Warner Bros – Movie World Australia

If you are the engineer in charge of constructing the roller coaster of the Theme Park, which part of the roller coaster track will you consider to be positioned at the highest point? Is it at the beginning of the ride, in the middle of the ride or actually it doesn’t really matter? The answers to these questions will be found in this section where I will talk about Mechanical Energy and how this concept applies to our daily life.

Different Kinds of Mechanical Energy
There are two types of mechanical energy that a body can possess. One is the Kinetic Energy (K.E.) and the other is the potential energy. For potential energy, we will focus on the Gravitational Potential Energy (G.P.E.).

Kinetic Energy (K.E.)

The K.E. is expressed as equal to mass of the body multiple by squared of the speed (i.e. speed x speed) and divided by half.

Gravitational Potential Energy (G.P.E.)
The G.P.E. is expressed as equal to the product of the object’s weight (mass x gravitational field strength (g)) and its height (h) above a reference level.

The “m” in both K.E. and G.P.E. stands for mass of the object. The “v” stands for speed.

Where to find maximum G.P.E.?
In the case of the roller coaster (refer to the simplified diagram below):

At which point (A, B or C) will you consider that the roller coaster possesses the maximum amount of G.P.E.? Take a few minutes to think about it…

As I have mentioned earlier on that G.P.E. needs to consider height, the height we are considering in this case is the vertical height as shown in the diagram. Point A should have the maximum G.P.E. as compared to point C. As you can see from the diagram, we need a reference line for us to determine the height in the G.P.E. Without any reference line, there is practically no point in referring to the G.P.E.

What if we change the reference line to other position as shown in the diagram below?

By having this new reference line or point of reference, the G.P.E. at point A will be lesser as compared to the previous reference line. Why is that so? We know that mass of the roller coaster is the same and gravitational field strength is the same, so what has changed here? Take a while to think...

You are right if you think that the vertical height has changed which causes the G.P.E. to be different in the above two cases.

Next, we look at how G.P.E. can change into K.E..

Looking at the above diagram, at point A, we know that the roller coaster possesses the greatest amount of G.P.E. What happens to the energy in the roller coaster at point B? Assuming negligible frictional force and air resistance acting on the roller coaster here, all the G.P.E at point A is converted into K.E. at point B, hence, the roller coaster possesses the maximum amount of K.E. In this ideal case, all the G.P.E. is converted to K.E. based on the Principle of Conservation of Energy. As you can probably find the statement in any typical physics textbook which states that:

Energy can neither be created nor destroyed in any process. It can be converted from one form to another or transferred from one body to another, but the total amount remains constant.

However, in reality, not all G.P.E is converted to K.E. If the above statement on Principle of Conservation of Energy is correct, why not all G.P.E is converted to K.E. in the case of the roller coaster? This is because some of the G.P.E. is converted to heat energy, sound energy and to overcome frictional force. The use of K.E. and G.P.E. concepts can also be applied to the water slides as shown below.

Water Slides in Singapore

The web-link will show you a video on how Kinetic and Potential Energy concepts are used from construction of the water slides like the one Jurong East Swimming Complex to the roller coaster in WB Movie World.
http://videos.howstuffworks.com/hsw/6175-work-and-energy-energy-video.htm