Physics for Scientists and Engineers with Modern Physics

Douglas C. Giancoli

Chapter 1

Introduction, Measurement, Estimating - all with Video Answers

Educators

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Chapter Questions

Problem 1

(1) The age of the universe is thought to be about 14 billion years. Assuming two significant figures, write this in powers of ten in $(a)$ years, $(b)$ seconds.

Averell Hause

Averell Hause

Carnegie Mellon University

Problem 2

(1) How many significant figures do each of the following numbers have:
$$ 214, \text { (b) } 81.60, \text { (c) } 7.03, \text { (d) } 0.03 $$
$$ (e) 0.0086,(f) 3236, \text { and }(g) 8700 ? $$

Zachary Warner

Numerade Educator

Problem 3

$$ \begin{array}{l}{\text { (1) Write the following numbers in powers of ten notation: }} \\ {\text { (a) } 1.156,(b) 21.8,(c) 0.0068,(d) 328.65,(e) 0.219, \text { and }(f) 444 \text { . }}\end{array} $$

Averell Hause

Carnegie Mellon University

Problem 4

(1) Write out the following numbers in full with the correct number of zeros:
$$ 8.69 \times 10^{4}, \text { (b) } 9.1 \times 10^{3} $$
$$ 8.8 \times 10^{-1},(d) 4.76 \times 10^{2}, \text { and }(e) 3.62 \times 10^{-5} . $$

Zachary Warner

Numerade Educator

Problem 5

(II) What is the percent uncertainty in the measurement 5.48$\pm 0.25 \mathrm{m} ?$

Averell Hause

Carnegie Mellon University

Problem 6

(II) Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 s, due to human reaction time at the start and stop moments. What is the percent uncertainty of a hand-timed measurement of $$ (a) 5 s,(b) 50 s,(c) 5 \min ? $$

Zachary Warner

Numerade Educator

Problem 7

(II) Add $$ \left(9.2 \times 10^{3} s\right)+\left(8.3 \times 10^{4} s\right)+\left(0.008 \times 10^{6} s\right) $$

Averell Hause

Carnegie Mellon University

Problem 8

$$ \begin{array}{l}{\text { (II) Multiply } 2079 \times 10^{2} \mathrm{m} \text { by } 0.082 \times 10^{-1} \text { , taking into }} \\ {\text { account significant figures. }}\end{array} $$

Zachary Warner

Numerade Educator

Problem 9

$$ \begin{array}{l}{\text { (III) For small angles } \theta \text { , the numerical value of } \sin \theta \text { is }} \\ {\text { approximately the same as the numerical value of tan } \theta \text { . }} \\ {\text { Find the largest angle for which sine and tangent agree to }} \\ {\text { within two significant figures. }}\end{array}
$$

Averell Hause

Carnegie Mellon University

Problem 10

$$ \begin{array}{l}{\text { (III) What, roughly, is the percent uncertainty in the volume }} \\ {\text { of a spherical beach ball whose radius is } r=0.84 \pm 0.04 \mathrm{m} \text { ? }}\end{array} $$

Zachary Warner

Numerade Educator

Problem 11

$$ \begin{array}{l}{\text { (1) Write the following as full (decimal) numbers with stan- }} \\ {\text { dard units: }(a) 286.6 \mathrm{mm},(b) 85 \mu \mathrm{V},(c) 760 \mathrm{mg},(d) 60.0 \mathrm{ps}} \\ {(e) 22.5 \mathrm{fm},(f) 2.50 \text { gigavolts. }}\end{array} $$

Averell Hause

Carnegie Mellon University

Problem 12

$$ \begin{array}{l}{\text { (1) Express the following using the prefixes of Table } 4 :} \\ {\text { (a) } 1 \times 10^{6} \text { volts, }(b) 2 \times 10^{-6} \text { meters, (c) } 6 \times 10^{3} \text { days, }} \\ {\text { (d) } 18 \times 10^{2} \text { bucks, and }(e) 8 \times 10^{-8} \text { seconds. }}\end{array} $$

Zachary Warner

Numerade Educator

Problem 13

$$ \begin{array}{l}{\text { 13. (I) } \quad \text { Determine }} \\ {\text { your own height in }} \\ {\text { meters, and your mass }} \\ {\text { in } \mathrm{kg}}\end{array} $$

Averell Hause

Carnegie Mellon University

Problem 14

(I) The Sun, on average, is 93 million miles from Earth. How many meters is this? Express $(a) \quad$ using powers of ten, and $(b)$ using a metric prefix.

Zachary Warner

Numerade Educator

Problem 15

(II) What is the conversion between $(a)$ ft $^{2}$ and $y d^{2},(b) m^{2}$ and $f t^{2} ?$

Averell Hause

Carnegie Mellon University

Problem 16

(II) An Airplane travels at 950 $\mathrm{km} / \mathrm{h}$ . How long does it take to travel 1.00 $\mathrm{km} ?$

Prabhat Tyagi

Numerade Educator

Problem 17

(II) A typical atom has a diameter of about $1.0 \times 10^{-10} \mathrm{m}$ (a) What is this in
inches? (b) Approximately how many atoms are there along a 1.0 -cm line?

Averell Hause

Carnegie Mellon University

Problem 18

18. (II) Express the following sum with the correct number of significant figures: $1.80 \mathrm{m}+$
$142.5 \mathrm{cm}+5.34 \times 10^{5} \mu \mathrm{m} .$

Zachary Warner

Numerade Educator

Problem 19

(II) Determine the conversion factor between $(a) \mathrm{km} / \mathrm{h}$
and $\mathrm{mi} / \mathrm{h},(b) \mathrm{m} / \mathrm{s}$ and $\mathrm{ft} / \mathrm{s},$ and $(c) \mathrm{km} / \mathrm{h}$ and $\mathrm{m} / \mathrm{s}$ .

Averell Hause

Carnegie Mellon University

Problem 20

(II) How much longer (percentage) is a one-mile race than a 1500 -m race ("the metric mile")?

Zachary Warner

Numerade Educator

Problem 21

$$ \begin{array}{l}{\text { (II) A light-year is the distance light travels in one year }} \\ {\text { (at speed }=2.998 \times 10^{8} \mathrm{m} / \mathrm{s} ) \text { . (a) How many meters are }} \\ {\text { there in } 1.00 \text { light-year? }(b) \text { An astronomical unit }(\mathrm{AU}) \text { is }}\end{array} $$
$$ \begin{array}{l}{\text { the average distance from the Sun to Earth, } 1.50 \times 10^{8} \mathrm{km} \text { . }} \\ {\text { How many } \mathrm{AU} \text { are there in } 1.00 \text { light-year? (c) What is the }} \\ {\text { speed of light in } \mathrm{AU} / \mathrm{h} \text { ? }}\end{array} $$

Averell Hause

Carnegie Mellon University

Problem 22

$$\begin{array}{l}{\text { (II) If you used only a keyboard to enter data, how many }} \\ {\text { years would it take to fill up the hard drive in your }} \\ {\text { computer that can store } 82 \text { gigabytes }\left(82 \times 10^{9} \text { bytes) of }\right.}\end{array} $$ data? Assume "normal" cight-hour working days, and that one byte is required to store one keyboard character, and that you can type 180 characters per minute.

Zachary Warner

Numerade Educator

Problem 23

(III) The diameter of the Moon is 3480 $\mathrm{km}$ . (a) What is the surface area of the Moon? (b) How many times larger is the surface area of the Earth?

Averell Hause

Carnegie Mellon University

Problem 24

(1) Estimate the order of magnitude (power of ten) of: $(a) 2800$ , (b) $86.30 \times 10^{2},(c) 0.0076,$ and $(d) 15.0 \times 10^{8} .$

Zachary Warner

Numerade Educator

Problem 25

(II) Estimate how many books can be shelved in a collicge library with 3500 $\mathrm{m}^{2}$ of floor space. Assume 8 shelves high, having books on both sides, with corridors 1.5 $\mathrm{m}$ wide.
Assume books are about the size of this onc, on average.

Averell Hause

Carnegie Mellon University

Problem 26

(II) Estimate how many hours it would take a runner to run (at 10 $\mathrm{km} / \mathrm{h}$ ) across the United States from New York to California.

Zachary Warner

Numerade Educator

Problem 27

(II) Estimate the number of liters of water a human drinks in a lifetime.

Averell Hause

Carnegie Mellon University

Problem 28

(II) Estimate how long it would take one person to mow a football ficld using an ordinary home lawn mower (Fig. 11$)$ . Assume the mower moves with a $1-\mathrm{km} / \mathrm{h}$ spced, and has a
0.5 $\mathrm{m}$ width.

Zachary Warner

Numerade Educator

Problem 29

(II) Estimate the number of dentists $(a)$ in San Francisco and $(b)$ in your town or city.

Supratim Pal

Numerade Educator

Problem 30

(III) The rubber worn from tires mostly enters the atmosphere as particulate pollurion. Estimate how much rubber (in kg) is put into the air in the United States every year. To get started, a good cstimate for a tire tread's depth is 1 $\mathrm{cm}$ when new, and rubber has a mass of about 1200 $\mathrm{kg}$ per $\mathrm{m}^{3}$ of volume.

Zachary Warner

Numerade Educator

Problem 31

(III) You are in a hot air balloon, 200 $\mathrm{m}$ above the flat Texas plains. You look out toward the horizon. How far out can you sec-that is, how far is your horizon? The Earth's radius is about 6400 $\mathrm{km}$ .

Averell Hause

Carnegie Mellon University

Problem 32

(III) I agree to hire you for 30 days and you can decide between two possible methods of payment: cither $(1) \$ 1000$ a day, or (2) one penny on the first day, two pennics on the scoond day and continue to double your daily pay cach day up to day 30. Use quick estimation to make your decision, and justify it.

Zachary Warner

Numerade Educator

Problem 33

(III) Many sailboats are moored at a marina 4.4 $\mathrm{km}$ away on the opposite side of a lake. You stare at one of the sailboats because, when you are lying flat at the water's cdge, you can just see its
deck but none of the side of the sailboat. You then go to that $$ \begin{array}{l}{\text { sailboat on the other side of the }} \\ {\text { lake and measure that the deck }} \\{\text { is } 1.5 \mathrm{m} \text { above the level of the }} \\ {\text { water. Using Fig, } 12, \text { where }} \\ {h=15 \mathrm{m}, \text { estimate the radius } R} \\ {\text { of the Farth. }}\end{array} $$

Averell Hause

Carnegie Mellon University

Problem 34

(III) Another experiment you can do also uses the radius of the Earth. The Sun sets, fully disappearing over the horizon as you lie on the beach, your cyes 20 $\mathrm{cm}$ above the sand. You
immediately jump up, your eyes now 150 $\mathrm{cm}$ above the sand, and you can again see the top of the Sun. If you count the number of seconds $(=t)$ until the Sun fully disappears again, you can estimate the radius of the Earth. But for this Problem, use the known radius of the Earth and calculate the time $t$ .

Zachary Warner

Numerade Educator

Problem 35

(1) What are the dimensions of density, which is mass per volume?

Averell Hause

Carnegie Mellon University

Problem 36

$$
\begin{array}{l}{\text { (II) The spced } v \text { of an object is given by the equation }} \\ {v=A t^{3}-B t, \text { where } t \text { refers to time. (a) What are the }} \\ {\text { dimensions of } A \text { and } B ?(b) \text { What are the SI units for the }} \\ {\text { constants } A \text { and } B ?}\end{array}
$$

Zachary Warner

Numerade Educator

Problem 37

$$ \begin{array}{l}{\text { (II) Three students derive the following cquations in which }} \\ {x \text { refers to distance traveled, } v \text { the specd, } a \text { the acceleration }} \\ {\left(m / s^{2}\right), t \text { the time, and the subscript zero }(a) \text { means a quantity }}\end{array} $$
$$\begin{array}{l}{\text { at time } t=0 : \text { (a) } x=u t^{2}+2 a t,(b) x=v_{0} t+\frac{1}{2} a t^{2}, \text { and }} \\ {(c) \quad x=v_{0} t+2 a t^{2} \text { . Which of these could possibly be }} \\ {\text { correct according to a dimensional check? }}\end{array} $$

Averell Hause

Carnegie Mellon University

Problem 38

$$ \begin{array}{l}{\text { (II) Show that the following combination of the three funda- }} \\ {\text { mental constants of nature that we used in Example } 10 \text { of }} \\ {\text { "Introduction, Measurement, Estimating" (that is } G, c, \text { and } h} \\ {\text { forms a quantity with the dimensions of time: }}\end{array} $$
$t_{\mathrm{P}}=\sqrt{\frac{G h}{c^{5}}}$
This quantity, $t_{1}$ , is called the Planck time and is thought to be the carliest time, after the creation of the Universe, at which the currently known laws of physics can be applied.

Zachary Warner

Numerade Educator

Problem 39

Global positioning satellites (GPS) can be used to determine positions with great accuracy. If one of the satellites is at a distance of $20,000 \mathrm{km}$ from you, what percent uncertainty in the distance does a 2 -m uncertainty represent? How many significant figures are nceded in the distance?

Averell Hause

Carnegie Mellon University

Problem 40

Computer chips (Fig. 13$)$ etched on circular silicon wafers of thickness 0.300 $\mathrm{mm}$ are sliced from a solid cylindrical silicon crystal of length 25 $\mathrm{cm}$ . If cach wafer can hold 100 chips, what is the maximum number of chips that can be produced from one entire cylinder?

Zachary Warner

Numerade Educator

Problem 41

(a) How many scconds are there in 1.00 year? (b) How many nanoseconds are there in 1.00 year? (c) How many years are there in 1.00 second?

Averell Hause

Carnegie Mellon University

Problem 42

American football uses a field that is 100 yd long, whereas a regulation soccer ficld is 100 $\mathrm{m}$ long. Which field is longer, and by how much (give yards, meters, and percent)?

Zachary Warner

Numerade Educator

Problem 43

A typical adult human lung contains about 300 million tiny
cavitics called alveoli. Estimate the average diameter of
a single alveolus.

Averell Hause

Carnegie Mellon University

Problem 44

One hectare is defined as $1.000 \times 10^{4} \mathrm{m}^{2}$ . One acre is
$4.356 \times 10^{4} \mathrm{ft}^{2}$ . How many acres are in one hectare?

Zachary Warner

Numerade Educator

Problem 45

Estimate the number of gallons of gasoline consumed by the total of all automobile drivers in the United States, per year.

Averell Hause

Carnegie Mellon University

Problem 46

$$ \begin{array}{l}{\text { Use Table } 3 \text { to estimate the total number of protons or }} \\ {\text { neutrons in }(a) \text { a bacterium, }(b) \text { a DNA moleculc, }(c) \text { the }} \\ {\text { human body, }(d) \text { our Galaxy. }}\end{array} $$

Zachary Warner

Numerade Educator

Problem 47

$$ \begin{array}{l}{\text { An average family of four uses roughly } 1200 \mathrm{L} \text { (about) }} \\ {300 \text { gallons) of water per day }\left(1 \mathrm{L}=1000 \mathrm{cm}^{3}\right) . \text { How much }} \\ {\text { depth would a lake lose per year if it uniformly covered an }} \\ {\text { arca of } 50 \mathrm{km}^{2} \text { and supplicd a local town with a population }} \\ {\text { of } 40,000 \text { people? Consider only population uses, and }} \\ {\text { neglect evaporation and so on. }}\end{array} $$

Averell Hause

Carnegie Mellon University

Problem 48

Estimate the number of gumballs in the machine of Fig. 14

Zachary Warner

Numerade Educator

Problem 49

Estimate how many kilograms of laundry soap are used in the U.S. in one year (and therefore pumped out of washing machines with the dirty water). Assume each load of laundry takes 0.1 $\mathrm{kg}$ of soap.

Averell Hause

Carnegie Mellon University

Problem 50

How big is a ton? That is, what is the volume of something that weighs a ton? To be specific, estimate the diameter of a 1-ton rock, but first make a wild guess. will it be 1 ft across. 3 ftr, or the size of a car? [Hint. Rock has mass per volume about 3 times that of water, which is 1 $\mathrm{kg}$ per liter $\left(10^{3} \mathrm{cm}^{3}\right)$ or 62 $\mathrm{lb}$ per cubic foot.

Zachary Warner

Numerade Educator

Problem 51

A certain audio compact dise (CD) contains 783.216 megabytes of digital information. Each byte consists of exactly 8 bits. When played, a CD player reads the CD's digital information at a constant rate of 1.4 megabits per scoond. How many minutes does it take the player to read the entire CD?

Averell Hause

Carnegie Mellon University

Problem 52

Hold a pencil in front of your eye at a position where its blunt end just blocks out the Moon (Fig. 15$)$ . Make appropriate measurements to estimate the diameter of the Moon, given that the Earth-Moon distance is $3.8 \times 10^{5} \mathrm{km}$ .

Zachary Warner

Numerade Educator

Problem 53

$$ \begin{array}{l}{\text { A heavy rainstorm dumps } 1.0 \mathrm{cm} \text { of rain on a city } 5 \mathrm{km} \text { wide }} \\ {\text { and } 8 \mathrm{km} \text { long in a } 2 \text { -h period. How many metric tons }} \\ {\left(1 \text { metric ton }=10^{3} \mathrm{kg}\right) \text { of water fell on the city? }\left(1 \mathrm{cm}^{3} \text { of }\right.} \\ {\text { water has a mass of } 1 \mathrm{g}=10^{-3} \mathrm{kg} . \text { ) How many gallons }} \\ {\text { of water was this? }}\end{array} $$

Averell Hause

Carnegie Mellon University

Problem 54

Noah's ark was ordered to be 300 cubits long, 50 cubits wide, and 30 cubits high. The cubit was a unit of measure equal to the length of a human forearm, clbow to the tip of the longest finger. Express the dimensions of Noah's ark in meters, and estimate its volume $\left(\mathrm{m}^{3}\right)$ .

Zachary Warner

Numerade Educator

Problem 55

Estimate how many days it would take to walk around the world, assuming 10 h walking per day at 4 $\mathrm{km} / \mathrm{h}$ .

Averell Hause

Carnegie Mellon University

Problem 56

One liter $\left(1000 \mathrm{cm}^{3}\right)$ of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the oil slick. Assume the oil molecules have a diameter of $2 \times 10^{-10} \mathrm{m}$ .

Zachary Warner

Numerade Educator

Problem 57

Jean camps beside a wide river and wonders how wide it is She spots a large rock on the bank directly across from her. She then walks upstream until she judges that the angle between her and the rock, which she can still sce clearly, is now at an angle of $30^{\circ}$ downstream (Fig. 16). Jean measures her stride to be about 1 yard long. The distance back to her camp is 120 strides. About how
yards and in meters, yards and in meters, is the river?

Averell Hause

Carnegie Mellon University

Problem 58

A watch manufacturer claims that its watches gain or lose no more than 8 seconds in a year. How accurate is this watch, expressed as a percentage?

Zachary Warner

Numerade Educator

Problem 59

$$ \begin{array}{l}{\text { An angstrom (symbol } \mathrm{A} ) \text { is a unit of length, defined as }} \\ {10^{-10} \mathrm{m}, \text { which is on the order of the diameter of an atom. }} \\ {\text { (a) How many nanometers are in } 1.0 \text { angstrom? (b) How }} \\ {\text { many femtometers or fermis (the common unit of length in }}\end{array} $$ nuclear physics are in 1.0 angstrom? $(c)$ How many
angstroms are in 1.0 $\mathrm{m} ?(d)$ How many angstroms are in 1.0 light-year (sce Problem 21$)$ ?

Averell Hause

Carnegie Mellon University

Problem 60

The diameter of the Moon is 3480 $\mathrm{km}$ . What is the volume of the Moon? How many Moons would be needed to create a volume equal to that of Earth?

Zachary Warner

Numerade Educator

Problem 61

Determine the peroent uncertainty in $\theta,$ and in $\sin \theta,$ when
(a) $\theta=15.0^{\circ} \pm 0.5^{\circ},(b) \quad \theta=75.0^{\circ} \pm 0.5^{\circ} .$

Averell Hause

Carnegie Mellon University

Problem 62

If you began walking along one of Earth's lines of longitude and walked north until you had changed latitude by 1 minute of arc (there are 60 minutes per degrce), how far would you have walked (in milcs)? This distance is called a "nautical mile."

Zachary Warner

Numerade Educator

Problem 63

Make a rough cstimate of the volume of your body (in m').

Averell Hause

Carnegie Mellon University

Problem 64

Estimate the number of bus drivers $(a)$ in Washington, D.C. and $(b)$ in your town.

Supratim Pal

Numerade Educator

Problem 65

$$
\begin{array}{c}{\text { The American Lung Association gives the following formula }} \\ {\text { for an average person's expected lung capacity } V \text { (in liters, }} \\ {\text { where } 1 \mathrm{L}=10^{3} \mathrm{cm}^{3} ) \text { : }} \\ {\quad V=4.1 \mathrm{H}-0.018 \mathrm{A}-2.69}\end{array}
$$

Averell Hause

Carnegie Mellon University

Problem 66

$$ \begin{array}{l}{\text { The density of an object is defined as its mass divided by its }} \\ {\text { volume. Suppose the mass and volume of a rock are }} \\ {\text { measured to be } 8 \mathrm{g} \text { and } 2.8325 \mathrm{cm}^{3} . \text { To the correct number }} \\ {\text { of significant figures, determine the rock's density. }}\end{array} $$

Zachary Warner

Numerade Educator

Problem 67

To the correct number of significant figures, use the information inside the front cover of this book to determine the ratio of (a) the surface area of Earth compared to the surface area of the Moon; (b) the volume of Earth compared to the volume of the Moon.

Breanna Ollech

Numerade Educator

Problem 68

One mole of atoms consists of $6.02 \times 10^{23}$ individual atoms. If a mole of atoms were spread uniformly over the surface of the Earth, how many atoms would there be per square meter?

Zachary Warner

Numerade Educator

Problem 69

Recent findings in astrophysics suggest that the observable Universe can be modeled as a sphere of radius $R=13.7 \times 10^{\circ}$ light-years with an average mass density of about $1 \times 10^{-26} \mathrm{kg} / \mathrm{m}^{3}$ , where only about 4$\%$ of the Universe's total mass is due to "ordinary" matter (such as protons, neutrons, and electrons). Use this information to estimate the total mass of ordinary matter in the observable Universe. (1 light-year =9.46 \times $10^{15} \mathrm{m.}$ .

Averell Hause

Carnegie Mellon University