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Chapter 3 Skill Building

# Chapter 3 Skill Building - MasteringPhysics Assignment...

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MasteringPhysics: Assignment Print View Vector Addition and Subtraction In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors , , and . Calculate the following, and express your answers as ordered triplets of values separated by commas. Part A ANSWER: = 3.00, - 5.00, - 4.00 Part B ANSWER: = - 5.00,4.00,0 Part C ANSWER: = - 6.00,4.00,3.00 Part D ANSWER: = - 3.00, - 2.00, - 11.0 Part E ANSWER: = - 11.0,14.0,8.00 Part F ANSWER: = 17.0, - 12.0, - 6.00 http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1040719 (1 of 21)4/11/2006 2:42:30 PM

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MasteringPhysics: Assignment Print View 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 . 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 Put the tail of on the tail of ; goes from the arrow of to the arrow of Put the tail of on http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1040719 (2 of 21)4/11/2006 2:42:31 PM
MasteringPhysics: Assignment Print View 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 Hint not displayed Part B.2 Part not displayed Express in terms of , , and angle . ANSWER: = Part C http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1040719 (3 of 21)4/11/2006 2:42:31 PM

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MasteringPhysics: Assignment Print View Find the angle that the vector makes with vector . Hint C.1 Hint not displayed Express in terms of and any of the quantities given in the problem introduction ( , , and/ or ) as well as any necessary constants. Use asin for arcsine ANSWER: = 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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