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Understanding Physics

Karen Cummings, Priscilla W. Laws, Edward F. Redish

Chapter 1

Measurement - all with Video Answers

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Chapter Questions

02:11

Problem 1

Speed of Light Express the speed of light, $3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}$, in
(a) feet per nanosecond and (b) millimeters per picosecond.

Dominador Tan
Dominador Tan
Numerade Educator
03:05

Problem 2

Fermi Physicist Enrico Fermi once pointed out that a standard lecture period (50 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 Fermi's approximation.

Dominador Tan
Dominador Tan
Numerade Educator
02:50

Problem 3

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.

Zachary Warner
Zachary Warner
Numerade Educator
03:18

Problem 4

A unit of time sometimes used in microscopic physics is the shake. One shake equals $10^{-8} \mathrm{~s}$. (a) 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 now is taken to be 1 "universe day," for how many "universe seconds" have humans existed?

Dominador Tan
Dominador Tan
Numerade Educator
01:22

Problem 5

An astronomical unit (AU) is the average distance of Earth from 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 terms of astronomical units per minute.

Dominador Tan
Dominador Tan
Numerade Educator
11:45

Problem 6

Three digital clocks $A, B$, and $C$ run at different rates and do not have simultaneous readings of zero. Figure $1-16$ shows simultaneous readings on pairs of the clocks for four occasions. (At the carlicst occasion, for cxample, $B$ reads $25.0 \mathrm{~s}$ and $C$. reads $92.0 \mathrm{~s}$.) 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.)

Ashwin Banarsee
Ashwin Banarsee
Numerade Educator
04:14

Problem 7

Assuming the length of the day uniformly increases by $0.0010 \mathrm{~s}$ per century, calculate the cumulative effect on the measure of time over 20 centuries. (Such slowing of Earth's rotation is indicated by observations of the occurrences of solar eclipses during this period.)

Dominador Tan
Dominador Tan
Numerade Educator
01:08

Problem 8

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 until your watch must be reset by $1.0 \mathrm{~h}$ ? (Hint: Earth rotates $360^{\circ}$ in about 24 h.)

Dominador Tan
Dominador Tan
Numerade Educator
01:52

Problem 9

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 10

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 $n o t$ mean $\pm 3 \mathrm{~ms}$ ). (a) How many times does PSR $1937+21$ rotate in $7.00$ days? (b) How much time does the pulsar take to rotate $1.0 \times$ $10^{6}$ times, and (c) what is the associated uncertainty?

Abhishek Jana
Abhishek Jana
Numerade Educator
02:08

Problem 11

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

Dominador Tan
Dominador Tan
Numerade Educator
07:12

Problem 12

Two types of barrel units were in use in the 1920 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
03:00

Problem 13

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?

Zachary Warner
Zachary Warner
Numerade Educator
02:28

Problem 14

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

Nishant Kumar
Nishant Kumar
Numerade Educator
01:13

Problem 15

Antarctica is roughly semicircular, with a radius of 2000 $\mathrm{km}$ (Fig. $1-17$ ). 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
04:58

Problem 16

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 40 perches by 1 perch, and 1 perch is $16.5 \mathrm{ft}$.

Vysakh M
Vysakh M
Numerade Educator
03:07

Problem 17

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 $30 \mathrm{~min}$ 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
05:10

Problem 18

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. $1-18$ ) 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
01:17

Problem 19

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
03:43

Problem 20

Gold, which has a mass of $19.32 \mathrm{~g}$ for each cubic centimeter of volume, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If $1.000 \mathrm{oz}$ 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?

Alex Garger
Alex Garger
Numerade Educator
03:45

Problem 21

(a) Assuming that each cubic centimeter of water has a mass of exactly $1 \mathrm{~g}$, 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?

Dominador Tan
Dominador Tan
Numerade Educator
02:50

Problem 22

What mass of water fell on the town in Problem 17 during the thunderstorm? One cubic meter of water has a mass of $10^{3} \mathrm{~kg}$.

Alex Garger
Alex Garger
Numerade Educator
04:46

Problem 23

Iron has a mass of $7.87 \mathrm{~g}$ per cubic centimeter of volume, 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?

Susan Hallstrom
Susan Hallstrom
Numerade Educator
06:05

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. A solid cube of silicon dioxide with a volume of $1.00 \mathrm{~m}^{3}$ has a mass of $2600 \mathrm{~kg}$. 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 $1 \mathrm{~m}$ on an edge?

Dominador Tan
Dominador Tan
Numerade Educator
01:55

Problem 25

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
03:20

Problem 26

A mole of atoms is $6.02 \times 10^{2.3}$ 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.

Alex Garger
Alex Garger
Numerade Educator
01:57

Problem 27

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
03:48

Problem 28

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 $1.0 \mu \mathrm{m}$ ? (c) How many microns are in $1.0 \mathrm{yd}$ ?

Zachary Warner
Zachary Warner
Numerade Educator
01:26

Problem 29

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
02:50

Problem 30

A gray 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 terms of points squared (points $^{2}$ )?

Dominador Tan
Dominador Tan
Numerade Educator
02:24

Problem 31

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 could not easily interfere. (Presumably, the police were originally upset because a Smoot is not an SI base unit, but these days they seem to have accepted the unit.) Figure $1-19$ 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?

Alex Garger
Alex Garger
Numerade Educator
03:01

Problem 32

Muffet An old English children's rhyme states, "Little Miss Muffet sat on her 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 $=0.50$ bushel, where 1 Imperial (British) bushel $=36.3687$ liters (L). What was Miss Muffet's stash in (a) pecks, (b) bushels, and (c) liters?

Dominador Tan
Dominador Tan
Numerade Educator
03:14

Problem 33

During the summers at high latitudes, ghostly, silver-blue clouds occasionally appear after sunset when common clouds are in Earth's shadow and are no longer visible. The ghostly clouds have been called noctilucent clouds (NLC), which means "luminous night clouds," but now are often called mesospheric clouds, after the mesosphere, the name of the atmosphere at the altitude of the clouds These clouds were first seen in June 1885 , after dust and water from the massive 1883 volcanic explosion of Krakatoa Island (near Java in the Southeast Pacific) reached the high altitudes in the Northern Hemisphere. In the low temperatures of the mesosphere, the water collected and froze on the volcanic dust (and perhaps on comet and meteor dust already present there) to form the particles that made up the first clouds. Since then, mesospheric clouds have generally increased in occurrence and brightness, probably because of the increased production of methane by industries, rice paddies, landfills, and livestock flatulence. The methane works its way into the upper atmosphere, undergoes chemical changes, and results in an increase of water molecules there, and also in bits of ice for the mesospheric clouds. If mesospheric clouds are spotted 38 min after sunset and then quickly dim, what is their altitude if they are directly over the observer?

Ashwin Banarsee
Ashwin Banarsee
Numerade Educator
04:44

Problem 34

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 would the staircase extend into the room at the foot of the stairs if this change in run were made?

Dominador Tan
Dominador Tan
Numerade Educator
03:51

Problem 35

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 "largc," 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?

Alex Garger
Alex Garger
Numerade Educator
06:25

Problem 36

A cubic centimeter in a typical cumulus cloud contains 50 to 500 water droplets, which have a typical radius of $10 \mu \mathrm{m} .$ (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 mass per unit volume (or density) of $1000 \mathrm{~kg} / \mathrm{m}^{3}$. How much mass does the water in the cloud have?

Alex Garger
Alex Garger
Numerade Educator
05:08

Problem 37

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 delivered 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?

Dominador Tan
Dominador Tan
Numerade Educator
04:40

Problem 38

A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car's fuel consumption 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: $$\begin{aligned}1 \text { U.K. gallon } &=4.5459631 \text { liters } \\1 \text { U.S. gallon } &=3.7853060 \text { liters. }\end{aligned}$$
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?

Dominador Tan
Dominador Tan
Numerade Educator
07:00

Problem 39

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 6 ). If the client actually meant displacement tons, how many extra U.S. bushels of the candies will you erroneously ship to the client if you interpret the order as (a) 73 freight tons and (b) 73 register tons? One cubic meter is equivalent to $28.378$ U.S bushels.

Dominador Tan
Dominador Tan
Numerade Educator
05:12

Problem 40

The wine for a large European 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, where the volumes of the larger bottles are given in terms of the volume of a standard wine bottle. Purchasing a larger bottle instead of multiple smaller bottles decreases the overall cost of the wine. To minimize that overall cost, (a) which bottle sizes should be purchased and how many of each should be purchased, and (b) how much wine is left over once the receptacle is filled?
1 standard
1 magnum $=2$ standard 1 jeroboam $=4$ standard 1 rehoboam $=6$ standard 1 methuselah $=8$ standard 1 salmanazar $=12$ standard 1 balthazar $=16$ standard $=11.356 \mathrm{~L}$
1 nebuchadnezzar $=20$ standard

Dominador Tan
Dominador Tan
Numerade Educator
03:10

Problem 41

The corn-hog ratio is a financial term commonly 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 1460 slugs to the market price of a U.S. bushel of corn. The slug is the unit of mass in the English system. (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 $\frac{\text { price of } 1 \text { kilogram of pig }}{\text { price of } 1 \text { liter of corn }} ?$

Dominador Tan
Dominador Tan
Numerade Educator
07:43

Problem 42

Measures in Spain 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 $1-3$ 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). (a) Complete the table, using three significant figures. Then express $7.00$ almude in terms of (b) medio, (c) cahiz, and (d) cubic centimeters $\left(\mathrm{cm}^{3}\right)$.

Alex Garger
Alex Garger
Numerade Educator
01:55

Problem 43

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
01:44

Problem 44

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, 1 day consisted of 10 hours, 1 hour consisted of 100 minutes, and 1 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?

Dominador Tan
Dominador Tan
Numerade Educator
02:56

Problem 45

During heavy rain, a rectangular section of a mountainside measuring $2.5 \mathrm{~km}$ wide (horizontally), $0.80 \mathrm{~km}$ long (up along the slope), and $2.0 \mathrm{~m}$ deep suddenly slips into a valley in a mud slide. Assume that the mud ends up uniformly distributed over a valley section measuring $0.40 \mathrm{~km} \times 0.40 \mathrm{~km}$ and that the mass of a cubic meter of mud is $1900 \mathrm{~kg}$. What is the mass of the mud sitting above an area of $4.0 \mathrm{~m}^{2}$ in that section?

Alex Garger
Alex Garger
Numerade Educator
06:20

Problem 46

Prior to adopting metric systems of measurement, the United Kingdom employed some challenging measures of liquid volume. A few are shown in Table $1-4$. (a) Complete the table, using three significant figures. (b) The volume of 1 bag is equivalent to a volume of $0.1091 \mathrm{~m}^{3}$. If an old British story has a witch cooking up some vile liquid in a cauldron with a volume of $1.5$ chaldrons, what is the volume in terms of cubic meters?

Alex Garger
Alex Garger
Numerade Educator
02:46

Problem 47

Traditional units of time have been based on astronomical measurements, such as the length of the day or year. However, one human-based measure of time can be found in Tibet, where the $d b u g$ is the average time between exhaled breaths. Estimate the number of dbugs in a day.

Alex Garger
Alex Garger
Numerade Educator
06:41

Problem 48

The following photograph of the Leaning Tower of Pisa was taken from an advertisement found in a 1994 airline magazine. Assume that the photo of the man talking on the telephone to the left has been dubbed in and is not part of the original photograph.
(a) Examine the photograph. Take the measurements in centimeters that are needed to find a scale factor that enables you to estimate the length of the tower in meters (i.e., its height if it were standing up straight.) Use only the evidence in the photograph $-$ no other data are allowed. Then estimate the tower length in meters.
(b) According to data published in Sir Bannester Fletcher's $A$ History of Architecture (U. of London Athlone Press, $1975, \mathrm{p} .470$ ) the diameter of the lower part of the tower is $16.0 \mathrm{~m}$. Using these data, find another scale factor for cstimating the length of the tower, and then re-estimate the length of the tower using this new scale factor.
(c) Which of the scale factors (a) or (b) do you think will give the best estimate of the length of the tower? Explain the reasons for your answer.
(d) Using the scale factor you found in part (b), what is the length of the tower without the belfry or narrow top segment (i.e., just consider the bottom 7 stories)?

Ashwin Banarsee
Ashwin Banarsee
Numerade Educator
03:41

Problem 49

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 $4000 \mathrm{SHU}$ and one habanero pepper has a spiciness of 300000 SHU. To salvage the situation, how many (total) habanero peppers should you substitute for the jalapeño peppers in the recipe for the convention?

Dominador Tan
Dominador Tan
Numerade Educator
02:56

Problem 50

Discuss the question: "Is 500 feet big or small?" Before you do so, carry out the following estimates.
(a) You are on the top floor of a 500 -ft-tall building. A fire breaks out in the building and the elevator stops working. You have to walk down to the ground floor. Estimate how long this would take you. (Your stairwell is on the other side of the building from the fire.)
(b) You are hiking the Appalachian Trail on a beautiful fall morning as part of a $10 \mathrm{mi}$ hike with a group of friends. You are walking along a well-tended, level part of the trail. Estimate how long it would take you to walk $500 \mathrm{ft}$.
(c) You are driving on the New Jersey Turnpike at $65 \mathrm{mi} / \mathrm{hr}$. You pass a sign that says "Lane ends 500 feet." How much time do you have in order to changelanes?

Khushbu Rani
Khushbu Rani
Numerade Educator
02:17

Problem 51

Historically the English had a doubling system when measuring volumes; 2 mouthfuls equal 1 jigger, 2 jiggers equal 1 jack (also called a jackpot); 2 jacks equal 1 jill; 2 jills $=$ 1 cup; 2 cups $=1$ pint; 2 pints $=1$ quart; 2 quarts $=1$ pottle; 2 pottles $=1$ gallon; 2 gallons $=1$ pail. (The nursery rhyme "Jack and Jill" refers to these units and was a protest against King Charles I of England for his taxes on the jacks of liquor sold in the tavern. (See
A. Kline, The World of Measurement, New York: Simon and Schuster, 1975, pp. $32-39 .$ American and British cooks today use teaspoons, tablespoons, and cups; 3 teaspoons $=1$ tablespoon; 4 tablespoons $=1 / 4$ cup. Assume that you find an old English recipe requiring 3 jiggers of milk. How many cups does this represent? How many tablespoons? You can assume that the cups in the two systems represent the same volume.

Alex Garger
Alex Garger
Numerade Educator
04:43

Problem 52

In America, we measure fuel efficiency of our cars by citing the number of miles you can drive on 1 gallon of gas (miles/gallon). In Europe, the same information is given by quoting how many liters of gas it takes to go 100 kilometers (liter/100 kilometers).
(a) My current car gets 21 miles/gallon in highway travel. What number (in liter/100 kilometers) should I give to my Swedish friend so that he can compare it to the mileage for his Volvo?
(b) The car I drove in England last summer needed 6 liters of gas to go 100 kilometers. How many miles/gallon did it get?
(c) If my car has a fuel efficiency, $f$, in miles/gallon, what is its European efficiency, $e$, in liters $/ 100$ kilometers? (Write an equation that would permit an easy conversion.)

Alex Garger
Alex Garger
Numerade Educator
05:08

Problem 53

Two terrapins decide to go to Jerry's for a pizza. When they get there they find that Jerry's is having a special: Raphael: "Great! Let's get a large one."
Donatello: "Don't be dumb. Let's get three of the small ones for the same price. That'll give us more pizza and be cheaper."
Raphael: "Why would it be a special if it's more than we could get for the regular price? Let's get the large."
Who's right? Which would you buy? What would the difference be if you were buying them at Ledo's (square pizzas)?

Susan Hallstrom
Susan Hallstrom
Numerade Educator
01:34

Problem 54

A student makes the following argument: "I can prove a dollar equals a penny. Since a dime ( 10 cents) is onetenth of a dollar, I can write:
$$10 \phi=\$ 0.1$$
Square both sides of the equation. Since squares of equals are equal,
$$100 \phi=\$ 0.1 \text { . }$$
What's wrong with the argument?

Paul Gabriel
Paul Gabriel
Numerade Educator
02:07

Problem 55

Here are two related problems - one precise, one an estimation. (a) A sculptor builds model for a statue 0 . a terrapin to replace Testudo." She discov. ers that to cast her
small scale model she needs $2 \mathrm{~kg}$ of bronze When she is done, she finds that she can give it two coats of finish. ing polyurethane varnish using exactly one small can of varnish. The final statue is supposed to be 5 times as large as the model in cach dimension. How much bronze will she need? How much varnish should she buy? (Hint: If this seems difficult, you might start by writing a simpler question that is easier to work on before tackling this one.)
(b) The human brain has 1000 times the surface area of a mouse's brain. The human brain is convoluted, the mouse's is not. How much of this factor is due just to size (the human brain is bigger)? How sensitive is your result to your estimations of the approximate dimensions of a human brain and a mouse brain?

AG
Ankit Gupta
Numerade Educator
01:21

Problem 56

Dose We know from our dimensional analysis that if an object maintains its shape but changes its size, its area changes as the square of its length and its volume changes as the cube of its length. Suppose you are a parent and your child is sick and has to take some medicine. You have taken this medicine previously and you know its dose for you. You are $5^{\prime} 10^{\prime \prime}$ tall and weigh $180 \mathrm{lb}$, and your child is $2^{\prime} 11^{\prime \prime}$ tall and wcighs $30 \mathrm{lb}$. Estimate an appropriate dosage for your child's medicine in the following cases. Be sure to discuss your reasoning.
(a) The medicine is one that will enter the child's bloodstream and reach cvery cell in the body. Your dose is $250 \mathrm{mg}$.
(b) The medicine is one that is meant to coat the child's throat. Your dose is $15 \mathrm{ml}$.

Rupsa Sarkar
Rupsa Sarkar
Numerade Educator
02:26

Problem 57

Estimate how many Ping-Pong balls it would take to fill your classroom (assuming all the doors and windows are closed).

Alex Garger
Alex Garger
Numerade Educator
02:08

Problem 58

When visiting the Como Park Zoo in St. Paul, Minnesota, with my young grandson, we encountered the sign shown at the right on the cage of the mountain lion. The detailed numbers surprised me. The amount of food given to the cat was specified to the tenth of a gram and the average cat's weight was specified to within 10 grams-about $1 / 3$ of an ounce. This seemed to be overly precise. Can you figure out what they were trying to say and what a plausible accuracy might be for those two numbers-the amount of food given and the average cat's weight?

Sanat Mukherjee
Sanat Mukherjee
Numerade Educator
00:42

Problem 59

Throughout your physics course, your instructor will expect you to be careful with the units in your calculations. Yet, some students tend to neglect them and just trust that they always work out properly. Maybe this real-world example will keep you from such a sloppy habit. On July 23, 1983 , Air Canada Flight 143 was being readied for its long trip from Montreal to Edmonton when the flight crew asked the ground crew to determine how much fuel was already onboard the airplane. The flight crew knew that they needed to begin the trip with $22300 \mathrm{~kg}$ of fuel. They knew that amount in kilograms because Canada had recently switched to the metric system: previously fuel had been measured in pounds. The ground crew could measure the onboard fuel only in liters, which they reported as $7682 \mathrm{~L}$. Thus, to determine how much fuel was onboard and how much additional fuel must be added, the flight crew asked the ground crew for the conversion factor from liters to kilograms of fuel. The response was $1.77$, which the flight crew used $(1.77 \mathrm{~kg}$ corresponds to $1 \mathrm{~L}$ ). (a) How many kilograms of fuel did the flight crew think they had? (In this problem, take all the given data as being exact.) (b) How many liters did they ask to be added to the airplane?

David Collins
David Collins
Numerade Educator