INTERACTIONS, SYSTEMS, AND POTENTIAL ENERGY. Systems, Potential Energy, and Action-at-a-Distance

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1 CHAPTER 3 Scientists Ideas INTERACTIONS, SYSTEMS, AND POTENTIAL ENERGY In this Chapter you developed some ideas involving three different action-at-adistance interactions, in which the objects involved exert forces on each other without touching. You also saw how a group of interacting objects could be considered as a system and how applying the idea of energy conservation you developed in Chapter 1 allowed you to deduce that there were changes in different forms of potential energy within such systems. Below we summarize some of the general ideas developed by scientists involving interacting systems, potential energy, and action-at-a-distance. Following these are scientists ideas about each of the types of interaction you examined in this chapter, including a brief historical account of the development of some of those ideas. For each of the scientists ideas listed that is not just a definition, you should think about the evidence from your own experiments that would support that idea. You should also be able to draw I/O energy diagrams for the systems involved in each interaction. Systems, Potential Energy, and Action-at-a-Distance In the first half of the 19 th century, when scientists first began to think about energy as a useful concept in the description of interactions, they concentrated on easily perceptible forms of energy, such as kinetic energy and thermal energy. Early ideas about the conservation of energy were confined to these types and energy was only regarded as being conserved under certain specific circumstances. However, it was recognized that some objects had the potential to develop real energy, such as an object held above the ground and then released, which develops kinetic energy as it falls. In 1853 William Rankine first used the term potential energy to signify energy that a system has the power to acquire, rather than energy it already has. In 1867 Rankine further defined potential energy as energy of configuration, that is that the real energy developed by a system depended on how the system was arranged to start with. However it was only in the years that followed that the idea of conservation of energy as a powerful universal law began to be recognized, and with it the idea that potential energy is a real form of energy that must be taken into account. Ancient Greeks scientists, such as Plato and Aristotle, knew of the phenomenon of action-at-a-distance as demonstrated by magnets and static electricity. They explained it in a number of ways, including supernatural intervention and the idea that some objects have a natural tendency or desire to be in certain places. However, the favored idea was that some invisible substance (called the ether) filled the space between objects and transmitted their influence. This latter idea was supported by Francis Bacon in the 11 th century and further developed by Rene Descartes in the 17 th century. While Isaac 2007 PET 3-87

2 Chapter 3 Newton recognized that his ideas about gravity also represented action-at-a-distance he was not convinced there was enough evidence to support the idea that the ether actually existed. In the mid-19 th century Michael Faraday proposed the idea of lines of force to explain magnetic interactions and this idea, which can also be thought of as a field of influence quickly proved useful in also explaining electric charge and gravitational interactions. Idea S1 - Definition of a System A System is a group of two or more interacting objects. The objects within the system may, or may not, interact with objects that are outside the system, as well as with each other. If the only interactions that occur are between objects that are both themselves components of the system then there are no energy inputs to or outputs from the system. (Scientists say that such a system is closed with respect to energy.) In this case the Law of Conservation of Energy, applied to the system as a whole, takes on the form: Energy Changes = 0 This means that any increase in one type of energy in the system must be compensated for by an equal decrease in another type of energy (or more than one type combined) in order for the total change to be zero. Objects in th e system Energy increases and decreases in th e system: add up to zero 3-88

3 Scientists Ideas: Interactions, Systems, and Potential Energy Idea S2 Potential Energy in Systems Potential Energy is energy that a system has because of the way the interacting objects within the system are arranged. When the objects within the system are rearranged, the amount of potential energy in the system may change. If there is no energy input or output for the system (a closed system), any change in potential energy will also result in a change in another form of energy within the system (usually kinetic energy). According to the conservation of energy, if the potential energy in such a closed system increases (decreases), then the other type of energy in the system will decrease (increase). Different specific types of potential energy are associated with different types of interactions between the objects in a system and are discussed below. Objects in th e system Decrease (increase) in potenti al energy Increase (decrease) in kinetic energy Idea S3 Potential Energy in Systems with attractive and repulsive forces If the mutual interactions between the components of a system are attractive, when the average separation between the components increases, the potential energy of the system increases also. If the mutual interactions between the components of a system are repulsive, when the average separation between the components increases, the potential energy of the system decreases. 3-89

4 Chapter 3 Magnetic Interactions Magnetism is one of the earliest known physical phenomena. The ancient Greeks studied naturally occurring magnets (called lodestones) and the basic properties of magnetic interactions were discovered before 600 BC. However many contributions to the understanding of such magnetic interactions were made later, by such scientists as William Gilbert (16 th century), Charles Coulomb (18 th century), Michael Faraday and James Clerk Maxwell (both 19 th century) Idea M1 - Magnetic Interactions between two magnets: A magnetic interaction occurs between a magnet and another nearby magnet. Two magnets will either attract or repel each other, depending on which ends face each other. Scientists call the two ends the North and South poles. Two magnets with like poles facing each other will repel. Two magnets with unlike poles facing each other will attract. Idea M2 - Magnetic interaction between a magnet and a ferromagnetic object: A magnet will always attract a nearby ferromagnetic object. Ferromagnetic objects include iron, nickel and cobalt. Other metals, as well as non-metals, will not interact with a magnet. Idea M3 Action at a distance: A magnet can exert forces on another magnet, or a ferromagnetic object, without touching it. (Scientists call this action-at-a-distance.) These forces can be represented on a force diagram in the same way as any other forces acting on the magnet: (on the left are unlike poles) Force exerted on Magnet B by Magnet A Force exerted on Magnet B by hand Magne t A Magne t B B 3-90

5 Scientists Ideas: Interactions, Systems, and Potential Energy (This phenomenon of action at a distance can be accounted for by the idea of an invisible magnetic field of influence that extends around a magnet. Any other magnets within this magnetic field will feel attractive and repulsive forces due to the influence of the field on them.) Idea M4 Magnetic Potential Energy: In any system of magnets (or magnets and ferromagnetic objects) there is magnetic potential energy, the amount of which depends on how the magnets (and ferromagnetic objects) are arranged with respect to each other. When the magnets (and ferromagnetic objects) are rearranged this magnetic potential energy may change. When this happens in a system with no energy inputs or outputs (a closed system), then, according to the Law of Conservation of Energy, if the magnetic potential energy in the closed system increases (decreases), then the kinetic energy of the objects in the system will decrease (increase), and vice versa. For example, when two carts with magnets attached push each other apart, the energy diagram for this system would be like this: Both Magnet-carts Decrease in magneti c potential energy Increase in kinetic energy During time that both magnet-carts are pushing each other further apart Other evidence/examples: 3-91

6 Chapter 3 Electric Charge Interactions Many of the same scientists who studied magnetic interactions also studied electric charge interactions. In fact, we owe the very word electric to the ancient Greeks, who studied electric charge interactions, as well as magnetic interactions. In their studies they rubbed samples of fossilized tree resin (which we call amber) with fur to charge them. The Greek word for amber is elektron! As early as the 4 th century B.C. Plato wrote about the effects of rubbed amber and magnets. Observations of electrical effects continued well into the 16 th century when scientists such as William Gilbert and others noted many similar effects with many other types of materials and the effect of repulsion was also added to the list of observed electrical phenomena. Idea EC1 - Electric Charge Interactions between charged objects: An electric charge interaction occurs between two nearby charged objects. Two like-charged objects will repel. Two unlike-charged objects will attract. (Scientists call the two types of charge positive and negative.) Idea EC2 - Electric Charge Interaction between charged and uncharged objects: A charged object will always attract a nearby uncharged object, regardless of the material of which the uncharged object is made. 3-92

7 Scientists Ideas: Interactions, Systems, and Potential Energy Idea EC3 - Action at a distance: A charged object can exert forces on another object (both charged and uncharged) without touching it. Such forces can be represented on a force diagram in the same way as any other forces acting on the object. (This can be accounted for by the idea of an invisible electrostatic field of influence that extends around a charged object. Any other objects within this electrostatic field will feel either an attractive or repulsive force due to the influence of the field on them.) Force exerted o n Tape T1 by Tape T2 T1 Idea EC4: Electrostatic Potential Energy. In any system that includes at least one charged object there is electrostatic potential energy, the amount of which depends on how the objects are arranged with respect to each other. When the objects in the system are rearranged this electrostatic potential energy may change. When it does so in a closed system then, according to the Law of Conservation of Energy, if the electrostatic potential energy in the closed system increases (decreases), then the kinetic energy of the objects in the system will decrease (increase), and vice versa. For example, when two charged tapes are attracted and start to move toward each other, the energy diagram for this system would be like this: Other evidence/examples: Both Charged tapes Decrease in electrostatic potential energy Increase in kinetic energy During time that the charged tapes are attracting and moving towards each other 3-93

8 Chapter 3 Idea EC4 - Model of Static Electricity: The process by which an object becomes charged with static electricity can be explained in terms of a model of charges in materials. This model assumes that inside all materials are tiny charges of two separate types, called positive and negative. It is further assumed that the negative charges are free to move, while the positive charges stay fixed in place. In an uncharged material there are equal numbers of positive and negative charges, so the object has no overall charge. However, by rubbing objects together (or other means) it is possible to move negative charges from one object to another. In this process one object gains extra negative charges, and so has an overall negative charge, while the other object has a deficit of negative charges, and so is left with an overall positive charge. Other examples: When an uncharged object is brought near a charged object, it becomes electrically polarized, with the two sides of the object becoming oppositely charged. This happens because the negative charges in the uncharged object redistribute themselves under the influence of the force exerted on them by the charged object. This causes the area of the uncharged object closest to the charged object to have the opposite type of charge and so the two attract. For example, when a negatively charged balloon is brought close to a wall, the negative charges in the wall are repelled, leaving the surface of the wall positively charged. Thus, the negatively charged balloon is attracted to the wall and may stick to it. Other examples: 3-94

9 Scientists Ideas: Interactions, Systems, and Potential Energy Gravitational Interactions and Potential Energy In the late 16 th and early 17 th centuries Galileo did much of the important early work on the motion of falling objects, showing that they speed up as they fall. Though seemingly unrelated, the next important step was the work of Kepler, who developed three laws that accurately describe the motion of the planets in their orbits around the sun. Sir Isaac Newton realized that he could explain both of these motions with a single force (gravity), if the strength of that force depended on the masses of both the interacting objects, and on the distance between them. Newton s Law of Universal Gravitation was his crowning achievement. His Laws of Motion, which you have already encountered, were developed along the path to his explanation for gravity. However, Newton was very concerned about one aspect of his ideas, that of action-at-a-distance. To him the idea that one object could influence another without touching it seemed too much like magic and while he thought there must be some unseen agent that transmitted the influence, he did not feel there was enough evidence to be convinced of the reality of the ether. Idea G1 - Gravitational Interactions: A gravitational interaction occurs between any two objects that have mass even though they are not touching. During this interaction the two objects always exert attractive forces on each other. (This can be accounted for by the idea of an invisible gravitational field that extends around all objects. Any other objects within this gravitational field will feel an attractive force due to the influence of the field itself on them.) This gravitational force can be represented on a force diagram (along with any other forces acting on the object). Gravitational force exerted on apple by the Earth 3-95

10 Chapter 3 Idea G2 - Strength of the Gravitational Force: The strength of the gravitational attraction between two objects is determined by the amount of mass of both of the objects involved and by the distance between their centers. The larger either of the masses, the stronger the gravitational attraction between them. However, with normal sized objects (like people, cars, buildings, etc.) the gravitational interaction between them is so small that it is not noticeable. Only when at least one of the objects is very, very massive (like the Earth), does the strength of the gravitational interaction become significant and cause noticeable effects. Also, the further apart the centers of the objects are, the weaker the strength of the gravitational interaction between them. Since the strength of the gravitational force on an object is proportional to its mass, then all objects fall with the same increasing rate of speed, independent of their mass. (This assumes that no other forces are affecting the objects.) Idea G3 Gravitational Potential Energy: In any system of objects there is gravitational potential energy, the amount of which depends on how the objects are arranged with respect to each other. When the objects are rearranged this gravitational potential energy may change. When it does so in a closed system, there will also be a change in the kinetic energy of the objects within the system. (When one of the objects involved in a gravitational interaction is very massive, like the Earth, the change in its kinetic energy is imperceptible.) For example, when a pencil falls because of the gravitational interaction between it and the Earth, the energy diagram for this system would be like this: Pencil and Earth Decrease in gravitational potential energy Increase in kinetic energy 3-96

11 Scientists Ideas: Interactions, Systems, and Potential Energy Idea G3 Effect of moving through air: Here on the Earth the way an object moves (including how it falls) can be affected by an opposing force exerted by the air. Scientists call this force air resistance or drag. This force affects light objects with a large surface area much more than small, heavy objects. Because the strength of this force also increases as the speed of an object increases, this can lead to a situation in which the forces acting on an accelerating object eventually become balanced when it reaches a certain speed. If this happens, the speed will then remain constant and is referred to as the object s terminal velocity. 3-97

12 Chapter

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