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Physics for Scientists and Engineers with Modern Physics

Raymond A. Serway, John W. Jewett, Jr.

Chapter 1

Physics and Measurement - all with Video Answers

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Chapter Questions

01:54

Problem 1

Use information on the endpapers of this book to calculate the average density of the Earth. Where does the value fit among those listed in Table 14.1? Look up the density of a typical surface rock, such as granite, in another source and compare the density of the Earth to it.

Mayukh Banik
Mayukh Banik
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Problem 2

The standard kilogram is a platinum-iridium cylinder 39.0 mm in height and 39.0 mm in diameter. What is the density of the material?

Ankur S
Ankur S
Numerade Educator
00:42

Problem 3

A major motor company displays a die-cast model of its first automobile, made from 9.35 kg of iron. To celebrate its one-hundredth year in business, a worker will recast the model in gold from the original dies. What mass of gold is needed to make the new model?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:16

Problem 4

A proton, which is the nucleus of a hydrogen atom, can be modeled as a sphere with a diameter of 2.4 fm and a mass of $1.67 \times 10^{-27} \mathrm{kg}$ . Determine the density of the proton and state how it compares with the density of lead, which is given in Table $14.1 .$

Mayukh Banik
Mayukh Banik
Numerade Educator
00:44

Problem 5

Two spheres are cut from a certain uniform rock. One has radius 4.50 cm. The mass of the second sphere is five times greater. Find the radius of the second sphere.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:29

Problem 6

A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in Figure Pl. 6 a. The atoms reside at the corners of cubes of side $L=0.200 \mathrm{nm} .$ One piece of evidence for the regular arrangement of atoms comes from the flat surfaces along which a crystal separates, or cleaves, when it is broken. Suppose this crystal cleaves along a face diagonal as shown in Figure P1.6b. Calculate the spacing $d$ between two adjacent atomic planes that separate when the crystal cleaves.

Vipender Yadav
Vipender Yadav
Numerade Educator
03:01

Problem 7

Which of the following equations are dimensionally correct? (a) $v_{f}=v_{i}+a x \quad$ (b) $y=(2 \mathrm{m}) \cos (k x),$ where $k=2 \mathrm{m}^{-1}$

Vishal Gupta
Vishal Gupta
Numerade Educator
01:06

Problem 8

Figure $\mathrm{P} 1.8$ shows a frustum of a cone. Of the following mensuration (geometrical) expressions, which describes
(i) the total circumference of the flat circular faces,
(ii) the volume, and
(iii) the area of the curved surface?
(a) $\pi\left(r_{1}+r_{2}\right)\left[h^{2}+\left(r_{2}-r_{1}\right)^{2}\right]^{1 / 2}$
(b) 2$\pi\left(r_{1}+r_{2}\right)$
(c) $\pi h\left(r_{1}^{2}+r_{1} r_{2}+r_{2}^{2}\right) / 3$

Mayukh Banik
Mayukh Banik
Numerade Educator
01:49

Problem 9

Newton's law of universal gravitation is represented by
$$F=\frac{G M m}{r^{2}}$$
Here $F$ is the magnitude of the gravitational force exerted by one small object on another, $M$ and $m$ are the masses of the objects, and $r$ is a distance. Force has the SI units $\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}^{2}$ . What are the SI units of the proportionality constant $G$ ?

Benjamin Arndell
Benjamin Arndell
Numerade Educator
03:04

Problem 10

Suppose your hair grows at the rate 1$/ 32$ in. per day. Find the rate at which it grows in nanometers per second. Because the distance between atoms in a molecule is on the order of 0.1 $\mathrm{nm}$ , your answer suggests how rapidly layers of atoms are assembled in this protein synthesis.

Benjamin Arndell
Benjamin Arndell
Numerade Educator
00:37

Problem 11

A rectangular building lot is 100 $\mathrm{ft}$ by 150 $\mathrm{ft}$ . Determine the area of this lot in square meters.

Mayukh Banik
Mayukh Banik
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03:21

Problem 12

An auditorium measures $40.0 \mathrm{m} \times 20.0 \mathrm{m} \times 12.0 \mathrm{m} .$ The density of air is $1.20 \mathrm{kg} / \mathrm{m}^{3} .$ What are (a) the volume of the room in cubic feet and (b) the weight of air in the room in pounds?

Benjamin Arndell
Benjamin Arndell
Numerade Educator
01:21

Problem 13

A room measures 3.8 m by 3.6 m, and its ceiling is 2.5 m high. Is it possible to completely wallpaper the walls of this room with the pages of this book? Explain your answer.

Mayukh Banik
Mayukh Banik
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04:16

Problem 14

Assume it takes 7.00 min to fill a 30.0-gal gasoline tank. (a) Calculate the rate at which the tank is filled in gallons per second. (b) Calculate the rate at which the tank is filled in cubic meters per second. (c) Determine the time interval, in hours, required to fill a $1.00-\mathrm{m}^{3}$ volume at the same rate. $\left(1 \mathrm{U.S} . \text { gal }=231 \mathrm{in.}^{3}\right)$

Benjamin Arndell
Benjamin Arndell
Numerade Educator
05:12

Problem 15

A solid piece of lead has a mass of 23.94 g and a volume of $2.10 \mathrm{cm}^{3} .$ From these data, calculate the density of lead in SI units $\left(\mathrm{kg} / \mathrm{m}^{3}\right) .$

Eduard Sanchez
Eduard Sanchez
Numerade Educator
01:29

Problem 16

An ore loader moves 1200 tons/h from a mine to the surface. Convert this rate to pounds per second, using 1 ton $=2000$ lb.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:10

Problem 17

At the time of this book's printing, the U.S. national debt is about $\$ 8$ trillion. (a) If payments were made at the rate of $\$ 1000$ per second, how many years would it take to pay off the debt, assuming no interest were charged? (b) A dollar bill is about 15.5 $\mathrm{cm}$ long. If eight trillion dollar bills were laid end to end around the Earth's equator, how many times would they encircle the planet: Take the radius of the Earth at the equator to be $6378 \mathrm{km} .$ Note: Before doing any of these calculations, try to guess at the answers. You may be very surprised.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:52

Problem 18

A pyramid has a height of 481 $\mathrm{ft}$ , and its base covers an area of 13.0 acres (Fig. Pl.18). The volume of a pyramid is given by the expression $V=\frac{1}{3} B h,$ where $B$ is the area of the base and $h$ is the height. Find the volume of this pyramid in cubic meters. ( 1 acre $=43560 \mathrm{ft}^{2} )$

Benjamin Arndell
Benjamin Arndell
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01:06

Problem 19

The pyramid described in Problem 18 contains approximately 2 million stone blocks that average 2.50 tons each. Find the weight of this pyramid in pounds.

Prashant Bana
Prashant Bana
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02:26

Problem 20

A hydrogen atom has a diameter of $1.06 \times 10^{-10} \mathrm{m}$ as defined by the diameter of the spherical electron cloud around the nucleus. The hydrogen nucleus has a diameter of approximately $2.40 \times 10^{-15} \mathrm{m} .$ (a) For a scale model, represent the diameter of the hydrogen atom by the playing length of an American football field $(100 \text { yards }=300 \mathrm{ft})$ and determine the diameter of the nucleus in millimeters. (b) The atom is how many times larger in volume than its nucleus?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:39

Problem 21

One gallon of paint (volume $=3.78 \times 10^{-3} \mathrm{m}^{3} )$ covers an area of 25.0 $\mathrm{m}^{2}$ . What is the thickness of the fresh paint on the wall?

Benjamin Arndell
Benjamin Arndell
Numerade Educator
02:32

Problem 22

The mean radius of the Earth is $6.37 \times 10^{6} \mathrm{m}$ and that of the Moon is $1.74 \times 10^{8} \mathrm{cm} .$ From these data calculate (a) the ratio of the Earth's surface area to that of the Moon and $(\mathrm{b})$ the ratio of the Earth's volume to that of the Moon. Recall that the surface area of a sphere is 4$\pi r^{2}$ and the volume of a sphere is $\frac{4}{3} \pi r^{3}$.

Chasen Shaw
Chasen Shaw
Numerade Educator
03:27

Problem 23

One cubic meter $\left(1.00 \mathrm{m}^{3}\right)$ of aluminum has a mass of $2.70 \times 10^{3} \mathrm{kg}$ , and the same volume of iron has a mass of $7.86 \times 10^{3} \mathrm{kg}$ . Find the radius of a solid aluminum sphere that will balance a solid iron sphere of radius 2.00 $\mathrm{cm}$ on an equal-arm balance.

Keshav Singh
Keshav Singh
Numerade Educator
03:30

Problem 24

Let $\rho_{\mathrm{Al}}$ represent the density of aluminum and $\rho_{\mathrm{Fe}}$ that of iron. Find the radius of a solid aluminum sphere that balances a solid iron sphere of radius $r_{\mathrm{Fe}}$ on an equal-arm balance.

Keshav Singh
Keshav Singh
Numerade Educator
02:53

Problem 25

Find the order of magnitude of the number of table-tennis balls that would fit into a typical-size room (without being crushed). In your solution, state the quantities you measure or estimate and the values you take for them.

Keshav Singh
Keshav Singh
Numerade Educator
00:48

Problem 26

An automobile tire is rated to last for 50 000 miles. To an order of magnitude, through how many revolutions will it turn? In your solution, state the quantities you measure or estimate and the values you take for them.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:06

Problem 27

Compute the order of magnitude of the mass of a bathtub half full of water. Compute the order of magnitude of the mass of a bathtub half full of pennies. In your solution, list the quantities you take as data and the value you measure or estimate for each.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:10

Problem 28

Suppose Bill Gates offers to give you $\$ 1$ billion if you can finish counting it out using only one-dollar bills. Should you accept his offer? Explain your answer. Assume you can count one bill every second, and note that you need at least 8 hours a day for sleeping and eating.

Mayukh Banik
Mayukh Banik
Numerade Educator
00:36

Problem 29

To an order of magnitude, how many piano tuners are in New York City? Physicist Enrico Fermi was famous for asking questions like this one on oral doctorate qualifying examinations. His own facility in making order-of-magnitude calculations is exemplified in Problem 48 of Chapter 45.

Mayukh Banik
Mayukh Banik
Numerade Educator
03:48

Problem 30

A rectangular plate has a length of $(21.3 \pm 0.2) \mathrm{cm}$ and a width of $(9.8 \pm 0.1) \mathrm{cm} .$ Calculate the area of the plate, including its uncertainty.

Guilherme Barros
Guilherme Barros
Numerade Educator
03:42

Problem 31

How many significant figures are in the following numbers: $(a) 78.9 \pm 0.2 \quad$ (b) $3.788 \times 10^{9} \quad(\mathrm{c}) 2.46 \times 10^{-6}$ (d) 0.0053$?$

Benjamin Arndell
Benjamin Arndell
Numerade Educator
02:47

Problem 32

The radius of a uniform solid sphere is measured to be $(6.50 \pm 0.20) \mathrm{cm},$ and its mass is measured to be $(1.85 \pm 0.02) \mathrm{kg} .$ Determine the density of the sphere in kilograms per cubic meter and the uncertainty in the density.

Mayukh Banik
Mayukh Banik
Numerade Educator
03:03

Problem 33

Carry out the following arithmetic operations: (a) the sum of the measured values $756,37.2,0.83,$ and 2$\quad(\mathrm{b})$ the product $0.0032 \times 356.3 \quad$ (c) the product $5.620 \times \pi$.

Keshav Singh
Keshav Singh
Numerade Educator
01:07

Problem 34

The tropical year, the time interval from one vernal equinox to the next vernal equinox, is the basis for our calendar. It contains 365.242199 days. Find the number of seconds in a tropical year.

Benjamin Arndell
Benjamin Arndell
Numerade Educator
01:23

Problem 35

A child is surprised that she must pay $\$ 1.36$ for a toy marked $\$ 1.25$ because of sales tax. What is the effective tax rate on this purchase, expressed as a percentage?

Benjamin Arndell
Benjamin Arndell
Numerade Educator
02:29

Problem 36

A student is supplied with a stack of copy paper, ruler, compass, scissors, and a sensitive balance. He cuts out various shapes in various sizes, calculates their areas, measures their masses, and prepares the graph of Figure P1.36. Consider the fourth experimental point from the top. How far is it from the best-fit straight line? (a) Express your answer as a difference in verticalaxis coordinate. (b) Express your answer as a difference in horizontal-axis coordinate. (c) Express both of the answers to parts (a) and (b) as a percentage. (d) Calculate the slope of the line. (e) State what the graph demonstrates, referring to the shape of the graph and the results of parts (c) and (d). (f) Describe whether this result should be expected theoretically. Describe the physical meaning of the slope.

Mayukh Banik
Mayukh Banik
Numerade Educator
00:27

Problem 37

A young immigrant works overtime, earning money to buy portable MP3 players to send home as gifts for family members. For each extra shift he works, he has figured out that he can buy one player and two-thirds of another one. An e-mail from his mother informs him that the players are so popular that each of 15 young neighborhood friends wants one. How many more shifts will he have to work?

Mayukh Banik
Mayukh Banik
Numerade Educator
00:51

Problem 38

In a college parking lot, the number of ordinary cars is larger than the number of sport utility vehicles by 94.7%. The difference between the number of cars and the number of SUVs is 18. Find the number of SUVs in the lot.

Mayukh Banik
Mayukh Banik
Numerade Educator
00:57

Problem 39

The ratio of the number of sparrows visiting a bird feeder to the number of more interesting birds is 2.25. On a morning when altogether 91 birds visit the feeder, what is the number of sparrows?

Mayukh Banik
Mayukh Banik
Numerade Educator
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Problem 40

Prove that one solution of the equation
$$2.00 x^{4}-3.00 x^{3}+5.00 x=70.0$$
is $x=-2.22$

James Kiss
James Kiss
Numerade Educator
00:30

Problem 41

for which the ratio of $\sin \theta$ to $\cos \theta$ is $-3.00$

Mayukh Banik
Mayukh Banik
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00:59

Problem 42

A highway curve forms a section of a circle. A car goes around the curve. Its dashboard compass shows that the car is initially heading due east. After it travels $840 \mathrm{m},$ it is heading $35.0^{\circ}$ south of east. Find the radius of curvature of its path. Suggestion: You may find it useful to learn a geometric theorem stated in Appendix B. 3.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:08

Problem 43

For a period of time as an alligator grows, its mass is proportional to the cube of its length. When the alligator’s length changes by 15.8%, its mass increases by 17.3 kg. Find its mass at the end of this process.

Mayukh Banik
Mayukh Banik
Numerade Educator
03:44

Problem 44

From the set of equations
$$\begin{aligned} p &=3 q \\ p r &=q s \\ \frac{1}{2} p r^{2}+\frac{1}{2} q s^{2} &=\frac{1}{2} q t^{2} \end{aligned}$$
involving the unknowns $p, q, r, s,$ and $t,$ find the value of the ratio of $t$ to $r .$

Benjamin Arndell
Benjamin Arndell
Numerade Educator
01:45

Problem 45

In a particular set of experimental trials, students examine a system described by the equation
$$\frac{Q}{\Delta t}=\frac{k \pi d^{2}\left(T_{h}-T_{c}\right)}{4 L}$$
We will see this equation and the various quantities in it in Chapter 20. For experimental control, in these trials all quantities except $d$ and $\Delta t$ are constant. (a) If $d$ is made three times larger, does the equation predict that $\Delta t$ will get larger or smaller? By what factor? (b) What pattern of proportionality of $\Delta t$ to $d$ does the equation predict? (c) To display this proportionality as a straight line on a graph, what quantities should you plot on the horizontal and vertical axes? (d) What expression represents the theoretical slope of this graph?

Mayukh Banik
Mayukh Banik
Numerade Educator
00:22

Problem 46

In a situation in which data are known to three significant digits, we write $6.379 \mathrm{m}=6.38 \mathrm{m}$ and $6.374 \mathrm{m}=6.37 \mathrm{m} .$ When a number ends in $5,$ we arbitrarily choose to write $6.375 \mathrm{m}=6.38 \mathrm{m} .$ We could equally well write $6.375 \mathrm{m}=$ $6.37 \mathrm{m},$ "rounding down" instead of "rounding up," because we would change the number 6.375 by equal increments in both cases. Now consider an order-of-
magnitude estimate, in which factors of change rather than increments are important. We write 500 $\mathrm{m} \sim 10^{3} \mathrm{m}$ because 500 differs from 100 by a factor of $5,$ whereas it differs from 1000 by only a factor of $2 .$ We write 437 $\mathrm{m} \sim$ $10^{3} \mathrm{m}$ and $305 \mathrm{m} \sim 10^{2} \mathrm{m} .$ What distance differs from 100 $\mathrm{m}$ and from 1000 $\mathrm{m}$ by equal factors so that we could equally well choose to represent its order of magnitude either as $\sim 10^{2} \mathrm{m}$ or as $\sim 10^{3} \mathrm{m} ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
04:09

Problem 47

A spherical shell has an outside radius of 2.60 $\mathrm{cm}$ and an inside radius of $a$ . The shell wall has uniform thickness and is made of a material with density $4.70 \mathrm{g} / \mathrm{cm}^{3} .$ The space inside the shell is filled with a liquid having a density of $1.23 \mathrm{g} / \mathrm{cm}^{3} .$ (a) Find the mass $m$ of the sphere, including its contents, as a function of $a .$ (b) In the answer to part (a), if $a$ is regarded as a variable, for what value of $a$ does $m$ have its maximum possible value? (c) What is this maximum mass? (d) Does the value from part (b) agree with the result of a direct calculation of the mass of a sphere of uniform density? (e) For what value of $a$ does the answer to part (a) have its minimum possible value? (f) What is this minimum mass? (g) Does the value from part (f) agree with the result of a direct calculation of the mass of a uniform sphere? (h) What value of $m$ is halfway between the maximum and minimum possible values? (i) Does this mass agree with the result of part (a) evaluated for $a=2.60 \mathrm{cm} / 2=1.30 \mathrm{cm} ?$ (j) Explain whether you should expect agreement in each of parts $(\mathrm{d}),$ (g), and (i). (k) What If? In part (a), would the answer change if the inner wall of the shell were not concentric with the outer wall?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:26

Problem 48

A rod extending between $x=0$ and $x=14.0 \mathrm{cm}$ has uniform cross-sectional area $A=9.00 \mathrm{cm}^{2} .$ It is made from a continuously changing alloy of metals so that along its length its density changes steadily from 2.70 $\mathrm{g} / \mathrm{cm}^{3}$ to $19.3 \mathrm{g} / \mathrm{cm}^{3} .$ (a) Identify the constants $B$ and $C$ required in the expression $\rho=B+C x$ to describe the variable density. (b) The mass of the rod is given by
$$m=\int_{\text { all material }} \rho d V=\int_{\text { all } x} \rho A d x=\int_{0}^{14 \mathrm{cm}}(B+C x)\left(9.00 \mathrm{cm}^{2}\right) d x$$
Carry out the integration to find the mass of the rod.

Vipender Yadav
Vipender Yadav
Numerade Educator
00:39

Problem 49

The diameter of our disk-shaped galaxy, the Milky Way, is about $1.0 \times 10^{5}$ light-years (ly). The distance to Andromeda, which is the spiral galaxy nearest to the Milky Way, is about 2.0 million ly. If a scale model represents the Milky Way and Andromeda galaxies as dinner plates 25 $\mathrm{cm}$ in diameter, determine the distance between the centers of the two plates.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:27

Problem 50

Air is blown into a spherical balloon so that, when its radius is 6.50 cm, its radius is increasing at the rate 0.900 cm/s. (a) Find the rate at which the volume of the balloon is increasing. (b) If this volume flow rate of air entering the balloon is constant, at what rate will the radius be increasing when the radius is 13.0 cm? (c) Explain physically why the answer to part (b) is larger or smaller than 0.9 cm/s, if it is different.

Ummatul Choudary
Ummatul Choudary
Numerade Educator
01:31

Problem 51

The consumption of natural gas by a company satisfies the empirical equation $V=1.50 t+0.00800 t^{2},$ where $V$ is the volume in millions of cubic feet and $t$ is the time in months. Express this equation in units of cubic feet and seconds. Assign proper units to the coefficients. Assume a month is 30.0 days.

Mayukh Banik
Mayukh Banik
Numerade Educator
00:57

Problem 52

In physics it is important to use mathematical approximations. Demonstrate that for small angles $\left(<20^{\circ}\right),$
$$\tan \alpha \approx \sin \alpha \approx \alpha=\frac{\pi \alpha^{\prime}}{180^{\circ}}$$
where $\alpha$ is in radians and $\alpha^{\prime}$ is in degrees. Use a calculator to find the largest angle for which tan $\alpha$ may be approximated by $\alpha$ with an error less than 10.0$\%$.

Mayukh Banik
Mayukh Banik
Numerade Educator
00:35

Problem 53

A high fountain of water is located at the center of a circular pool as shown in Figure P1.53. Not wishing to get his feet wet, a student walks around the pool and measures its circumference to be $15.0 \mathrm{m} .$ Next, the student stands at the edge of the pool and uses a protractor to gauge the angle of elevation of the top of the fountain to be $55.0^{\circ} .$ How high is the fountain?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:51

Problem 54

Collectible coins are sometimes plated with gold to enhance their beauty and value. Consider a commemorative quarter-dollar advertised for sale at $\$ 4.98$ . It has a diameter of 24.1 $\mathrm{mm}$ and a thickness of $1.78 \mathrm{mm},$ and it is completely covered with a layer of pure gold 0.180$\mu \mathrm{m}$ thick. The volume of the plating is equal to the thickness of the layer times the area to which it is applied. The patterns on the faces of the coin and the grooves on its edge have a negligible effect on its area. Assume the price of gold is $\$ 10.0$ per gram. Find the cost of the gold added to the coin. Does the cost of the gold significantly enhance the value of the coin? Explain your answer.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:11

Problem 55

One year is nearly $\pi \times 10^{7}$ s. Find the percentage error in this approximation, where "percentage error" is defined as Percentage error $=\frac{\text { lassumed value }-\text { true value } |}{\text { true value }} \times 100 \%.$

Mayukh Banik
Mayukh Banik
Numerade Educator
01:12

Problem 56

A creature moves at a speed of 5.00 furlongs per fort-night (not a very common unit of speed). Given that 1 furlong $=220$ yards and 1 fortnight $=14$ days, determine the speed of the creature in meters per second. Explain what kind of creature you think it might be.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:03

Problem 57

A child loves to watch as you fill a transparent plastic bottle with shampoo. Horizontal cross sections of the bottle are circles with varying diameters because the bottle is much wider in some places than others. You pour in bright green shampoo with constant volume flow rate 16.5 $\mathrm{cm}^{3} / \mathrm{s}$ . At what rate is its level in the bottle rising(a) at point where the diameter of the bottle is 6.30 $\mathrm{cm}$ and $(b)$ at a point where the diameter is 1.35 $\mathrm{cm}$ ?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:47

Problem 58

The data in the following table represent measurements of the masses and dimensions of solid cylinders of aluminum, copper, brass, tin, and iron. Use these data to calculate the densities of these substances. State how your results for aluminum, copper, and iron compare with those given in Table 14.1.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:02

Problem 59

Assume there are 100 million passenger cars in the United States and the average fuel consumption is 20 $\mathrm{mi} /$ gal of gasoline. If the average distance traveled by each car is 10000 $\mathrm{mi} / \mathrm{yr}$ , how much gasoline would be saved per year if average fuel consumption could be increased to 25 $\mathrm{mi} / \mathrm{gal}$ ?

Averell Hause
Averell Hause
Carnegie Mellon University
01:38

Problem 60

The distance from the Sun to the nearest star is about $4 \times 10^{16} \mathrm{m}$ . The Milky Way galaxy is roughly a disk of diameter $\sim 10^{21} \mathrm{m}$ and thickness $\sim 10^{19} \mathrm{m} .$ Find the order of magnitude of the number of stars in the Milky Way. Assume the distance between the Sun and our nearest neighbor is typical.

Mayukh Banik
Mayukh Banik
Numerade Educator