Physics

Robert Resnick, David Halliday, Kenneth S. Krane

Chapter 1

Measurement - all with Video Answers

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Chapter Questions

Problem 1

Use the prefixes in Table $1-2$ to express (a) $10^{6}$ phones, $(b)$ $10^{-6}$ phones, (c) $10^{1}$ cards, (d) $10^{9}$ lows, (e) $10^{12}$ bulls, $(f)$ $10^{-1}$ mates, $(g) 10^{-2}$ pedes,
(h) $10^{-9}$ Nannettes, (i) $10^{-12}$ boos,
( j) $10^{-18}$ boys, $(k) 2 \times 10^{2}$ withits, $(l) 2 \times 10^{3}$ mockingbirds. Now that you have the idea, invent a few more similar expressions. (See p. 61 of $A$ Random Walk in Science, compiled by
R. L. Weber; Crane, Russak \& Co., New York, 1974.)

Jonathon Brumley

Jonathon Brumley

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Problem 2

Some of the prefixes of the SI units have crept into everyday language. ( $a$ ) What is the weekly equivalent of an annual salary of $36 \mathrm{~K}(=36 \mathrm{k} \$) ?(b)$ A lottery awards 10 megabucks as the top prize, payable over 20 years. How much is received in each monthly check? ( $c$ ) The hard disk of a computer has a capacity of $30 \mathrm{~GB}$ ( $=30$ gigabytes). At 8 bytes/word, how many words can it store?

Dominador Tan

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Problem 3

Enrico Fermi once pointed out that a standard lecture period $(50 \mathrm{~min})$ is close to 1 microcentury. How long is a microcentury in minutes, and what is the percentage difference from Fermi's approximation?

Dominador Tan

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Problem 4

New York and Los Angeles are about $3000 \mathrm{mi}$ apart; the time difference between these two cities is 3 h. Calculate the circumference of the Earth.

Dominador Tan

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Problem 5

A convenient substitution for the number of seconds in a year is $\pi$ times $10^{7}$. To within what percentage error is this correct?

Dominador Tan

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Problem 6

(a) A unit of time sometimes used in microscopic physics is the shake. One shake equals $10^{-8} \mathrm{~s}$. Are there more shakes in a second than there are seconds in a year? (b) Humans have existed for about $10^{6}$ years, whereas the universe is about $10^{10}$ years old. If the age of the universe is taken to be 1 day, for how many seconds have humans existed?

Dominador Tan

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Problem 7

In two different track meets, the winners of the mile race ran their races in $3 \mathrm{~min} 58.05 \mathrm{~s}$ and $3 \mathrm{~min} 58.20 \mathrm{~s}$. In order to conclude that the runner with the shorter time was indeed faster, what is the maximum tolerable error, in feet, in laying out the distances?

Matthew Baker

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Problem 8

A certain pendulum clock (with a 12 -h dial) happens to gain 1 min/day. After setting the clock to the correct time, how long must one wait until it again indicates the correct time?

Matthew Baker

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Problem 9

The age of the universe is about $5 \times 10^{17} \mathrm{~s} ;$ the shortest light pulse produced in a laboratory (1990) lasted for only $6 \times$ $10^{-15} \mathrm{~s}$ (see Table $1-3$ ). Identify a physically meaningful time interval approximately halfway between these two on a logarithmic scale.

Ashwin Banarsee

Ashwin Banarsee

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Problem 10

Assuming that the length of the day uniformly increases by $0.001 \mathrm{~s}$ in a century, calculate the cumulative effect on the measure of time over 20 centuries. Such a slowing down of the Earth's rotation is indicated by observations of the occurrences of solar eclipses during this period.

Matthew Baker

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Problem 11

The time it takes the Moon to return to a given position as seen against the background of fixed stars, $27.3$ days, is called a sidereal month. The time interval between identical phases of the Moon is called a lunar month. The lunar month is longer than a sidereal month. Why and by how much?

Matthew Baker

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Problem 12

Your French pen pal Pierre writes to say that he is $1.9 \mathrm{~m}$ tall. What is his height in British units?

Dominador Tan

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Problem 13

(a) In track meets both 100 yards and 100 meters are used as distances for dashes. Which is longer? By how many meters is it longer? By how many feet? (b) Track and field records are kept for the mile and the so-called metric mile $(1500 \mathrm{me}-$ ters). Compare these distances.

Dominador Tan

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Problem 14

The stability of the cesium clock used as an atomic time standard is such that two cesium clocks would gain or lose $1 \mathrm{~s}$ with respect to each other in about $300,000 \mathrm{y}$. If this same precision were applied to the distance between New York and San Francisco ( $2572 \mathrm{mi}$ ), by how much would successive measurements of this distance tend to differ?

Matthew Baker

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Problem 15

Antarctica is roughly semicircular in shape with a radius of $2000 \mathrm{~km}$. The average thickness of the ice cover is $3000 \mathrm{~m}$. How many cubic centimeters of ice does Antarctica contain? (Ignore the curvature of the Earth.)

Dominador Tan

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Problem 16

A unit of area, often used in expressing areas of land, is the hectare, defined as $10^{4} \mathrm{~m}^{2}$. An open-pit coal mine consumes 77 hectares of land, down to a depth of $26 \mathrm{~m}$, each year. What volume of earth, in cubic kilometers, is removed in this time?

Dominador Tan

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Problem 17

Earth is approximately a sphere of radius $6.37 \times 10^{6} \mathrm{~m} .(a)$ What is its circumference in kilometers? (b) What is its surface area in square kilometers? ( $c$ ) What is its volume in cubic kilometers?

Rashmi Sinha

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Problem 18

The approximate maximum speeds of various animals follow, but in different units of speed. Convert these data to $\mathrm{m} / \mathrm{s}$, and thereby arrange the animals in order of increasing maximum speed: squirrel, $19 \mathrm{~km} / \mathrm{h}$; rabbit, 30 knots; snail, $0.030 \mathrm{mi} / \mathrm{h}$; spider, $1.8 \mathrm{ft} / \mathrm{s}$; cheetah, $1.9 \mathrm{~km} / \mathrm{min}$; human, $1000 \mathrm{~cm} / \mathrm{s} ;$ fox, $1100 \mathrm{~m} / \mathrm{min} ;$ lion, $1900 \mathrm{~km} /$ day.

Ashwin Banarsee

Ashwin Banarsee

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Problem 19

A certain spaceship has a speed of $19,200 \mathrm{mi} / \mathrm{h}$. What is its speed in light-years per century?

Dominador Tan

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Problem 20

A new car is equipped with a "real-time" dashboard display of fuel consumption. A switch permits the driver to toggle back and forth between British units and SI units. However, the British display shows mi/gal while the SI version is the inverse, $\mathrm{L} / \mathrm{km}$. What SI reading corresponds to $30.0$ mi/gal?

Dominador Tan

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Problem 21

Astronomical distances are so large compared to terrestrial ones that much larger units of length are used for easy comprehension of the relative distances of astronomical objects. An astronomical unit $(\mathrm{AU})$ is equal to the average distance from Earth to the Sun, $1.50 \times 10^{8} \mathrm{~km}$. A parsec (pc) is the distance at which 1 AU would subtend an angle of 1 second of arc. A light-year (ly) is the distance that light, traveling through a vacuum with a speed of $3.00 \times 10^{5} \mathrm{~km} / \mathrm{s}$, would cover in 1 year. ( $a$ ) Express the distance from Earth to the Sun in parsecs and in light-years. (b) Express a light-year and a parsec in kilometers. Although the light-year is much used in popular writing, the parsec is the unit preferred by astronomers.

Ashwin Banarsee

Ashwin Banarsee

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Problem 22

The effective radius of a proton is about $1 \times 10^{-15} \mathrm{~m} ;$ the radius of the observable universe (given by the distance to the farthest observable quasar) is $2 \times 10^{26} \mathrm{~m}$ (see Table $1-4$ ). Identify a physically meaningful distance that is approximately halfway between these two extremes on a logarithmic scale.

Ashwin Banarsee

Ashwin Banarsee

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Problem 23

Using conversions and data in the chapter, determine the number of hydrogen atoms required to obtain $1.00 \mathrm{~kg}$ of hydrogen.

Dominador Tan

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Problem 24

One molecule of water $\left(\mathrm{H}_{2} \mathrm{O}\right)$ contains two atoms of hydrogen and one atom of oxygen. A hydrogen atom has a mass of $1.0 \mathrm{u}$ and an atom of oxygen has a mass of $16 \mathrm{u}$. ( $a$ ) What is the mass in kilograms of one molecule of water? $(b)$ How many molecules of water are in the oceans of the world? The oceans have a total mass of $1.4 \times 10^{21} \mathrm{~kg}$.

Dominador Tan

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Problem 25

In continental Europe, one "pound" is half a kilogram. Which is the better buy: one Paris pound of coffee for $$\$ 9.00$$ or one New York pound of coffee for $$\$ 7.20 ?$$

Willis James

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Problem 26

A room has dimensions of $21 \mathrm{ft} \times 13 \mathrm{ft} \times 12 \mathrm{ft}$. What is the mass of the air it contains? The density of air at room temperature and normal atmospheric pressure is $1.21 \mathrm{~kg} / \mathrm{m}^{3}$.

Dominador Tan

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Problem 27

A typical sugar cube has an edge length of $1 \mathrm{~cm} .$ If you had a cubical box that contained 1 mole of sugar cubes, what would its edge length be?

Dominador Tan

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Problem 28

A person on a diet loses $0.23 \mathrm{~kg}$ (corresponding to about $0.5$ lb) per week. Express the mass loss rate in milligrams per second.

Dominador Tan

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Problem 29

For the period $1960-1983$, the meter was defined to be $1,650,763.73$ wavelengths of a certain orange-red light emitted by krypton atoms. Compute the distance in nanometers corresponding to one wavelength. Express your result using the proper number of significant figures.

Dominador Tan

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Problem 30

(a) Evaluate $37.76+0.132$ to the correct number of significant figures. (b) Evaluate $16.264-16.26325$ to the correct number of significant figures.

Dominador Tan

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Problem 31

Porous rock through which groundwater can move is called an aquifer. The volume $V$ of water that, in time $t$, moves through a cross section of area $A$ of the aquifer is given by
$$
V / t=K A H / L
$$
where $H$ is the vertical drop of the aquifer over the horizontal distance $L$; see Fig. $1-5 .$ This relation is called Darcy's law. The quantity $K$ is the hydraulic conductivity of the aquifer. What are the SI units of $K ?$

Matthew Baker

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Problem 32

In Sample Problem $1-5$, the constants $h, G$, and $c$ were combined to obtain a quantity with the dimensions of time. Repeat the derivation to obtain a quantity with the dimensions of length, and evaluate the result numerically. Ignore any dimensionless constants. This is the Planck length, the size of the observable universe at the Planck time.

Cyra Jelle Calleja

Cyra Jelle Calleja

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Problem 33

Repeat the procedure of Exercise 32 to obtain a quantity with the dimensions of mass. This gives the Planck mass, the mass of the observable universe at the Planck time.

Cyra Jelle Calleja

Cyra Jelle Calleja

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