Instructors_Guide_Ch08

# This can lead into a discussion of how two objects

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0. This can lead into a discussion of how two objects interacting through a massless string act as if they exert action/reaction forces on each other. Block m B String m S Frictionless What is tension T 2 at this point? Pull with tension T 1 DAY 3: Finally, you can turn to working standard third-law example problems. These will be easier after two days of identifying action/reaction pairs and drawing free-body diagrams, but you should still discuss and show these steps as you work. Because third-law problems tend to be lengthy, you’ll probably want to do more of the work yourself rather than having students do it. Even so, it’s good to have them do one piece of each example—draw the free-body diagrams for one, identify the acceleration constraint of another, and write down Newton’s second law for each system in a third. It’s not unusual for a third-law problem to have four equations of motion ( x - and y -components of the second law for each of two moving objects), one or two third-law relationships, one or two friction models, and an acceleration constraint. Eight or nine independent equations and relationships are not uncommon. Students are not used to problems with this level of complexity, and many become overwhelmed. Sympathize with them, but keep pointing out that the problem- solving strategies and the worksheets are a systematic way of keeping track of all the information. Equation hunting won’t help them now; they have to understand and follow the procedures. Simple substitutions usually reduce everything to two simultaneous equations. Even though the substitutions are simple, you need to work through all the details in at least one example. Many students get lost with assertions that “If you substitute the first equation into the second you end

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8-8 Instructor’s Guide up with …” Also be aware that some students have had little experience with simultaneous algebraic equations. Once again, they’ll need to see one solution worked and explained in detail. This is the high point of Newtonian mechanics. Although the concepts of upcoming chapters may be difficult, students won’t face this level of detail and complexity again until they reach electricity and magnetism. Ample praise for their efforts and for the amount they’ve learned to this point is certainly called for. Part I Summary Chapter 8 is followed by the first of seven part summaries. Each summary consists of a “knowledge structure” plus a short diversion relevant to the part just completed. Because this is the first summary, you may want to call students’ attention to the knowledge structure. Each knowledge structure summarizes the essential information of the preceding chapters in an expert-like hierarchical arrangement. Students should note that, thus far, there are only three physical principles: Newton’s laws. We’ve considered three general types of motion, each of which uses the second law in a slightly different way. Each form of motion then branches into more specialized kinematic results. At an even finer scale, not shown here, is information about specific types of forces. Suggest that students photocopy this page and keep it in front of them as they study for the exam on Part I. They can look up specific details as needed, but this table describes the basic
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