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Unformatted text preview: AP1200 Foundation Physics Chapter 1: Mechanics – Supplement on the Swing 1.18 The Swing In class, we discussed the “standing swing”, shown at right in Fig. 1.41. Using the principles of mechanics that we know, we can start to understand how the swing works. We will see that you can model the swing with different levels of accuracy, as is generally true of real-life problems in physics: rough results are often easy to get, while very accurate results can be very difficult or impossible to get. Fig. 1.41 Different kinds of swings The basic motion that you apply to gain height on the swing is to stand up when the swing goes through its low point, and crouch down when it reaches its high point. We can describe this motion at different levels of complexity, so that we have different physical models of the swing: 1. At the simplest level, we may think of kinetic energy only and model your motion as if you were standing on a train: by standing up very quickly from a crouching position, you increase your potential energy and use that increase in potential energy to gain height during your swinging. This simplest model can be handled by using conservation of kinetic energy only and leads to very simple mathematics. 2. At a slightly more complicated level, we may take into account your rotation during swinging . This in fact has two possibilities: you may consider your rotation around the swing axle (where the ropes, chains or bars of the swing are fixed), but you may also consider the rotation of your body around its center of gravity , using a fixed moment of inertia. In both cases, you can solve the problem by applying conservation of angular momentum in addition to conservation of kinetic energy. The mathematics remains relatively simple in this model. The advantage of such relatively simple models is that, using only conservation laws, you do not need to follow the motion moment by moment: you can describe what happens at specific positions of particular interest and ignore what happens in between those positions. 3. If you swing above the horizontal and use soft ropes (or loose chains), you may fall freely if your speed is insufficient to carry you “over the top”: then you could try to model what happens as you fall and the ropes straighten out. 4. Next, you may complicate the model by allowing your body’s moment of inertia to change as you stand up or crouch down, since you then change the shape of your body. This makes the mathematics significantly more complex, because your moment of inertia changes gradually (not suddenly) while you stand up from a crouching position or crouch down from a standing position. The result now depends on exactly how you stand up or crouch down....
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- Spring '10