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

Density, Mass and Volume

We know that Density is equal to the mass of the object divided by the volume of the object. But how does this formula tells us about our every day experience like why cruise can float on the water even though it’s very heavy, why iceberg floats in water and not fully submerged? If you ever wear a life vest or jacket before going out to water activities like canoeing, wind surfing and wakeboarding, you will notice that you can float in the sea water when you have it on. However, without it, you will find that it is harder to float in the water! Intuitively, adding more additional materials onto our body should make us sink into the water but why with life vest, it is the opposite? Take a few minutes to think…

Well, it depends on what kinds of materials you are carrying. Strictly speaking, it is the density of the material that makes the different. Let’s take the life vest as an example. By wearing the life vest, you are actually increasing the volume of your body size. If you have ever held a life vest before, you will find that it is quite light in weight. A light weight life vest means that it's mass is small too, since from W = mg, we know that weight of the object is proportional to the mass of the object as the gravitational field strength is assumed to be

10 N/kg (constant) on earth. As Density = Mass/Volume, small mass divided by a BIG VOLUME (body + life vest) will give you a small density value. That’s why you could float much easier in sea water if you have a life vest on. Could you imagine what will happen if you wear a life vest made of metal? You could try this by finding any piece of metal and place it into water, but please don’t try wearing one of this life vest (if it’s available), as you could probably guess what will happen to you…

The web-link below will show you a video on how density is an important consideration for a scuba diver to submerge in a swimming pool water and sea water. Will the scuba diver sink into the water in the same way for both water conditions? Make a guess and find out from this video to see if you are right…

http://videos.howstuffworks.com/hsw/23849-density-in-liquids-the-density-of-water-video.htm

For more exploration on density and buoyancy, refer to this video from YouTube...

http://www.youtube.com/watch?v=VDSYXmvjg6M

Moments or Torque

Based on any physics text, the Moment or Torque will be defined for you as equal to Force times the perpendicular distance. As you could see, the sentence is pretty long for such a simple formula. We can perhaps simplify it by using aphlabets and mathematical symbols to represent the sentence above.

In short: T = F x d

where T is Torque or Moment (Nm)
F is the Force applied (N)
d is the perpendicular distance (m)

Now, you may ask, what is the use of understanding this formula? Is there any real world applications? My answer to you is Yes! There are many applications to these simple formula.

Have you ever wonder why the handle on any door is always designed almost right at the side of the door? Have you ever questioned why the handle is not placed somewhere at the middle of the door or perhaps even near to the hinged side of the door? Take a few minutes to think about it and try to give an answer…

Well, the reason is found in the formula T = F x d. So, what is the link here? As illustrated in the door, the “Torque or Moment” produced will basically be seem as when someone pulled or pushed the handle with the door turning clockwise or anticlockwise. So where is this “Force”, it is the “action” produced when you pull or push on the handle. Lastly, the perpendicular distance will be between the point where you applied your effort and the other end of the hinged door. The diagram (illustrated in plan view) below demonstrates what we have just discussed.

In the first Plan view diagram, we can see how the force applied and the perpendicular distance from the pivot point (hinged-point of the door) produced the torque or moment.

Second Diagram:

Third Diagram:

In the second and third plan view diagrams, you can see that the handle has been shifted for both cases. Assuming that the applied force is the same for both cases, do you think the torque or turning effect produced will be the same? Try and find out your own answer based on what you have learned so far...

Have you found your answer? The moments created by the above two cases will be different since the perpendicular distances for both cases is different. With the assumptions that the applied force is the same for both cases, the Moment created in the second diagram will be greater than the third diagram since we already know that Moment = F x d. Hence, a greater Moment can be created (even though with the same applied force) with the help of increasing the distance from the pivot point (hinged point).

The weblink below shows how moments is applied in a lever balance, explore how moments create balance and unbalance (rotation) from this applet…
http://www.vjc.moe.edu.sg/academics/dept/physics_dept/applet/lever/lever.htm

and perhaps you could try it out in one of those toilet door where it allows you to push the door at different parts of it...

What exactly is Physics?

First question that came into my mind, “Is physics a subject that produced facts that are fixed and all the information that we gained from text is nothing but the truth? Unfortunately, the information that we acquired in school are only part of the knowledge gained or found over the last 2000 years! To date, we may have taken for granted that such information is true and nothing can change.

Physics is not a hard factual subject for which the subject is fixed. In fact, research has been done to date and still in progress. What we found in physics are theories that are created by many physicists over many centuries. Why these theories seem to be stone-carved in texts? This is because these theories predicted results which matched with the experimental results. If such theory can be used to predict to the accuracy of 0.0000000001 plus or minus error, we could use this theory to apply to engineering fields like aerospace, civil, robotic and many more. This is where the theories are used in real world! Example of theory which still works to date is Newton’s 3 laws, conservation of energy, laws of Thermodynamic etc.

About this Blog

This blog is created to showcase how understanding physics can help us to appreciate the physical world that we are living in and how physics concepts applied into our lives. It is also my hope that this blog could bring my students and others who wanted to know more about physics but always find themselves lost or disconnected to the so called “dry” and “boring” subject. As a matter of fact, learning and understanding physics can be fun if you start connecting what you learn into your everyday lives.