Newton's Third Law of Motion

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26. Now see the complete picture. For every force there is an equal and opposite reaction force. But the forces on any one of the three bodies are not in equilibrium. Therefore, the cart, the horse and the ground are all accelerating (though in different degrees). 27. As final example we consider the motion of the earth and the moon due to the gravitational attraction between the two. Note the distance between the centres of the earth and the moon, and the masses of the earth and the moon. The gravitational force with which the earth is pulling the moon is 20.6 × 10 19 N. 28. As a result the moon is accelerating toward the earth and is moving in a circle. 29. The earth is experiencing a force of exactly the same magnitude of 20.6 × 10 19 N but directed toward the moon. However, the mass of the earth is about 83 times the mass of the moon. Therefore the earth is undergoing a much smaller acceleration of 3.44 × 10 −5 m/s 2 . As a result the centre of the earth is also moving in a circle, a much smaller circle. 220 Physics Education • July − September 2009
30. Both the moon and the earth are accelerating toward each other according to the Third Law of Motion. The centre of each is moving in a circle, one circle being much larger than the other because one mass is much smaller than the other. 2 Free Body Diagrams Newton’s first law of motion is difficult to believe. Why should anyone believe that an object keeps moving forever along a straight line in the absence of external interferences, when our everyday encounters seem to contradict the statement? Similarly Newton’s third law of motion is rarely believed. It is easy to “imagine” equal and opposite action-reaction forces when, for example, a stone is resting on a table. But how to trust the same statement when the table breaks and the stone crashes down? The confusion is understandable, and persists. The reason − our apathy to explain the theory properly with effective drawings. For understanding concepts and principles of mechanics drawing freebody diagrams is an essential first step. Without this Newton’s laws of motion can never be appreciated. 2.1 What is a Freebody Diagram? A freebody diagram (FBD) is a pictorial formulation of the mechanics problem through figures in which each object in a system of interacting bodies is shown separately and the forces acting on this body (and on this body alone) are clearly delineated and also shown separately. The slides presented in the previous section have shown many examples of FBDs. Some of the important ones are the following • A runner and the ground in Slide 9 (The gravity force has been suppressed); • A car and the ground in Slide 10; • A falling stone and the earth in Slides 16- 17; • A football player, football and the ground in Slides 19- 21; • A cart, a horse pulling it, and the ground in Slides 23-26; • The earth and the moon in Slides 27-29. 2.2 The Golden Rules for Understanding Newton’s Laws of Motion For understanding Newton’s laws of motion properly, especially their applications to extended objects, it is essential that the following golden rules be kept in mind. 1. Clearly identify the “system” whose motion you are going to analyze. Sometimes it may be useful to draw a boundary around this system in order to identify it and isolate it from all neighbouring systems. 2. All the forces that are coming from outside this system you have just identified − by this I mean the forces that are coming from outside the boundary you have drawn - are to be called external forces. Forces of “interaction” among objects inside the system that is, forces coming from objects that are confined within the boundary you have drawn − are all internal forces. 3. Therefore draw a freebody diagram (FBD) of all the external forces. You must remember that FBDs are a must for understanding mechanics. It is impossible Physics Education • July − September 2009 221
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Newton's Third Law of Motion

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