Introduction and Vectors
CHAPTER OUTLINE
1.1 Standards of Length,
Mass, and Time
1.2 Dimensional Analysis
1.3 Conversion of Units
1.4 OrderofMagnitude
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
ProblemSolving 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
1 87 10 yr 9 109
d
yr
d d
s
d
s s
.
. ~
FH G
IK J
+ = FH G
IK J = ¡¿ .
Many college students are just approaching 1 Gs.
Q1.7 Zero significant digits. An orderofmagnitude 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 directionangle of
rA
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.
2 Introduction and Vectors
Q1.12 The books displacement is zero, as it ends up at the point from which it started. The distance
traveled is 6.0 meters.
