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Unformatted text preview: PH 1110 Term A07 STUDY GUIDE 2: 2-D Motion, Newton's Laws of Motion Objectives 9. Solve problems concerning the motion in a plane, including the motion of projectiles in a uniform gravitational field. 10. Solve problems concerning the displacement, velocity, and acceleration of a particle moving along a circular path. 11. State Newton's first, second, and third laws. Be able to identify the reaction force to any force acting on a body. Distinguish between mass and weight. 12. Draw a diagram representing a body isolated from its environment in an inertial coordinate frame, indicate with arrows all forces that act on it, and identify the source of each force. Such a diagram is called a "free-body diagram ". 13. Apply Newton's laws to determine the acceleration of an object and present a clear, concise written solution of the problem. 14. Solve more complicated Newton's 2nd law problems, particularly those involving friction forces and/or circular motion. Suggested Study Procedure for Chapter 3. Study Secs. 3.1 through 3.4. Study particularly Examples 1ac, 2b, 3, 4, 5, 6, 7, 8, 9, 11, 12. Answer Discussion Questions 1, 2, 4, 7, 10, 12. Do Exercises 3bc, 7, 9, 19, 25, 31, 33, 35. Do Problems 47, 53, 63, 67. A. In Secs. 3.1 and 3.2 you find how displacement, velocity, and acceleration are handled when motion is NOT constrained to lie along a single straight-line direction. Note that we simply apply the machinery of one-dimensional motion and of vectors in order to generalize to ANY possible motion. 1. In multi-dimensional cases, remember that "constant velocity" means constant in DIRECTION as well as MAGNITUDE (the object moves in a straight line at a constant speed -- this is quite uncommon as far as the motion of "everyday" objects is concerned). An object that changes direction under ANY circumstances is accelerating. 2. Similarly, "constant acceleration" means that the acceleration vector is constant in magnitude AND direction throughout the motion. When acceleration is not zero, the velocity vector MUST necessarily be changing with time, either in magnitude, in direction, or both. 3. The component of acceleration perpendicular to G v changes the DIRECTION but not the magnitude of G v . The component of acceleration parallel to G v changes the MAGNITUDE of G v (the speed) but not the direction. Try applying this rule to the various examples in Chapt. 4 and see if it doesn't help demystify seemingly complex two- and three-dimensional motions. B. Sec. 3.3 introduces an important special case of motion where the vertical component of acceleration is CONSTANT and the horizontal component is ZERO. Provided that we can ignore air friction, this case describes the motion of objects tossed around just above the Earth's surface. Notice how following the Problem-Solving Strategy (p. 82) applies to the Examples, Exercises, and Problems. C. Sec. 3.4 introduces another VERY IMPORTANT special case of motion namely, circular motion at constant speed. Here is the acid test of whether you have yet bought into the vector nature of velocity...
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- Fall '08