ACTIVITY #4: The Energy of Pendulums We’ve all seen children swinging on a swing set at the playground. Have you ever wondered how the energy of a swinging child changes during the back-and-forth motion? The answer is most likely no, but if you happen to be the person having to push the youngster to keep him or her swinging, you may have thought about how your energy was being drained in the process. In this activity, we will look at a swinging mass (called a pendulum) instead of a rolling mass. The swinging child is a good example of a pendulum that you may experience in your everyday life. Pendulums can be found all around us, from the swinging girl in the picture to the long pendulum in the grandfather clock. How does the energy of the pendulum change form within each swing? Does the total energy of a swinging pendulum change as it swings back and forth? All freely swinging pendulums eventually come to rest. As the arc of the swinging pendulum gradually becomes shorter and shorter, where is the energy of the pendulum going?

GOALS: GOALS: In this lab activity, you will …  Use the concept of energy transformation to describe how the energy of a pendulum changes during each swing.  Use your knowledge of kinetic and potential energy to identify the different forms of energy of a pendulum and how each form changes in size during the swing of the pendulum Using the Particle Model and the concept of energy transfer to explain where the energy of the swinging pendulum eventually goes. (review -slide4) MAIN IDEAS: MAIN IDEAS: The important concepts and skills covered in this activity are … Under the right conditions, the stored energy of an object can transform into kinetic energy, and this kinetic energy can then transform back into stored energy. Whenever an object moves through the air, part of its kinetic energy is transferred to the particles of air. The energy of an object may be transferred to other objects or substances or transformed into types of energy that are difficult to detect, but the energy is never consumed and never disappears

Activity Overview: Activity Overview: A synopsis of this lesson is as follows… This demonstration will allow us to discuss the kinetic energy, the potential energy, and the heat energy associated with the swinging pendulum. We should be able to draw upon the discoveries from the previous activities to describe the energy transfers and transformations during this pendulum swing. During the second part of the demonstration, the water is emptied from the bottle and the activity is repeated. The outcome is drastically different, and you will be asked to apply what they have learned about the effect of mass on the kinetic and potential energies of an object to explain why. Now is the time for a dramatic demonstration. I will take a plastic 2 liter soda bottle and tie it to one end of a string (1 -2 m long). Then connect the other end of the string to the ceiling. Use the bottle as if were a pendulum. I will pull it back (up to about 45  ) hold it close to my face and then release it. I won’t flinch! LOL

A REVIEW OF THE PARTICLE MODEL Matter is composed of tiny particles. The particles of a single substance are the same, whether the substance is a solid, liquid or gas. Only the nature of the connections between particles changes when the phase of the substance changes. Particles are always moving (even in solids). Particles in solids vibrate around a fixed position. The extent of their motion is severely limited. The connections that bind the particles of a solid together are closely packed. Particles in liquids move more freely than do solids. The connections between particles in a liquid are weaker than in a solid, but strong enough to keep the particles close together. Particles in gases are moving freely and move as far apart from each other as their container allows. Adding energy, like heat, causes the particles to move more quickly and further apart.The size does not change the particles, but the total volume will tend to increase as the particles move away from one another as they vibrate more and more

PART A - A Pendulum Made With a Full Water Bottle With the pendulum hang vertically, and when it comes to rest answer the question Question #1: Does the bottle and water have any energy right now? Now I will grab the bottle and keeping the string taut, slowly step backwards lifting the bottle. As I lift the bottle, answer the question … Question #2: What is happening to the energy of the bottle of water? (Where is the energy given to the bottle coming from?) As I raise the bottle up near my face or nose area. Describe what the motion of the bottle will be like when I release it and what will happen to the energy of the bottle during its motion. I will release the bottle and allow the bottle to swing back and forth twice, and then I will stop it. Question #3: Describe what forms of energy the pendulum has while it swings back and forth.

Lets discuss two important ‘forms’ of energy in this activity, kinetic energy and the gravitational potential energy. ‘Height’ is recognized as a measure of potential energy, and speed as a measure of kinetic energy. At most points in the motion, the bottle of water has both height and speed, so it must have both potential and kinetic energy Question #4: Describe the energy transformations that take place in each cycle of the motion. Question #5: Is any evidence that energy is leaving the pendulum As the bottle is swinging, answer the question … Question #6: Is the motion of the pendulum the same for each cycle? If it is, can you describe how the motion changes? (where is the energy of the pendulum is going? )

PART B - A Pendulum Made With an Empty Bottle Question #7: What variables are different in this part of experiment and what variables remain the same. Question #8: If the variables that have been changed will they affect the energy of the pendulum. Question #9: Predict how the motion of the ‘empty’ bottle will be different from the bottle filled with water. Question #10: Does the empty bottle slow down faster because it feels more resistance or because it has less energy to begin with? I will release the pendulum and we will discuss how well the hypotheses fit the motion

The motion of the empty bottle is different from the full bottle. The reason the empty bottle comes to rest so rapidly is because it has much less energy to begin with. The particles of air are extremely small, but there are huge numbers of them in the path of the bottle. The bottle pushes them out of the way as it moves forward, and in doing so, gives them some of its kinetic energy. The air particles are constantly in motion, and they blindly rush back to fill the space behind moving bottle. As a consequence, the bottle must re-clear its path of particles when it swings back again. The bottle transfers energy to air particles no matter which direction it is moving in. Whether the bottle is filled with liquid or empty, it will push the same number of air particles out of the way as it moves through the air. Emptying the bottle of its contents does not change the shape or size, so with or without water inside, the bottle will create the same size ‘tunnel’ as it moves through the air.

The energy transferred from the bottle to air particles will be the same for each swing, whether the bottle contains water or not. The same number of air particles will receive the same amount of kinetic energy as the bottle moves through its path. This assumes the swings span the same distance. As the length of the arc of travel shortens, fewer air particles need to be moved out of the way, and the energy transferred to these air particles decreases With each pass of the swinging bottle, more of the bottle’s energy is transferred to the air. The empty bottle stops swinging quickly because it has less energy to begin with. Why does the empty bottle have less energy to begin with? The empty bottle has only a small fraction of the mass of the filled bottle. The potential energy due to gravity depends on the height to which the object is lifted, AND its mass. The filled 20 oz. bottle has more than a hundred times as much mass as the empty 20 oz. bottle, so it will have more than a hundred times the energy of the empty bottle when both are lifted to the same height

sdphul/labs/demos/movies/bowlingball.mov What forms of energy are present in a swinging pendulum? How is energy transferred to the air particles?