Force and Motion-II Applying Newton’s Second Law to More Complex Problems: The Atwood Machine and the Inclined Plane. Lecture 5 Thursday:29 January 2004 Applying Newton’s Second Law (F=ma) to more complex problems. Recall, F ma, in 2 dimensions : F ma , F ma x x y y Motion in Two-Dimensions • Motion in x direction is completely independent of motion in y direction. • Break problem into two parts. One regarding x-motion, one regarding y-motion • Each part is then handled just like motion in 1-Dim. A Common Example: Atwood’s machine What do we know? • Is tension the same for both masses? • Is acceleration the same for both masses? • Is the acceleration equal to g? Atwood’s Machine T mg ma Mg T Ma Add these to eliminate T . Mg mg Ma ma ( M m) g ( M m)a M m a g M m Inclined Plane Problem Solving Tip: Rotate your coordinate system for the inclined plane. Make one axis along the direction of motion. You can leave the coordinate system in the “traditional” form for the hanging weight. N - m1g cos q 0 m1g sin q = m1a m2g T = m2a • Add the two equations involving T, in order to eliminate T. Inclined Plane m2 g m1 g sin q m2 a m1a m2 m1 sin q a g m2 m1 T m2 g m2 a T m1 g sin q m1a