MasteringPhysics-chapter 3

MasteringPhysics-chapter 3 - MasteringPhysics Assignment...

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MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm. .. 1 of 18 9/16/07 1:43 AM [ Print View ] physics 2211 MP03: Chapter 3 Due at 5:30pm on Wednesday, September 19, 2007 View Grading Details Vector Addition: Geometry and Components Learning Goal: To understand how vectors may be added using geometry or by representing them with components. Fundamentally, vectors are quantities that possess both magnitude and direction. In physics problems, it is best to think of vectors as arrows, and usually it is best to manipulate them using components. In this problem we consider the addition of two vectors using both of these methods. We will emphasize that one method is easier to conceptualize and the other is more suited to manipulations. Consider adding the vectors and , which have lengths and , respectively, and where makes an angle from the direction of . In vector notation the sum is represented by . Addition using geometry Part A Which of the following procedures will add the vectors and ? ANSWER: Put the tail of on the arrow of ; goes from the tail of to the arrow of

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MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm. .. 2 of 18 9/16/07 1:43 AM Put the tail of on the tail of ; goes from the arrow of to the arrow of Put the tail of on the tail of ; goes from the arrow of to the arrow of Calculate the magnitude as the sum of the lengths and the direction as midway between and . It is equally valid to put the tail of on the arrow of ; then goes from the tail of to the arrow of . Part B Find , the length of , the sum of and . Hint B.1 Law of cosines The law of cosines relates the lengths of the sides of any triangle of sides , , and . Using the geometric notation where is the angle opposite side : . Part B.2 Interior and exterior angles Note that is an exterior angle that is the supplement of angle . Express in terms of and relevant constants such as , using radian measure for known angles. ANSWER: = in terms of , , and angle , using radian measure for known angles.
MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm. .. 3 of 18 9/16/07 1:43 AM ANSWER: = Part C Find the angle that the vector makes with vector . Hint C.1 Law of sines Although this angle can be determined by using the law of cosines with as the angle, this results in more complicated algebra. A better way is to use the law of sines, which in this case is . Express in terms of and any of the quantities given in the problem introduction ( , and/or ) as well as any necessary constants. Use radian measure for known angles. Use asin for arcsine = Addition using vector components Part D To manipulate these vectors using vector components, we must first choose a coordinate system. In this case choosing means specifying the angle of the x axis. The y axis must be perpendicular to this and by convention is oriented radians counterclockwise from the x axis.

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This note was uploaded on 10/11/2008 for the course PHYS 2211 taught by Professor Duncan during the Fall '08 term at Georgia Perimeter.

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MasteringPhysics-chapter 3 - MasteringPhysics Assignment...

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