KINETIC AND POTENTIAL ENERGY

Unit Overview

In addition to knowing the forms of energy, there are other ways of analyzing energy, such as knowing that energy can be stored or active. In this unit, we will discuss which forms of energy fall into each category. We will then determine what factors influence two types of stored or potential energy and what factors influence active or kinetic energy. Finally, the conversion of potential to kinetic energies and vice-versa will be studied.

Work and Energy

In our last unit, we discussed how energy can cause work to be done and work done on an object can cause energy to be stored in the object. So, work and energy are related to one another in that they can be changed from one to the other. Let’s look at a couple of examples to make this clearer. If a balloon is blown up, then work has been done on the balloon, since it took some effort on your part to blow the air into the balloon. You had to use a force, a push, to cause the air to leave your lungs and enter the balloon. Now the expanded balloon has stored energy because it has the possibility of doing work. If you let go of the untied balloon, it will randomly fly around the room as the air leaves the opening. The air inside the balloon is doing work because it is pushing the balloon in an opposite direction from which it is leaving the balloon. The balloon also does work on the air because it pushes the air out.

Suppose you have to push a car to the side of the road because it ran out of gas. As you push on the car, your energy does work on the car, and you give the car energy by causing it to move. The further you push the car, the more work is done and the more energy it takes. The stored energy in your body from the food you ate, allowed your muscles to contract to push the car. This is active energy because it is causing a change. As the car moves you are transferring some of your energy to the car, giving it active energy as well.

Potential Energy

One way to classify energy is whether it is active or not. If it is not active, we say the energy is stored, waiting to be used, and stored energy is called potential energy. We have already stated in earlier lessons that the energy in foods and fuels is stored by the action of photosynthesis. All foods and fuels directly or indirectly receive this energy from the action of green plants, algae, or certain bacteria. It is stored within the bonds of the molecules within these materials. Remember that a molecule is a group of atoms held together by chemical bonds. This type of energy is called chemical energy and is, therefore, a form of potential energy.

Some scientists consider nuclear energy to be potential energy as well. The energy we get from uranium and plutonium and other radioactive elements is due to the stored energy within their nuclei, the centers of their atoms. Because the nuclei are not held together very well, they tend to disintegrate by throwing off high-energy particles and rays. Under certain circumstances these disintegrations can be harnessed to release a huge amount of energy.

Mechanical energy, the energy of motion, can under certain circumstances be stored. There are two cases that we will investigate. Have you ever dropped something? Of course, you have. What happened? The object fell to the floor or the ground. It must have had stored energy or it would not have been able to begin moving. But how did it get the energy in the first place? Let’s say the object was a ball, and you evidently picked up the ball. In picking it up, you did work on the ball by lifting it. It took a force because the ball has weight. The force of gravity upon the ball causes the weight. By doing work on the ball, you gave the ball stored or potential energy. This is known as gravitational potential energy because it is due to the force of gravity upon the object. This means that any object that is in a position to fall has gravitational potential energy. This includes a rock on a cliff, water behind a dam, a skier on a hill, or a roller coaster car at the top of a hill.

How much gravitational energy do the riders on the roller coaster have? It can be calculated using a mathematical formula but for now, let’s just consider what factors might influence the amount of energy. Why is the first hill on a roller coaster, which is known as the lift hill, always the highest? Because all the energy needed to keep the coaster going throughout the entire ride must be stored in the coaster by the time it reaches the top of the lift hill. Usually the greatest drop is right after that hill and it is at the bottom of this hill that the coaster is going the fastest. All that stored energy is being released as motion, so the higher the hill, the more energy is stored.

Let’s look at another example to show how height affects the amount of gravitational potential energy. If a baseball is dropped from a height of one foot and hits your toe, you probably would not complain because it would not hurt. What if it were dropped from a height of ten feet? You would certainly feel it, and it might cause some pain. That is because more energy is stored in the ball when it is raised higher in the air. Therefore, we can state that the height an object is above a surface helps determine how much potential energy it has, but is there anything else? Do all objects at that height have the same potential energy? What if the object were a concrete block instead of a baseball? Even when dropped from a height of one foot, the block could do serious injury to your toe. That is because the block has more energy at that height than the baseball. Why? What is different? If you think for a while, you may decide that it is not the shape or the type of material, but the weight of the object that influences the amount of potential energy. Because the block weighs a lot more than the baseball, more work is done in raising it and therefore it has more stored energy. So there are two factors that determine this gravitational potential energy, the height of the object above the ground and weight of the object.

There is yet another type of potential energy based upon the position of the object. This is known as elastic potential energy. This type of energy exists in objects that can be compressed or squeezed together or stretched. Some springs for example can be stretched, others compressed. Other objects that can be compressed are balls, like a basketball that hits the gym floor. Other objects that can be stretched are bungee cords, trampolines, rubber bands, or bows. If you are getting ready to shoot an arrow at a target, you position the arrow on the bow and begin to pull back on the bowstring. As you pull you must exert more and more force as you stretch the string. You are putting work into the bowstring, giving it elastic potential energy. When you release the bowstring, it pushes against the arrow giving it the stored energy. The arrow then begins to move, changing this stored energy into motion.

The boy in the foreground has stored potential energy in his bow. He did work on the bow by pulling back on the bow. The boy in the background has a relaxed bow and no energy is stored in it. In a similar manner energy is being stored in the slingshot below.

What determines how much energy can be stored as elastic potential energy? If you consider the work that needs to be done to compress or stretch the object, you will agree that some objects are easier to compress or stretch than others. That is due to the nature of the object; that is, it depends upon what it is made of. A rubber band is easier to stretch than a bungee cord, for example. Another factor is how much it is compressed or stretched. A slightly stretched bow stores less energy than one that is stretched to its maximum. That is why the arrow goes further when the bow is stretched to its maximum. It has more energy to give to the arrow. So two factors are important – how much the object is stretched or compressed and the material out of which it is made.

Kinetic Energy

If energy is actively being used, then it is classified as kinetic energy or the energy of motion. Looking at the various forms of energy, we can classify many of them as being kinetic energy. Mechanical energy as energy in motion is kinetic energy. If an object is moving, it possesses kinetic energy. If you are watching a sporting event, you are seeing many examples of kinetic energy. Players running, balls being thrown or kicked or dribbled, cars racing, or bats being swung are just a few examples.

These are examples of kinetic energy or energy in motion. The bowling balls are about to strike the pins and transfer some of their energy to them. The racecar has lots of kinetic energy as it races around the track.

Other forms of energy can be classified as kinetic energy as well. Electrical energy is kinetic energy on a subatomic level because it involves the movement of electrons. We have to look with our mind’s eye to “see” the movement. The force that makes the electrons move is the repulsion electrons have for each other and the attraction they have for the positive charges. Still looking with our mind’s eye we see that thermal energy is kinetic energy on the molecular level since this is the energy of molecular motion. If an object has a higher temperature than another object, its particles will be moving faster. Since radiant energy travels in waves or rays, it, too, must be moving and can be classified as kinetic energy. There are even times when radiant energy behaves as little packets of energy striking objects. Lastly, sound which travels in sound waves that involve the vibration of some material must be called a type of kinetic energy. As the sound wave passes through a material it causes the particles of that material to move back and forth.

What factors affect kinetic energy? How can we increase the kinetic energy of an object? If we think of a racecar, we can increase its energy by making it go faster. Increasing the speed of the car increases the kinetic energy. Therefore, the velocity or speed of the car helps to determine its kinetic energy. Another factor to consider is the mass or amount of material in the object. Which do you think has the most kinetic energy – a car or a semi if both are traveling at the same speed? If you guessed the semi, you were correct. Mass is important, just like speed, for if an object has more mass than another object, then it has more kinetic energy.

Energy Conversions

There would be little purpose in storing energy if it could not be used later. If plants stored chemical energy in glucose but could never release this energy, they would never be able to grow and reproduce. Nor could we use this stored energy for food to gain energy for our body processes. Plants were able to store this energy in the first place because they were able to capture it from the radiant energy in sunshine, so they took kinetic energy and changed it into potential. Later on, they and other organisms would change it back to kinetic energy in one of the various forms.

To keep our study somewhat simple, we are going to look at some common conversions between kinetic and potential energy in mechanical energy. This is one form that can be either potential or kinetic. Looking at the picture of the skydivers, we can see that they have a great deal of potential energy because they are very far from the earth and height is one thing that determines the amount of potential energy. What happens the second they jump from the plane? They begin to fall, and as they fall, they begin to pick up speed as any falling object does. That is why something dropped from a greater height, hits the ground with greater impact than it would if falling from a lower height. Since they are now moving, they have kinetic energy. If they are picking up speed, their kinetic energy is increasing. Where did this kinetic energy come from? Except in the case of nuclear reactions, energy cannot be created or destroyed. This is known as the Law of Conservation of Energy. So, some of the potential energy of the divers must have been changed to kinetic energy. Why did this happen? If we look at the divers a few seconds after their jump, we will notice that they are closer to the earth than in the beginning of their jump. This means their height is less, so their potential energy is less. Where did it go? It changed into kinetic energy and will continue to do so. Other forces, such as air resistance and the force exerted by the parachute, will eventually cause the skydivers to slow down.

A simpler example of a falling object would be a pendulum. Even though the bob of the pendulum is attached to a string, it still falls through the air. Since it only falls for a short distance and therefore does not pick up much speed, it is not affected very much by air resistance so we can neglect this effect. (Air resistance is greater if the speed is greater. If you have ever stuck your hand out of the window of a moving vehicle, you have experienced the feel of greater air resistance at greater speeds.) When the pendulum is at the highest part of its swing, it has its maximum potential energy. At that point, whether swinging to the right or left, its kinetic energy at that point is zero because for that fraction of a second it is not moving. It is changing its motion from going up to going down. If it is not moving, then it has no kinetic energy or energy of motion. However, when it is at its lowest point (at the center of its swing) its kinetic energy is at its greatest so it is moving as fast as possible. This makes its kinetic energy as large as possible. Its potential energy is zero at that spot, because it has no height. It is as low as it can get. What happens when it is only halfway to the bottom? If the height is half of the original height, then it has half of its original potential energy, the rest is kinetic.

This means the total amount of mechanical energy in the pendulum remains constant but it is constantly being changed from kinetic to potential and potential to kinetic. If it has ten units of potential energy and zero units of kinetic energy at its greatest height, then it will have zero units of potential energy and ten units of kinetic energy at its lowest position. Halfway between these positions, it will have five units of potential and five units of kinetic energy. Regardless of the pendulum’s position, it will always have a total of ten units of mechanical energy. This is in line with the Law of Conservation of Energy. A swing is a modified pendulum, so when you swing, you have maximum potential energy at the height of your swing and maximum kinetic energy and speed at the bottom of your swing when you are closest to the ground.

PhET Simulation

Click on the PhET icon below to play with one or two pendulums and discover how the period of a simple pendulum depends on the length of the string, the mass of the pendulum bob, and the amplitude of the swing. It's easy to measure the period using the photogate timer. You can vary friction and the strength of gravity. Use the pendulum to find the value of g on planet X. Notice the anharmonic behavior at large amplitude.

Another example of the mechanical energy of an object changing from potential to kinetic energy is that of a ball being dropped. Looking at the diagram on the left, the ball is at its highest position at position A. Therefore, its potential energy is at its maximum or greatest amount. However, the ball is not moving so it has zero kinetic energy. At the split second before the ball hits the floor, position C, the ball has no height so its potential energy is zero. All of the potential energy has been changed to kinetic energy so its kinetic energy is maximum at this point, which means it is moving at its greatest speed. If position B is halfway between position A and C, what can we say about the kinetic and potential energies there? If you say that each energy is equal you would be right! Half of the energy is potential and half is kinetic. Because the height is half of the original, it only has half of the original potential energy. The rest of that energy has been turned into kinetic as the ball gains speed while falling.

Lastly, let’s consider the roller coaster, a great example of the conversion from potential energy to kinetic and back to potential. At the beginning of this lesson we briefly discussed the lift hill of the coater. It is at the top of this hill that the coaster has its greatest potential energy because its height is greatest here. As the coaster goes down the lift hill, it constantly picks up speed. What about the energy? If it is picking up speed, then it is gaining kinetic energy. But, since it is now not as high in the air as it once was, it has lost potential energy. At the bottom of the lift hill, its lowest point, its speed is at maximum. Therefore, it has maximum kinetic energy. Then what happens as it starts up the next hill? It is going up so it is gaining potential energy, but it is also slowing down, so it is losing kinetic energy. At the top of this hill, it still has some kinetic energy because it is still moving although not as fast as it did at the bottom of the lift hill. Some of that kinetic energy is now potential energy because the coaster has gone up in the air somewhat. And so it goes throughout the ride. The coaster gains kinetic energy as it falls and gains potential as it rises. In reality though, the coaster can never go as high as it went on the lift hill. Friction between the carts and the rails continues to slow it down by creating some heat energy, which robs the coaster of useful energy.

Unit Conclusion

The seven forms of energy can be further classified as either kinetic or potential depending upon whether the energy is stored or being actively used. Furthermore, kinetic and potential energy can be transformed from one to the other. In simple systems where there are no external forces acting on the objects, the total amount of energy remains constant as in the case of a falling ball or a pendulum. Other examples of this conversion that do include external forces, namely friction and air resistance, are roller coasters and skydivers. In these cases the mechanical energy does not remain constant.