Ch0116 - Chapter 16 Newtons Laws #3: Components, Friction,...

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Chapter 16 Newton’s Laws #3: Components, Friction, Ramps, Pulleys, and Strings 95 16 Newton’s Laws #3: Components, Friction, Ramps, Pulleys, and Strings When, in the case of a tilted coordinate system, you break up the gravitational force vector into its component vectors, make sure the gravitational force vector itself forms the hypotenuse of the right triangle in your vector component diagram. All too often, folks draw one of the components of the gravitational force vector in such a manner that it is bigger than the gravitational force vector it is supposed to be a component of. The component of a vector is never bigger than the vector itself . Having learned how to use free body diagrams, and then having learned how to create them, you are in a pretty good position to solve a huge number of Newton’s 2 nd Law problems. An understanding of the considerations in this chapter will enable to you to solve an even larger class of problems. Again, we use examples to convey the desired information. Example 16-1 A professor is pushing on a desk with a force of magnitude F at an acute angle θ below the horizontal. The desk is on a flat, horizontal tile floor and it is not moving. For the desk, draw the free body diagram that facilitates the direct and straightforward application of Newton’s 2 nd Law of motion. Give the table of forces. While not a required part of the solution, a sketch often makes it easier to come up with the correct free body diagram. Just make sure you don’t combine the sketch and the free body diagram. In this problem, a sketch helps clarify what is meant by “at an acute angle below the horizontal.” Pushing with a force that is directed at some acute angle below the horizontal is pushing horizontally and downward at the same time.
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Chapter 16 Newton’s Laws #3: Components, Friction, Ramps, Pulleys, and Strings 96 Here is the initial free body diagram and the corresponding table of forces. Note that there are no two mutually perpendicular lines to which all of the forces are parallel. The best choice of mutually perpendicular lines would be a vertical and a horizontal line. Three of the four forces lie along one or the other of such lines. But the force of the professor does not. We cannot use this free body diagram directly. We are dealing with a case which requires a second free body diagram. Cases Requiring a Second Free Body Diagram in Which One of More of the Forces that was in the First Free Body Diagram is Replaced With its Components Establish a pair of mutually perpendicular lines such that most of the vectors lie along one or the other of the two lines. After having done so, break up each of the other vectors, the ones that lie along neither of the lines, (let’s call these the rogue vectors) into components along the two lines. (Breaking up vectors into their components involves drawing a vector component diagram.) Draw a second free body diagram, identical to the first, except with rogue vectors replaced by their component vectors. In the new free
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Ch0116 - Chapter 16 Newtons Laws #3: Components, Friction,...

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