Chapter 8 devotes considerable attention to tension

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Chapter 8 devotes considerable attention to tension and to the motion of objects connected by strings or ropes. As the research of McDermott et al. has shown, tension is a difficult concept for students. The textbook approach is to make an imaginary cut through the string, then to ask how the left and right sides of the string “hold on” to each other. The idea of internal forces is new to most students, but this approach is generally effective.
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Chapter 8: Newton’s Third Law 8-5 A standard application of tension is the Atwood machine or the “modified” Atwood machine of a hanging mass connected to a mass on a horizontal surface. Both involve pulleys, and pulleys introduce another complication. Most textbooks assume, with no discussion, that the tension forces at the two ends of the rope are the same—i.e., that the tension forces are an action/reaction pair of forces. But this directly contradicts the third law since these forces are not in opposite directions! It’s important to lead students through the reasoning behind the massless string and massless, frictionless pulley approximations, concluding that the tension forces at the ends of a massless rope act as if they are an action/reaction pair, even when the forces are not in opposite directions. Students also have a difficult time with the acceleration constraint of connected objects. Most texts rarely note that the acceleration constraint is an independent equation needed to solve the simultaneous equations typical of third-law problems. Although most students quickly recognize that a A = a B if A and B are connected by a string (at least for simple connections; pulleys can make for more complex relationships), most need several practice examples to learn how to express this in terms of the vector components used in the problem. Note that some students interpret the statement a A x = a B y to mean that a A x has to be a negative number. They have a hard time seeing this as simply a relational statement. Although Newton’s third law and the physics of interacting systems is difficult, it is not above the capability of introductory students. However, true understanding rarely occurs spontaneously on the basis of expository readings and lectures. These are very counterintuitive ideas, and they hit all of the misconception “hot buttons” of most students. Coming to an understanding takes explicit instruction and practice with the techniques of identifying interaction forces. Students need opportunities to use Newton’s laws to reason their way to an explanation of observed phenomena. Providing them with such opportunities and practice is a powerful teaching tool for coming to grips with the essence of Newtonian mechanics. But the time is well spent. By the end of Chapter 8, most students are coming to realize that this systematic approach to problem solving is paying off. They are beginning to solve difficult problems that they could never have solved with an equation-hunting strategy. (It’s good to remind them of this!) It is an empowering experience for many students to realize they are solving “hard” problems that seemed far out of their reach just a few short weeks ago.
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