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# SM_PDF_chapter1 - Introduction and Vectors CHAPTER OUTLINE...

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1 Introduction and Vectors CHAPTER OUTLINE 1.1 Standards of Length, Mass, and Time 1.2 Dimensional Analysis 1.3 Conversion of Units 1.4 Order-of-Magnitude Calculations 1.5 Significant Figures 1.6 Coordinate Systems 1.7 Vectors and Scalars 1.8 Some Properties of Vectors 1.9 Components of a Vector and Unit Vectors 1.10 Modeling, Alternative Representations, and Problem-Solving Strategy ANSWERS TO QUESTIONS Q1.1 Atomic clocks are based on electromagnetic waves which atoms emit. Also, pulsars are highly regular astronomical clocks. Q1.2 Density varies with temperature and pressure. It would be necessary to measure both mass and volume very accurately in order to use the density of water as a standard. Q1.3 (a) 0.3 millimeters (b) 50 microseconds (c) 7.2 kilograms Q1.4 (b) and (d). You cannot add or subtract quantities of different dimension. Q1.5 A dimensionally correct equation need not be true. Example: 1 chimpanzee = 2 chimpanzee is dimensionally correct. If an equation is not dimensionally correct, it cannot be correct. Q1.6 On February 7, 2005, I am 59 years and 39 days old. 59 365 25 1 39 21 589 86 400 1 187 10 10 99 yr d yr d d s d s s . .~ F H G I K J += F H G I K J . Many college students are just approaching 1 Gs. Q1.7 Zero significant digits. An order-of-magnitude calculation is accurate only within a factor of 10. Q1.8 With one datum known to one significant digit, we have 80 million yr + 24 yr = 80 million yr. Q1.9 No, the magnitude of the displacement is always less than or equal to the distance traveled. If two displacements in the same direction are added, then the magnitude of their sum will be equal to the distance traveled. Two vectors in any other orientation will give a displacement less than the distance traveled. If you first walk 3 meters east, and then 4 meters south, you will have walked a total distance of 7 meters, but you will only be 5 meters from your starting point. Q1.10 Only force and velocity are vectors. None of the other quantities requires a direction to be described. Q1.11 If the direction-angle of r A is between 180 degrees and 270 degrees, its components are both negative. If a vector is in the second quadrant or the fourth quadrant, its components have opposite signs.

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2 Introduction and Vectors Q1.12 The book’s displacement is zero, as it ends up at the point from which it started. The distance traveled is 6.0 meters. Q1.13 85 miles. The magnitude of the displacement is the distance from the starting point, the 260-mile mark, to the ending point, the 175-mile mark. Q1.14 Vectors r A and r B are perpendicular to each other. Q1.15 No, the magnitude of a vector is always positive. A minus sign in a vector only indicates direction, not magnitude. Q1.16 Any vector that points along a line at 45° to the x and y axes has components equal in magnitude. Q1.17 Addition of a vector to a scalar is not defined. Think of apples and oranges.
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SM_PDF_chapter1 - Introduction and Vectors CHAPTER OUTLINE...

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