Physics Principles with Applications

Douglas C. Giancoli

Chapter 1

Introduction, Measurement, Estimating - all with Video Answers

Educators

+ 2 more educators

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

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

Sheh Lit Chang

University of Washington

Problem 3

(I) Write the following numbers in powers of ten notation: $(a) 1.156,(b) 21.8,(c) 0.0068,(d) 27.635,(e) 0.219$ and $(f) 444$

Donald Albin

Numerade Educator

Problem 4

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

Mukesh Devi

Numerade Educator

Problem 5

(II) What, approximately, is the percent uncertainty for the measurement given as 1.57 $\mathrm{m}^{2} ?$

Supratim Pal

Numerade Educator

Problem 6

(II) What is the percent uncertainty in the measurement $3.76 \pm 0.25 \mathrm{m} ?$

Donald Albin

Numerade Educator

Problem 7

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

Donald Albin

Numerade Educator

Problem 8

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

Averell Hause

Carnegie Mellon University

Problem 9

(II) Multiply $2.079 \times 10^{2} \mathrm{m}$ by $0.082 \times 10^{-1}$ , taking into account significant figures.

Donald Albin

Numerade Educator

Problem 10

(III) What is the area, and its approximate uncertainty, of a circle of radius $3.8 \times 10^{4} \mathrm{cm} ?$

Donald Albin

Numerade Educator

Problem 11

(III) What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is $r=$
$2.86 \pm 0.09 \mathrm{m} ?$

Donald Albin

Numerade Educator

Problem 12

(I) Write the following as full (decimal) numbers with standard units: $(a) \quad 286.6 \mathrm{mm},$ (b) $85 \mu V,$ (c) 760 $\mathrm{mg}$ $(d) 60.0 \mathrm{ps},(e) 22.5 \mathrm{fm},(f) 2.50$ gigavolts.

Donald Albin

Numerade Educator

Problem 13

(1) Express the following using the prefixes of Table $1-4$ :
(a) $1 \times 10^{6}$ volts, $(b) 2 \times 10^{-6}$ meters, $(c) 6 \times 10^{3}$ days,
(d) $18 \times 10^{2}$ bucks, and $(e) 8 \times 10^{-9}$ pieces.

Donald Albin

Numerade Educator

Problem 14

(I) Determine your own height in meters, and your mass in $\mathrm{kg.}$

Donald Albin

Numerade Educator

Problem 15

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

Sheh Lit Chang

University of Washington

Problem 16

(II) What is the conversion factor between $(a) \mathrm{ft}^{2}$ and $\mathrm{yd}^{2}$ , (b) $\mathrm{m}^{2}$ and $\mathrm{ft}^{2} ?$

Donald Albin

Numerade Educator

Problem 17

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

Vipender Yadav

Numerade Educator

Problem 18

(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?

Sheh Lit Chang

University of Washington

Problem 19

(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 20

(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 21

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

Zachary Warner

Numerade Educator

Problem 22

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

Ma Ednelyn Lim

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

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

Averell Hause

Carnegie Mellon University

Problem 25

(II) Estimate how many books can be shelved in a college library with 3500 square meters 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 one, on average.

Rachel Wellington

Rachel Wellington

University of Georgia

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 how long it would take one person to mow a football field using an ordinary home lawn mower (Fig. $1-13 )$ . Assume the mower moves with a 1 $\mathrm{km} / \mathrm{h}$ speed, and has a 0.5 $\mathrm{m}$ width.

Averell Hause

Carnegie Mellon University

Problem 28

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

Averell Hause

Carnegie Mellon University

Problem 29

(II) Make a rough estimate of the volume of your body $\left(\text { in } \mathrm{cm}^{3}\right) .$

Donald Albin

Numerade Educator

Problem 30

(II) Make a rough estimate, for a typical suburban house, of the $\%$ of its outside wall area that consists of window area.

Donald Albin

Numerade Educator

Problem 31

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

Donald Albin

Numerade Educator

Problem 32

(II) The speed, $v,$ of an object is given by the equation $v=A t^{3}-B t,$ where $t$ refers to time. What are the dimensions of $A$ and $B ?$

Donald Albin

Numerade Educator

Problem 33

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

Vishal Gupta

Numerade Educator

Problem 34

Global positioning satellites (GPS) can be used to determine positions with great accuracy. The system works by determining the distance between the observer and each of several satellites orbiting Earth. If one of the satellites is at a distance of $20,000 \mathrm{km}$ from you, what percent accuracy in the distance is required if we desire a 2 -meter uncertainty? How many significant figures do we need to
have in the distance?

Brandy Heflin

Numerade Educator

Problem 35

Computer chips (Fig. $1-14$ ) are etched on circular silicon wafers of thickness 0.60 $\mathrm{mm}$ that are sliced from a solid cylindrical silicon crystal of length 30 $\mathrm{cm}$ . If each wafer can
hold 100 chips, what is the maximum number of chips that can be produced from one entire cylinder?
figure can't copy

Donald Albin

Numerade Educator

Problem 36

(a) How many seconds 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?

Donald Albin

Numerade Educator

Problem 37

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

Averell Hause

Carnegie Mellon University

Problem 38

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

Donald Albin

Numerade Educator

Problem 39

Use Table $1-3$ to estimate the total number of protons or neutrons in $(a)$ a bacterium, $(b)$ a DNA molecule, $(c)$ the human body, $(d)$ our Galaxy.

Donald Albin

Numerade Educator

Problem 40

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 41

Estimate the number of gumballs in the machine of Fig. $1-15 .$
figure can't copy

Donald Albin

Numerade Educator

Problem 42

An average family of four uses roughly 1200 liters (about 300 gallons) of water per day. (One liter = 1000 $\mathrm{cm}^{3}$ ) How much depth would a lake lose per year if it uniformly covered an area of 50 square kilometers and supplied a local town with a population of $40,000$ people? Consider only population uses, and neglect evaporation and so on.

Sarah Parrigin

Numerade Educator

Problem 43

How big is a ton? That is, what is the volume of some- thing 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 $\mathrm{ft}$ , 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. $]$

Donald Albin

Numerade Educator

Problem 44

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

Donald Albin

Numerade Educator

Problem 45

Hold a pencil in front of your eye at a position where its blunt end just blocks out the Moon (Fig. $1-16$ ).
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 46

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

Averell Hause

Carnegie Mellon University

Problem 47

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, elbow 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 48

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 49

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 see clearly, is now at an angle of $30^{\circ}$ downstream (Fig. $1-17 )$ . Jean measures her stride to be about one yard long. The distance back to her camp is 120 strides. About how far across, both in yards and in meters, is the river?
figure can't copy

Donald Albin

Numerade Educator

Problem 50

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 51

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 52

An angstrom (symbol $\hat{\mathrm{A}} )$ is a unit of length, defined as $10^{-10} \mathrm{m},$ which is on the order of the diameter of an atom.
(a) How many nanometers are in 1.0 angstrom?
(b) How many femtometers or fermis (the common unit of length in nuclear physics) are in 1.0 angstrom? (c) How many angstroms are in 1.0 meter?
(d) How many angstroms are in 1.0 light-year (see Problem 22)?

Donald Albin

Numerade Educator

Problem 53

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

Averell Hause

Carnegie Mellon University

Problem 54

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

Donald Albin

Numerade Educator