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Fundamentals of Physics

David Halliday, Robert Resnick, Jearl Walker

Chapter 1

Measurement - all with Video Answers

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Chapter Questions

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Problem 1

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

Rashmi Sinha
Rashmi Sinha
Numerade Educator
01:31

Problem 2

A gry is an old English measure for length, defined as $1 / 10$ of a line, where line is another old English measure for length, defined as $1 / 12$ inch. A common measure for length in the publishing business is a point, defined as $1 / 72$ inch. What is an area of $0.50$ gry $^{2}$ in points squared (points $\left.^{2}\right)$ ?

Narayan Hari
Narayan Hari
Numerade Educator
03:48

Problem 3

The micrometer $(1 \mu \mathrm{m})$ is often called the micron. (a) How many microns make up $1.0 \mathrm{~km}$ ? (b) What fraction of a centimeter equals $1.0 \mu \mathrm{m} ?(\mathrm{c})$ How many microns are in $1.0 \mathrm{yd}$ ?

Zachary Warner
Zachary Warner
Numerade Educator
02:28

Problem 4

Spacing in this book was generally done in units of points and picas: 12 points $=1$ pica, and 6 picas $=1$ inch. If a figure was misplaced in the page proofs by $0.80 \mathrm{~cm}$, what was the misplacement in (a) picas and (b) points?

Nishant Kumar
Nishant Kumar
Numerade Educator
03:23

Problem 5

Horses are to race over a certain English meadow for a distance of $4.0$ furlongs. What is the race distance in (a) rods and (b) chains? (1 furlong $=201.168 \mathrm{~m}, 1$ rod $=5.0292 \mathrm{~m}$, and 1 chain $=20.117 \mathrm{~m}$. )

Zachary Warner
Zachary Warner
Numerade Educator
05:29

Problem 6

You can easily convert common units and measures electronically, but you still should be able to use a conversion table, such as those in Appendix D. Table $1-6$ is part of a conversion table for a system of volume measures once common in Spain; a volume of 1 fanega is equivalent to $55.501 \mathrm{dm}^{3}$ (cubic decimeters). To complete the table, what numbers (to three significant figures) should be entered in (a) the cahiz column, (b) the fanega column, (c) the cuartilla column, and (d) the almude column, starting with the top blank? Express $7.00$ almudes in (e) medios, (f) cahizes, and (g) cubic centimeters $\left(\mathrm{cm}^{3}\right)$.
Table 1-6 Problem 6
$$
\begin{array}{lccccc}
\hline & \text { cahiz } & \text { fanega } & \text { cuartilla } & \text { almude } & \text { medio } \\
\hline 1 \text { cahiz }= & 1 & 12 & 48 & 144 & 288 \\
1 \text { fanega }= & & 1 & 4 & 12 & 24 \\
1 \text { cuartilla }= & & & 1 & 3 & 6 \\
1 \text { almude }= & & & & 1 & 2 \\
1 \text { medio }= & & & & & 1 \\
\hline
\end{array}
$$

Donald Albin
Donald Albin
Numerade Educator
03:07

Problem 7

Hydraulic engineers in the United States often use, as a unit of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre of land to a depth of $1 \mathrm{ft}$. A severe thunderstorm dumped $2.0$ in. of rain in 30 min on a town of area 26 $\mathrm{km}^{2}$. What volume of water, in acre-feet, fell on the town?

Zachary Warner
Zachary Warner
Numerade Educator
03:51

Problem 8

Harvard Bridge, which connects MIT with its fraternities across the Charles River, has a length of $364.4$ Smoots plus one ear. The unit of one Smoot is based on the length of Oliver Reed Smoot, Jr., class of 1962, who was carried or dragged length by length across the bridge so that other pledge members of the Lambda Chi Alpha fraternity could mark off (with paint) 1-Smoot lengths along the bridge. The marks have been repainted biannually by fraternity pledges since the initial measurement, usually during times of traffic congestion so that the police cannot easily interfere. (Presumably, the police were originally upset because the Smoot is not an SI base unit, but these days they seem to have accepted the unit.) Figure $1-4$ shows three parallel paths, measured in Smoots (S), Willies (W), and Zeldas (Z). What is the length of $50.0$ Smoots in (a) Willies and (b) Zeldas?

Abhishek Jana
Abhishek Jana
Numerade Educator
01:13

Problem 9

Antarctica is roughly semicircular, with a radius of $2000 \mathrm{~km}$ (Fig. $1-5)$. The average thickness of its ice cover is $3000 \mathrm{~m}$. How many cubic centimeters of ice does Antarctica contain? (Ignore the curvature of Earth.)

Zachary Warner
Zachary Warner
Numerade Educator
01:04

Problem 10

Until 1883, every city and town in the United States kept its own local time. Today, travelers reset their watches only when the time change equals $1.0 \mathrm{~h}$. How far, on the average, must you travel in degrees of longitude between the time-zone boundaries at which your watch must be reset by $1.0 \mathrm{~h}$ ? (Hint: Earth rotates $360^{\circ}$ in about $24 \mathrm{~h}$.)

Abhishek Jana
Abhishek Jana
Numerade Educator
03:25

Problem 11

For about 10 years after the French Revolution, the French government attempted to base measures of time on multiples of ten: One week consisted of 10 days, one day consisted of 10 hours, one hour consisted of 100 minutes, and one minute consisted of 100 seconds. What are the ratios of (a) the French decimal week to the standard week and (b) the French decimal second to the standard second?

Zachary Warner
Zachary Warner
Numerade Educator
03:50

Problem 12

The fastest growing plant on record is a Hesperoyucca whipplei that grew $3.7 \mathrm{~m}$ in 14 days. What was its growth rate in micrometers per second?

Abhishek Jana
Abhishek Jana
Numerade Educator
05:52

Problem 13

Three digital clocks $A, B$, and $C$ run at different rates and do not have simultaneous readings of zero. Figure $1-6$ shows simultaneous readings on pairs of the clocks for four occasions. (At the earliest occasion, for example, $B$ reads $25.0 \mathrm{~s}$ and $C$ reads $92.0$ s.) If two events are $600 \mathrm{~s}$ apart on clock $A$, how far apart are they on (a) clock $B$ and (b) clock $C ?$ (c) When clock $A$ reads $400 \mathrm{~s}$, what does clock $B$ read? (d) When clock $C$ reads $15.0 \mathrm{~s}$, what does clock $B$ read? (Assume negative readings for prezero times.)

Zachary Warner
Zachary Warner
Numerade Educator
05:52

Problem 14

A lecture period $(50 \mathrm{~min})$ is close to 1 microcentury. (a) How long is a microcentury in minutes? (b) Using
percentage difference $=\left(\frac{\text { actual }-\text { approximation }}{\text { actual }}\right) 100$
find the percentage difference from the approximation.

Abhishek Jana
Abhishek Jana
Numerade Educator
01:52

Problem 15

A fortnight is a charming English measure of time equal to $2.0$ weeks (the word is a contraction of "fourteen nights"). That is a nice amount of time in pleasant company but perhaps a painful string of microseconds in unpleasant company. How many microseconds are in a fortnight?

Zachary Warner
Zachary Warner
Numerade Educator
05:41

Problem 16

Time standards are now based on atomic clocks. A promising second standard is based on pulsars, which are rotating neutron stars (highly compact stars consisting only of neutrons). Some rotate at a rate that is highly stable, sending out a radio beacon that sweeps briefly across Earth once with each rotation, like a lighthouse beacon. Pulsar PSR $1937+21$ is an example; it rotates once every $1.55780644887275 \pm 3 \mathrm{~ms}$, where the trailing $\pm 3$ indicates the uncertainty in the last decimal place (it does not mean $\pm 3 \mathrm{~ms}$ ). (a) How many rotations does PSR $1937+21$ make in $7.00$ days? (b) How much time does the pulsar take to rotate exactly one million times and (c) what is the associated uncertainty?

Abhishek Jana
Abhishek Jana
Numerade Educator
16:33

Problem 17

Five clocks are being tested in a laboratory. Exactly at noon, as determined by the WWV time signal, on successive days of a week the clocks read as in the following table. Rank the five clocks according to their relative value as good timekeepers, best to worst. Justify your choice.
$$
\begin{array}{lccccccc}
\hline \text { Clock } & \text { Sun. } & \text { Mon. } & \text { Tues. } & \text { Wed. } & \text { Thurs. } & \text { Fri. } & \text { Sat. } \\
\hline \text { A } & 12: 36: 40 & 12: 36: 56 & 12: 37: 12 & 12: 37: 27 & 12: 37: 44 & 12: 37: 59 & 12: 38: 14 \\
\text { B } & 11: 59: 59 & 12: 00: 02 & 11: 59: 57 & 12: 00: 07 & 12: 00: 02 & 11: 59: 56 & 12: 00: 03 \\
\text { C } & 15: 50: 45 & 15: 51: 43 & 15: 52: 41 & 15: 53: 39 & 15: 54: 37 & 15: 55: 35 & 15: 56: 33 \\
\text { D } & 12: 03: 59 & 12: 02: 52 & 12: 01: 45 & 12: 00: 38 & 11: 59: 31 & 11: 58: 24 & 11: 57: 17 \\
\text { E } & 12: 03: 59 & 12: 02: 49 & 12: 01: 54 & 12: 01: 52 & 12: 01: 32 & 12: 01: 22 & 12: 01: 12 \\
\hline
\end{array}
$$

Donald Albin
Donald Albin
Numerade Educator
05:05

Problem 18

Because Earth's rotation is gradually slowing, the length of each day increases: The day at the end of $1.0$ century is $1.0 \mathrm{~ms}$ longer than the day at the start of the century. In 20 centuries, what is the total of the daily increases in time?

Abhishek Jana
Abhishek Jana
Numerade Educator
03:36

Problem 19

Suppose that, while lying on a beach near the equator watching the Sun set over a calm ocean, you start a stopwatch just as the top of the Sun disappears. You then stand, elevating your eyes by a height $H=1.70 \mathrm{~m}$, and stop the watch when the top of the Sun again disappears. If the elapsed time is $t=11.1 \mathrm{~s}$, what is the radius $r$ of Earth?

Zachary Warner
Zachary Warner
Numerade Educator
06:20

Problem 20

The record for the largest glass bottle was set in 1992 by a team in Millville, New Jersey-they blew a bottle with a volume of 193 U.S. fluid gallons. (a) How much short of $1.0$ million cubic centimeters is that? (b) If the bottle were filled with water at the leisurely rate of $1.8 \mathrm{~g} / \mathrm{min}$, how long would the filling take? Water has a density of $1000 \mathrm{~kg} / \mathrm{m}^{3}$.

Abhishek Jana
Abhishek Jana
Numerade Educator
01:17

Problem 21

Earth has a mass of $5.98 \times 10^{24} \mathrm{~kg}$. The average mass of the atoms that make up Earth is $40 \mathrm{u}$. How many atoms are there in Earth?

Anand Jangid
Anand Jangid
Numerade Educator
07:17

Problem 22

Gold, which has a density of $19.32 \mathrm{~g} / \mathrm{cm}^{3}$, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold, with a mass of $27.63 \mathrm{~g}$, is pressed into a leaf of $1.000 \mu \mathrm{m}$ thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius $2.500$ $\mu \mathrm{m}$, what is the length of the fiber?

Abhishek Jana
Abhishek Jana
Numerade Educator
03:04

Problem 23

(a) Assuming that water has a density of exactly $1 \mathrm{~g} / \mathrm{cm}^{3}$, find the mass of one cubic meter of water in kilograms.
(b) Suppose that it takes $10.0 \mathrm{~h}$ to drain a container of $5700 \mathrm{~m}^{3}$ of water. What is the "mass flow rate," in kilograms per second, of water from the container?

Zachary Warner
Zachary Warner
Numerade Educator
06:21

Problem 24

Grains of fine California beach sand are approximately spheres with an average radius of $50 \mu \mathrm{m}$ and are made of silicon dioxide, which has a density of $2600 \mathrm{~kg} / \mathrm{m}^{3} .$ What mass of sand grains would have a total surface area (the total area of all the individual spheres) equal to the surface area of a cube $1.00 \mathrm{~m}$ on an edge?

Abhishek Jana
Abhishek Jana
Numerade Educator
02:56

Problem 25

During heavy rain, a section of a mountainside measuring $2.5 \mathrm{~km}$ horizontally, $0.80 \mathrm{~km}$ up along the slope, and $2.0 \mathrm{~m}$ deep slips into a valley in a mud slide. Assume that the mud ends up uniformly distributed over a surface area of the valley measuring $0.40 \mathrm{~km} \times 0.40 \mathrm{~km}$ and that mud has a density of $1900 \mathrm{~kg} / \mathrm{m}^{3}$. What is the mass of the mud sitting above a $4.0 \mathrm{~m}^{2}$ area of the valley floor?

Zachary Warner
Zachary Warner
Numerade Educator
07:54

Problem 26

One cubic centimeter of a typical cumulus cloud contains 50 to 500 water drops, which have a typical radius of $10 \mu \mathrm{m}$. For that range, give the lower value and the higher value, respectively, for the following. (a) How many cubic meters of water are in a cylindrical cumulus cloud of height $3.0 \mathrm{~km}$ and radius $1.0 \mathrm{~km} ?$ (b) How many 1-liter pop bottles would that water fill? (c) Water has a density of $1000 \mathrm{~kg} / \mathrm{m}^{3}$. How much mass does the water in the cloud have?

Abhishek Jana
Abhishek Jana
Numerade Educator
03:44

Problem 27

Iron has a density of $7.87 \mathrm{~g} / \mathrm{cm}^{3}$, and the mass of an iron atom is $9.27 \times 10^{-26} \mathrm{~kg}$. If the atoms are spherical and tightly packed, (a) what is the volume of an iron atom and (b) what is the distance between the centers of adjacent atoms?

Zachary Warner
Zachary Warner
Numerade Educator
02:41

Problem 28

A mole of atoms is $6.02 \times 10^{23}$ atoms. To the nearest order of magnitude, how many moles of atoms are in a large domestic cat? The masses of a hydrogen atom, an oxygen atom, and a carbon atom are $1.0 \mathrm{u}, 16 \mathrm{u}$, and $12 \mathrm{u}$, respectively. (Hint: Cats are sometimes known to kill a mole.)

Abhishek Jana
Abhishek Jana
Numerade Educator
03:04

Problem 29

On a spending spree in Malaysia, you buy an ox with a weight of $28.9$ piculs in the local unit of weights: 1 picul = 100 gins, $1 \operatorname{gin}=16$ tahils, 1 tahil $=10$ chees, and 1 chee $=$ 10 hoons. The weight of 1 hoon corresponds to a mass of $0.3779$ g. When you arrange to ship the ox home to your astonished family, how much mass in kilograms must you declare on the shipping manifest? (Hint: Set up multiple chain-link conversions.)

Zachary Warner
Zachary Warner
Numerade Educator
02:00

Problem 30

Water is poured into a container that has a small leak. The mass $m$ of the water is given as a function of time $t$ by $m=5.00 t^{0.8}-3.00 t+20.00$, with $t \geq 0, m$ in grams, and $t$ in seconds. (a) At what time is the water mass greatest, and (b) what is that greatest mass? In kilograms per minute, what is the rate of mass change at (c) $t=2.00 \mathrm{~s}$ and $($ d $) t=5.00 \mathrm{~s}$ ?

Donald Albin
Donald Albin
Numerade Educator
03:04

Problem 31

A vertical container with base area measuring $14.0 \mathrm{~cm}$ by $17.0 \mathrm{~cm}$ is being filled with identical pieces of candy, each with a volume of $50.0 \mathrm{~mm}^{3}$ and a mass of $0.0200 \mathrm{~g}$. Assume that the volume of the empty spaces between the candies is negligible. If the height of the candies in the container increases at the rate of $0.250 \mathrm{~cm} / \mathrm{s}$, at what rate (kilograms per minute) does the mass of the candies in the container increase?

Zachary Warner
Zachary Warner
Numerade Educator
05:10

Problem 32

In the United States, a doll house has the scale of $1: 12$ of a real house (that is, each length of the doll house is $\frac{1}{12}$ that of the real house) and a miniature house (a doll house to fit within a doll house) has the scale of $1: 144$ of a real house. Suppose a real house (Fig. 1-7) has a front length of $20 \mathrm{~m}$, a depth of $12 \mathrm{~m}$, a height of $6.0 \mathrm{~m}$, and a standard sloped roof (vertical triangular faces on the ends) of height $3.0 \mathrm{~m}$. In cubic meters, what are the volumes of the corresponding (a) doll house and (b) miniature house?

Abhishek Jana
Abhishek Jana
Numerade Educator
04:39

Problem 33

A ton is a measure of volume frequently used in shipping, but that use requires some care because there are at least three types of tons: A displacement ton is equal to 7 barrels bulk, a freight ton is equal to 8 barrels bulk, and a register ton is equal to 20 barrels bulk. A barrel bulk is another measure of volume: 1 barrel bulk $=0.1415 \mathrm{~m}^{3}$. Suppose you spot a shipping order for "73 tons" of M\&M candies, and you are certain that the client who sent the order intended "ton" to refer to volume (instead of weight or mass, as discussed in Chapter 5 ). If the client actually meant displacement tons, how many extra U.S. bushels of the candies will you erroneously ship if you interpret the order as (a) 73 freight tons and (b) 73 register tons? $\left(1 \mathrm{~m}^{3}=28.378 \quad\right.$ U.S. bushels.)

Zachary Warner
Zachary Warner
Numerade Educator
07:12

Problem 34

Two types of barrel units were in use in the $1920 \mathrm{~s}$ in the United States. The apple barrel had a legally set volume of 7056 cubic inches; the cranberry barrel, 5826 cubic inches. If a merchant sells 20 cranberry barrels of goods to a customer who thinks he is receiving apple barrels, what is the discrepancy in the shipment volume in liters?

Elyse Gonzalez
Elyse Gonzalez
Numerade Educator
02:29

Problem 35

An old English children's rhyme states, "Little Miss Muffet sat on a tuffet, eating her curds and whey, when along came a spider who sat down beside her...." The spider sat down not because of the curds and whey but because Miss Muffet had a stash of 11 tuffets of dried flies. The volume measure of a tuffet is given by 1 tuffet $=2$ pecks $=0.50$ Imperial bushel, where 1 Imperial bushel $=36.3687$ liters (L). What was Miss Muffet's stash in (a) pecks, (b) Imperial bushels, and (c) liters?

Zachary Warner
Zachary Warner
Numerade Educator
12:46

Problem 36

36 Table $1-7$ shows some old measures of liquid volume. To complete the table, what numbers (to three significant figures) should be entered in (a) the wey column, (b) the chaldron column, (c) the bag column, (d) the pottle column, and (e) the gill column, starting from the top down? (f) The volume of 1 bag is equal to $0.1091 \mathrm{~m}^{3} .$ If an old story has a witch cooking up some vile liquid in a cauldron of volume $1.5$ chaldrons, what is the volume in cubic meters?
Table 1-7 Problem 36
$$
\begin{array}{lccccc}
\hline & \text { wey } & \text { chaldron } & \text { bag } & \text { pottle } & \text { gill } \\
\hline \text { 1 wey }= & 1 & 10 / 9 & 40 / 3 & 640 & 120240 \\
1 \text { chaldron }= & & & & & \\
1 \text { bag }= & & & & & \\
1 \text { pottle }= & & & & & \\
1 \text { gill }= & & & & & \\
\hline
\end{array}
$$

Donald Albin
Donald Albin
Numerade Educator
01:57

Problem 37

A typical sugar cube has an edge length of $1 \mathrm{~cm}$. If you had a cubical box that contained a mole of sugar cubes, what would its edge length be? (One mole $=6.02 \times 10^{23}$ units.)

Zachary Warner
Zachary Warner
Numerade Educator
04:38

Problem 38

An old manuscript reveals that a landowner in the time of King Arthur held $3.00$ acres of plowed land plus a livestock area of $25.0$ perches by $4.00$ perches. What was the total area in (a) the old unit of roods and (b) the more modern unit of square meters? Here, 1 acre is an area of 40 perches by 4 perches, 1 rood is an area of 40 perches by 1 perch, and 1 perch is the length $16.5 \mathrm{ft}$.

Abhishek Jana
Abhishek Jana
Numerade Educator
04:42

Problem 39

A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car's fuel con- sumption was at the rate of 40 miles per gallon on the open road.
The tourist does not realize that the U.K. gallon differs from the
U.S. gallon:
$$
\begin{gathered}
\text { 1 U.K. gallon }=4.5460900 \text { liters } \\
\text { 1 U.S. gallon }=3.785411 \text { 8 liters. }
\end{gathered}
$$
For a trip of 750 miles (in the United States), how many gallons of fuel does (a) the mistaken tourist believe she needs and (b) the car actually require?

Donald Albin
Donald Albin
Numerade Educator
01:26

Problem 40

Using conversions and data in the chapter, determine the number of hydrogen atoms required to obtain $1.0 \mathrm{~kg}$ of hydrogen. A hydrogen atom has a mass of $1.0 \mathrm{u}$.

Abhishek Jana
Abhishek Jana
Numerade Educator
02:01

Problem 41

A cord is a volume of cut wood equal to a stack $8 \mathrm{ft}$ long, $4 \mathrm{ft}$ wide, and $4 \mathrm{ft}$ high. How many cords are in $1.0 \mathrm{~m}^{3}$ ?

Zachary Warner
Zachary Warner
Numerade Educator
02:54

Problem 42

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 $16 \mathrm{u}$, approximately. (a) What is the mass in kilograms of one molecule of water? (b) How many molecules of water are in the world's oceans, which have an estimated total mass of $1.4 \times 10^{21} \mathrm{~kg}$ ?

Abhishek Jana
Abhishek Jana
Numerade Educator
01:55

Problem 43

A person on a diet might lose $2.3 \mathrm{~kg}$ per week. Express the mass loss rate in milligrams per second, as if the dieter could sense the second-by-second loss.

Zachary Warner
Zachary Warner
Numerade Educator
02:35

Problem 44

What mass of water fell on the town in Problem 7? Water has a density of $1.0 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$.

Abhishek Jana
Abhishek Jana
Numerade Educator
03:38

Problem 45

(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 defined as 1 "universe day," where a universe day consists of "universe seconds" as a normal day consists of normal seconds, how many universe seconds have humans existed?

Zachary Warner
Zachary Warner
Numerade Educator
01:10

Problem 46

A unit of area often used in measuring land areas is the hectare, defined as $10^{4} \mathrm{~m}^{2}$. An open-pit coal mine consumes 75 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?

Abhishek Jana
Abhishek Jana
Numerade Educator
01:53

Problem 47

An astronomical unit $(\mathrm{AU})$ is the average distance between Earth and the Sun, approximately $1.50 \times 10^{8} \mathrm{~km}$. The speed of light is about $3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}$. Express the speed of light in astronomical units per minute.

Zachary Warner
Zachary Warner
Numerade Educator
05:22

Problem 48

The common Eastern mole, a mammal, typically has a mass of $75 \mathrm{~g}$, which corresponds to about $7.5$ moles of atoms. (A mole of atoms is $6.02 \times 10^{23}$ atoms.) In atomic mass units (u), what is the average mass of the atoms in the common Eastern mole?

Abhishek Jana
Abhishek Jana
Numerade Educator
02:37

Problem 49

A traditional unit of length in Japan is the ken (1 ken = $1.97 \mathrm{~m})$. What are the ratios of (a) square kens to square meters and (b) cubic kens to cubic meters? What is the volume of a cylindrical water tank of height $5.50$ kens and radius $3.00$ kens in (c) cubic kens and (d) cubic meters?

Zachary Warner
Zachary Warner
Numerade Educator
01:55

Problem 50

You receive orders to sail due east for $24.5 \mathrm{mi}$ to put your salvage ship directly over a sunken pirate ship. However, when your divers probe the ocean floor at that location and find no evidence of a ship, you radio back to your source of information, only to discover that the sailing distance was supposed to be $24.5$ nautical miles, not regular miles. Use the Length table in Appendix D to calculate how far horizontally you are from the pirate ship in kilometers.

Abhishek Jana
Abhishek Jana
Numerade Educator
04:40

Problem 51

The cubit is an ancient unit of length based on the distance between the elbow and the tip of the middle finger of the measurer. Assume that the distance ranged from 43 to $53 \mathrm{~cm}$, and suppose that ancient drawings indicate that a cylindrical pillar was to have a length of 9 cubits and a diameter of 2 cubits. For the stated range, what are the lower value and the upper value, respectively, for (a) the cylinder's length in meters, (b) the cylinder's length in millimeters, and (c) the cylinder's volume in cubic meters?

Zachary Warner
Zachary Warner
Numerade Educator
03:26

Problem 52

As a contrast between the old and the modern and between the large and the small, consider the following: In old rural England 1 hide (between 100 and 120 acres ) was the area of land needed to sustain one family with a single plough for one year. (An area of 1 acre is equal to $4047 \mathrm{~m}^{2}$.) Also, 1 wapentake was the area of land needed by 100 such families. In quantum physics, the cross-sectional area of a nucleus (defined in terms of the chance of a particle hitting and being absorbed by it) is measured in units of barns, where 1 barn is $1 \times 10^{-28} \mathrm{~m}^{2}$. (In nuclear physics jargon, if a nucleus is "large," then shooting a particle at it is like shooting a bullet at a barn door, which can hardly be missed.) What is the ratio of 25 wapentakes to 11 barns?

Donald Albin
Donald Albin
Numerade Educator
06:49

Problem 53

An astronomical unit $(\mathrm{AU})$ is equal to the average distance from Earth to the Sun, about $92.9 \times 10^{6} \mathrm{mi}$. A parsec $(\mathrm{pc})$ is the distance at which a length of 1 AU would subtend an angle of exactly 1 second of angle of exactly 1 second of arc (Fig. 1-8). A light-year (ly) is the distance that light, traveling through a vacuum with a speed of $186000 \mathrm{mi} / \mathrm{s}$, would cover in $1.0$ year. Express the Earth-Sun distance in (a) parsecs and (b) light-years.

Donald Albin
Donald Albin
Numerade Educator
01:17

Problem 54

The description for a certain brand of house paint claims a coverage of $460 \mathrm{ft}^{2} /$ gal. (a) Express this quantity in square meters per liter. (b) Express this quantity in an SI unit (see Appendices $\mathrm{A}$ and D). (c) What is the inverse of the original quantity, and (d) what is its physical significance?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
07:12

Problem 55

Strangely, the wine for a large wedding reception is to be served in a stunning cut-glass receptacle with the interior dimensions of $40 \mathrm{~cm} \times 40 \mathrm{~cm} \times 30 \mathrm{~cm}$ (height). The receptacle is to be initially filled to the top. The wine can be purchased in bottles of the sizes given in the following table. Purchasing a larger bottle instead of multiple smaller bottles decreases the overall cost of the wine. To minimize the cost, (a) which bottle sizes should be purchased and how many of each should be purchased and, once the receptacle is filled, how much wine is left over in terms of (b) standard bottles and (c) liters?
1 standard bottle
1 magnum $=2$ standard bottles
1 jeroboam $=4$ standard bottles
1 rehoboam $=6$ standard bottles
1 methuselah $=8$ standard bottles
1 salmanazar $=12$ standard bottles
1 balthazar $=16$ standard bottles $=11.356 \mathrm{~L}$
1 nebuchadnezzar $=20$ standard bottles

Donald Albin
Donald Albin
Numerade Educator
02:00

Problem 56

The corn-hog ratio is a financial term used in the pig market and presumably is related to the cost of feeding a pig until it is large enough for market. It is defined as the ratio of the market price of a pig with a mass of $3.108$ slugs to the market price of a U.S. bushel of corn. (The word "slug" is derived from an old German word that means "to hit"; we have the same meaning for "slug" as a verb in modern English.) A U.S. bushel is equal to $35.238 \mathrm{~L}$. If the corn-hog ratio is listed as $5.7$ on the market exchange, what is it in the metric units of
$$
\frac{\text { price of } 1 \text { kilogram of pig }}{\text { price of } 1 \text { liter of corn }} ?
$$
(Hint: See the Mass table in Appendix D.)

Abhishek Jana
Abhishek Jana
Numerade Educator
02:37

Problem 57

You are to fix dinners for 400 people at a convention of Mexican food fans. Your recipe calls for 2 jalapeño peppers per serving (one serving per person). However, you have only habanero peppers on hand. The spiciness of peppers is measured in terms of the scoville heat unit (SHU). On average, one jalapeño pepper has a spiciness of 4000 SHU and one habanero pepper has a spiciness of 300000 SHU. To get the desired spiciness, how many habanero peppers should you substitute for the jalapeño peppers in the recipe for the 400 dinners?

Zachary Warner
Zachary Warner
Numerade Educator
01:43

Problem 58

A standard interior staircase has steps each with a rise (height) of $19 \mathrm{~cm}$ and a run (horizontal depth) of $23 \mathrm{~cm}$. Research suggests that the stairs would be safer for descent if the run were, instead, $28 \mathrm{~cm}$. For a particular staircase of total height $4.57 \mathrm{~m}$, how much farther into the room would the staircase extend if this change in run were made?

Abhishek Jana
Abhishek Jana
Numerade Educator
04:04

Problem 59

In purchasing food for a political rally, you erroneously order shucked medium-size Pacific oysters (which come 8 to 12 per U.S. pint) instead of shucked medium-size Atlantic oysters (which come 26 to 38 per U.S. pint). The filled oyster container shipped to you has the interior measure of $1.0 \mathrm{~m} \times 12 \mathrm{~cm} \times 20 \mathrm{~cm}$, and a U.S. pint is equivalent to $0.4732$ liter. By how many oysters is the order short of your anticipated count?

Zachary Warner
Zachary Warner
Numerade Educator
09:49

Problem 60

An old English cookbook carries this recipe for cream of nettle soup: "Boil stock of the following amount: 1 breakfastcup plus 1 teacup plus 6 tablespoons plus 1 dessertspoon. Using gloves, separate nettle tops until you have $0.5$ quart; add the tops to the boiling stock. Add 1 tablespoon of cooked rice and 1 saltspoon of salt. Simmer for 15 min." The following table gives some of the conversions among old (premetric) British measures and among common (still premetric) U.S. measures. (These measures just scream for metrication.) For liquid measures, 1 British teaspoon $=$ 1 U.S. teaspoon. For dry measures, 1 British teaspoon $=2$ U.S. teaspoons and 1 British quart $=1$ U.S. quart. In U.S. measures, how much (a) stock, (b) nettle tops, (c) rice, and (d) salt are required in the recipe?
$$
\begin{array}{ll}
\hline \text { Old British Measures } & \text { U.S. Measures } \\
\hline \text { teaspoon }=2 \text { saltspoons } & \text { tablespoon }=3 \text { teaspoons } \\
\text { dessertspoon }=2 \text { teaspoons } & \text { half cup }=8 \text { tablespoons } \\
\text { tablespoon }=2 \text { dessertspoons } & \operatorname{cup}=2 \text { half cups } \\
\text { teacup }=8 \text { tablespoons } & \\
\text { breakfastcup }=2 \text { teacups } &
\end{array}
$$

Donald Albin
Donald Albin
Numerade Educator