Instructors_Guide_ch06 - 6 Dynamics II Motion in a Plane...

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6 Dynamics II, Motion in a Plane Recommended class days: 2 Background Information Chapters 6 and 7 are a continuation of single-particle dynamics, first to two-dimensional problems in which the x - and y -motions are independent (e.g., projectile motion) and then to circular motion. Many of the student difficulties with force and motion that seem to have been resolved in Chapters 1–5 resurface when students consider motion in a plane. The fact that these issues reappear in each new context shows how difficult it is for students to adopt a Newtonian thought pattern. On the other hand, two-dimensional motion provides an opportunity to spiral back to many earlier topics for additional practice. Chapter 1 introduced velocity and acceleration vectors for curvilinear motion, but the subsequent chapters have focused on motion in one dimension. Determining the direction of the acceleration vector remains difficult for many students. For example, few students can correctly identify the acceleration direction at each lettered point for a ball rolling along the ramp shown below. (This is Exercise 4 from the Student Workbook .) Other students will still be having trouble with vector components. These are serious impediments to understanding motion in a plane. A recitation hour spent on another round of motion-diagram exercises and vector exercises is well worthwhile as a prelude to this chapter. Many student ideas about a “force of motion” take on new life in two-dimensional situations. Clement (1982) posed the following problem to engineering students in a calculus-based physics course: A rocket is moving sideways in deep space, with its engine off, from A to B. It is not near any stars or planets or other outside forces. Its engine is fired at point B and left on for 2 s while the rocket travels from point B to some point C. Draw in the shape of the path from B to C. Then show the path from point C, after the engine is turned off. This figure shows the most common response. An incorrect linear trajectory between B and C was drawn by 89% of students. This is perhaps not too surprising because few students would have any reason to recognize that this situation gives a parabolic (or even curved) trajectory. More interesting is that 62% of students predicted that the rocket would return to its original direction after the engine is shut off at C. Interviews with students found many giving explanations such as “Whatever was making it go to the right 6-1
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6-2 Instructor’s Guide before will take over again after point C.” This reflects a belief in a continuing “force of motion” toward the right. Projectile motion, which occupies much of this chapter, has been delayed from its usual appear- ance in the chapter on kinematics. There are two reasons for this placement. First, many students have a sufficiently difficult time with one-dimensional kinematics. They’ve now had more time to practice those ideas and techniques before extending them to two dimensions. Second, the fact that
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This note was uploaded on 01/14/2011 for the course CD 254 taught by Professor Kant during the Spring '10 term at Central Oregon Community College.

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Instructors_Guide_ch06 - 6 Dynamics II Motion in a Plane...

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