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FORCES, WORK, AND ENERGY You have seen that there are many different ways in which energy can be transferred from one system to another, or from one place to another. Included in the ways would be energy transfer by light, sound, electricity, convection, and thermal conduction. However, perhaps the most tangible method of transferring energy has yet to be discussed; the transfer of energy via forces. Intuitively speaking, a force is simply a push or a pull. When you push against or pull on an object, we say that a force has been exerted. Quite clearly, exerting a force on an object can change an object’s energy. For example, if you kick a stationary soccer ball, you will increase the ball’s kinetic energy, because the ball will be set into motion. In order to be systematic in the consideration of forces and changes in energy, it is helpful at times to have a more rigorous definition for force than the intuitive one given above. The intuitive definition, while easy to understand, has many misconceptions associated with it, and it is best if these can be avoided. As an example, many people think that only humans and animals are capable of exerting forces. They can imagine a person pushing on a wall, but they can not imagine the opposite: a wall pushing on a person. (But of course, a wall can push on a person; and quite hard. Imagine how hard a brick wall could hit you if you ran full speed into it. The damage done to you would be due to the wall hitting you.) At any rate, a more rigorous definition for force is needed at times, and it must be sufficiently precise that one can refer to it without ambiguity. A more formal definition for force is “a specific interaction capable of changing the speed or direction of motion of an object.” Although this definition presents a more abstract notion of a force than simply calling it a push or a pull (and while also acknowledging that this definition would be unintelligible to a child), there is a precision in this definition which will be helpful for our purposes. At the heart of this definition of force is the realization that a force might cause a change in motion. This change in motion might occur for a single atom, or it might be the entire earth which experiences a change in motion. Nevertheless, the point is made that forces cause changes in motion. It is somewhat helpful to compare this definition of a force with the definition for energy. In Unit 3 it was said that energy is a measure of the amount of change which might occur in a system. Thus, energy does not provide an explanation for what might cause a change. It simply informs you of how much change is possible. On the other hand, forces are a possible mechanisms for causing this change. It is therefore not surprising that forces and energy can be closely related. Consider the following situation: a woman is vigorously stirring a beaker of water with a spoon. How would you scientifically describe what is going on? Well, from an energy perspective, one sees the following chain of energy transfers: Stored chemical energy in the woman’s muscles is converted into the kinetic energy of her moving hand and spoon, which in turn will cause the temperature of the water in the beaker to increase because the water molecules are being given additional kinetic energy. In summary, energy stored in the woman is transferred to the water. But what caused this transfer to take place? It was the spoon pushing on the water molecules which caused them to speed up. That is to say, the force of the spoon against the water caused a change in the energy of the water. Whenever a force causes a change in energy as it did in the previous example, we say that work has been done. Consider another set of examples: Suppose your car is out of gas, and you need to push it to a gas station. You do work as you begin to push your car, because your car gains kinetic energy. However, suppose instead that you can not make your car move because you have left the parking brake on. No matter how hard you push, your car will not go anywhere. In this case you are not doing any work (by the scientific definition) because you are not transferring any energy to the car. Of course, you will eventually become tired if you keep pushing against an immobile car, because you will use up your energy stores. But since this energy would not be transferred to the car, no work would be done. Therefore, forces can cause changes in energy, but they do not always UNIT 4 ENERGY AND INTERACTIONS IV - 59 © CALVIN COLLEGE FORCES, WORK, AND ENERGY do so. In summary, the important thing to remember about work is that it is a useful way to describe how forces can cause changes in the energy of objects or systems. But you must also keep in mind that there are many examples in which forces do not cause a change in energy. In those cases no work is done. Calculating energy changes One of the most useful aspects of the concept of work is that in many instances it affords a method for calculating the magnitude of the change in energy which will occur in a system. In order to see how this works, a few quantities have to be defined. The unit of force is called a Newton. (In the English system the unit of force is a pound.) 1 Newton = 1 kg m / sec2 The amount of work done by a force on an object is equal to the magnitude of the force times the distance through which the force pushes or pulls the object. Work = Force x distance If the object does not move in the direction in which the force is pushing or pulling, then no work is done. The unit of work is a joule. 1 joule = 1 Newton x meter Several examples of calculating energy changes using work are given below. Example 1 Suppose a 6 kg rock is dropped from a cliff 10 meters high. How fast will the rock be going when it hits the ground? In this example, the force of gravity will do work on the rock as the rock falls. The force of gravity exerted on any object near the surface of the earth is just equal to the mass of the object times the number g = 9.8 m/s 2. Therefore, the work done by the force of gravity will equal this force times the distance the rock moves, 10 meters. Work = 6 kg x 9.8 m/s2 x 10 m = 588 joules The work done on the rock will increase the kinetic energy of the rock by this amount. mass x v2 / 2 = 588 joules When you solve for the velocity of the rock you find v = 14 m/s. Try this example again for a 12 kg rock. What do you find the final velocity to be? Example 2 How much work would you do on a bowling ball (7.27 kg) if you carried it to the top of the Gateway Arch in St. Louis (height = 192 m). The work done would go into increasing the gravitational potential energy of the ball. Therefore, work = m x g x h = (7.27 kg) x (9.8 m/s2) x (192 m) = 13,679.2 joules UNIT 4 ENERGY AND INTERACTIONS IV - 60 © CALVIN COLLEGE FORCES, WORK, AND ENERGY Example 3 A woman stirred a 500 ml (= 500 gm) cup of water for two minutes. She did 13,700 joules of work in doing this. If the water was in a well insulated styrofoam cup (so that no heat was able to escape) by how many degrees did the water heat up? The work the woman did went into heating the water. The specific heat capacity of water is 1 calorie/gm °C = 4.186 joules/gm °C Therefore, the rise in temperature would be given by: T = 13,679.2 joules/500 gm x 4.186 joules. T = 6.5° C Forces, Work, and Energy Homework 1. a. b. c. d. e. f. Consider the following situations, and tell why you do or do not think work is being done on the object written in bold type. A man is carrying a suitcase along a level sidewalk and moving at a constant speed. A man is carrying a suitcase up a hill and moving at a constant speed. A girl is pushing against the side of a brick building. A girl is standing and holding a baseball in her outstretched hand. A boy is pushing a heavy box at constant speed across a rough floor. Gravity is pulling on a mass hung from the ceiling 2. The value of g on the moon is one sixth its value on the earth. By how much would your weight change if you went to the moon? 3. A 2.0 kg object is dropped from a height of 3.0 m. How fast is it going just before it hits the ground? Would your answer be different if the mass were 1.0 kg? UNIT 4 ENERGY AND INTERACTIONS IV - 61 © CALVIN COLLEGE