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1 Chapter continued
49. Explain the difference between a scientific
theory and a scientific law.
A scientific law is a rule of nature, where
a scientific theory is an explanation of
the scientific law based on observation.
A theory explains why something happens; a law describes what happens.
50. Density The density of a substance is its
mass per unit volume.
a. Give a possible metric unit for density.
possible answers include g/cm3 or
kg/m3
b. Is the unit for density a base unit or a
derived unit?
derived unit
51. What metric unit would you use to measure
each of the following?
a. the width of your hand
cm
b. the thickness of a book cover
mm
c. the height of your classroom
Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
m
d. the distance from your home to your
classroom
km
52. Size Make a chart of sizes of objects.
Lengths should range from less than 1 mm
to several kilometers. Samples might
include the size of a cell, the distance light
travels in 1 s, and the height of a room.
sample answer:
radius of the atom, 5 10 11 m; virus,
10 7 m; thickness of paper, 0.1 mm;
width of paperback book, 10.7 cm;
height of a door, 1.8 m; width of town,
7.8 km; radius of Earth, 6 106 m;
distance to the Moon, 4 108 m
53. Time Make a chart of time intervals.
Sample intervals might include the time
between heartbeats, the time between
presidential elections, the average lifetime
of a human, and the age of the United
Physics: Principles and Problems
States. Find as many very short and very
long examples as you can.
sample answer:
half-life of polonium-194, 0.7 s;
time between heartbeats, 0.8 s; time to
walk between physics class and math
class, 2.4 min; length of school year,
180 days; time between elections for
the U.S. House of Representatives,
2 years; time between U.S. presidential
elections, 4 years; age of the United
States, (about) 230 years
54. Speed of Light Two students measure
the speed of light. One obtains
(3.001 0.001) 108 m/s; the other obtains
(2.999 0.006) 108 m/s.
a. Which is more precise?
(3.001
0.001) 108 m/s
b. Which is more accurate?
(2.999
0.006) 108 m/s
55. You measure the dimensions of a desk as
132 cm, 83 cm, and 76 cm. The sum of
these measures is 291 cm, while the product
is 8.3 105 cm3. Explain how the significant
digits were determined in each case.
In addition and subtraction, you ask
what place the least precise measure is
known to: in this case, to the nearest
cm. So the answer is rounded to the
nearest cm. In multiplication and
division, you look at the number of
significant digits in the least precise
answer: in this case, 2. So the answer is
rounded to 2 significant digits.
56. Money Suppose you receive $5.00 at the
beginning of a week and spend $1.00 each
day for lunch. You prepare a graph of the
amount you have left at the end of each day
for one week. Would the slope of this graph
be positive, zero, or negative? Why?
negative, because the change in
vertical distance is negative for a
positive change in horizontal distance
Solutions Manual
7
Chapter 1 continued
57. Data are plotted on a graph, and the value
on the y-axis is the same for each value of
the independent variable. What is the
slope? Why? How does y depend on x?
Zero. The change in vertical distance is
zero. y does not depend on x.
58. Driving The graph of braking distance
versus car speed is part of a parabola. Thus,
the equation is written d av2 bv c.
The distance, d, has units in meters, and
velocity, v, has units in meters/second.
How could you find the units of a, b, and c?
What would they be?
The units in each term of the equation
must be in meters because distance, d,
is measured in meters.
av 2 a(m/s)2, so a is in s2/m;
bv
b(m/s), b so is in s 1.
59. How long is the leaf in Figure 1-22?
Include the uncertainty in your
measurement.
c. What is the number of significant digits
for the total mass?
four
d. Why is the number of significant digits
different for the total mass and the
individual masses?
When adding measurements, the
precision matters: both masses are
known to the nearest hundredth of a
gram, so the total should be given to
the nearest hundredth of a gram.
Significant digits sometimes are
gained when adding.
61. History Aristotle said that the speed of a
falling object varies inversely with the density
of the medium through which it falls.
a. According to Aristotle, would a rock fall
faster in water (density 1000 kg/m3), or
in air (density 1 kg/m3)?
Lower density means faster speed,
so the rock falls faster in air.
b. How fast would a rock fall in a vacuum?
Based on this, why would Aristotle say
that there could be no such thing as a
vacuum?
s
62. Explain the difference between a hypothesis
and a scientific theory.
Figure 1-22
8.3 cm
0.05 cm, or 83 mm
0.5 mm
60. The masses of two metal blocks are
measured. Block A has a mass of 8.45 g
and block B has a mass of 45.87 g.
a. How many significant digits are
expressed in these measurements?
A: three; B: four
b. What is the total mass of block A plus
block B?
A scientific theory has been tested
and supported many times before it
becomes accepted. A hypothesis is an
idea about how things might workit
has much less support.
63. Give an example of a scientific law.
Newtons laws of motion, law of conservation of energy, law of conservation of
charge, law of reflection
54.32 g
8 Solutions Manual
Physics: Principles and Problems
Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Because a vacuum would have a
zero density, the rock should fall
infinitely fast. Nothing can fall that
fast.
Chapter 1 continued
64. What reason might the ancient Greeks
have had not to question the hypothesis
that heavier objects fall faster than lighter
objects? Hint: Did you ever question which
falls faster?
Air resistance affects many light
objects. Without controlled experiments, their everyday observations told
them that heavier objects did fall faster.
65. Mars Explain what observations led to
changes in scientists ideas about the surface
of Mars.
As telescopes improved and later
probes were sent into space, scientists
gained more information about the
surface. When the information did
not support old hypotheses, the
hypotheses changed.
66. A graduated cylinder is marked every mL.
How precise a measurement can you make
with this instrument?
0.5 mL
Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Mastering Problems
pages 2628
1.1 Mathematics and Physics
67. Convert each of the following
measurements to meters.
a. 42.3 cm
0.423 m
b. 6.2 pm
6.2 10 12 m
68. Add or subtract as indicated.
a. 5.80 109 s
3.20 108 s
6.12 109 s
b. 4.87 10 6 m
1.93 10 6 m
2.94 10 6 m
c. 3.14 10 5 kg
9.36 10 5 kg
1.250 10 4 kg
d. 8.12 107 g
6.20 106 g
7.50 107 g
69. Rank the following mass measurements
from least to greatest: 11.6 mg, 1021 g,
0.000006 kg, 0.31 mg.
0.31 mg, 1021 g, 0.000006 kg, 11.6 mg
70. State the number of significant digits in
each of the following measurements.
a. 0.00003 m
1
b. 64.01 fm
4
c. 80.001 m
5
d. 0.720 g
3
e. 2.40 106 kg
3
f.
6 108 kg
1
g. 4.07 1016 m
3
c. 21 km
2.1 104 m
d. 0.023 mm
2.3 10 5 m
e. 214 m
2.14 10 4 m
f.
57 nm
5.7 10 8 m
71. Add or subtract as indicated.
a. 16.2 m
5.008 m
13.48 m
34.7 m
b. 5.006 m
12.0077 m
8.0084 m
25.022 m
c. 78.05 cm2
32.046 cm2
46.00 cm2
d. 15.07 kg
12.0 kg
3.1 kg
Physics: Principles and Problems
Solutions Manual
9

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University of Florida - PHY - 2050

Chapter 1 continued78. How precise a measurement could youmake with the scale shown in Figure 1-23?72. Multiply or divide as indicated.a. (6.22.91018109m)(4.7 1010m)m2b. (5.6 10 7 m)/(2.8 10 12 s)2.0 105 m/sc. (8.1 10 4 km)(1.6 10 3 km)1.3

University of Florida - PHY - 2050

Chapter 1 continuedb. Describe the resulting curve.a straight linec. Use the graph to write an equationrelating the volume to the mass of thealcohol.m0.79Vd. Find the units of the slope of the graph.What is the name given to this quantity?g/cm3;

University of Florida - PHY - 2050

Chapter 2 continuedA position vector goes from the originto the object. When the origins are different, the position vectors are different.On the other hand, a displacement vector has nothing to do with the origin.8. Critical Thinking A car travels st

University of Florida - PHY - 2050

Chapter 2 continuedPractice Problems2.4How Fast?pages 4347page 4525. The graph in Figure 2-22 describes themotion of a cruise ship during its voyagethrough calm waters. The positived-direction is defined to be south.26. Describe, in words, the m

University of Florida - PHY - 2050

Chapter 2 continuedIt is possible to calculate the averagevelocity from the information given, butit is not possible to find the instantaneous velocity.46. Figure 2-26 is a graph of two people running.Position (m)42. If you know the positions of a m

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Chapter 2 continuedJoszi and Heike paddling canoes in a localriver.Car B16Joszi14Heike1210Position (km)20018Position (km)250170150Car A1201005086041.01.61.4 2.03.0200.51.01.52.0Time (h)sTime (h)2.5Figure 2-30a. At w

University of Florida - PHY - 2050

Chapter 2 continuedobjects position-time graph to be a horizontal line? A vertical line? If you answeryes to either situation, describe the associated motion in words.It is possible to have a horizontal lineas a position-time graph; this wouldindicat

University of Florida - PHY - 2050

Chapter 3 continuedis 15 m east of the origin and the other is15 m west.a. What would be the difference(s) in theposition-time graphs of their motion?Both lines would have the sameslope, but they would rise from thed-axis at different points, 15 m,

University of Florida - PHY - 2050

Chapter 3 continuedvf2520vivftVelocity (m/s)5Time (s)3500400030002500200015005101000500015dvi)vtvi) t2(22 m/s44 m/s)(11 s)2vt(1.5 m/s)(20.0 min)(60 s/min)1800 m1.8 kmtime to walk back to the car:dv1800 m1.2 m/s1500 s

University of Florida - PHY - 2050

Chapter 3 continued36. Distance An in-line skater first accelerates from 0.0 m/s to 5.0 m/s in 4.5 s, thencontinues at this constant speed for another 4.5 s. What is the total distance traveled by the in-line skater?Acceleratingdfvivt fvf20.0 m/s

University of Florida - PHY - 2050

Chapter 3 continuedvf2vi22a dvf2vi2g d where a0 at the height of the toss, soand vf(0.0 m/s)2vig(2)(9.80 m/s2)(0.25 m)2.2 m/sb. If you catch it at the same height as you released it, how much time did itspend in the air?vfvivi2.2 m/s an

University of Florida - PHY - 2050

Chapter 3 continuedlonger it drops, the faster it goes, butthe acceleration is constant at g.60. If an objects velocity-time graph is a straightline parallel to the t-axis, what can you conclude about the objects acceleration? (3.1)When the velocity-

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Chapter 3 continuedTotal distance is 2.03102 km;1.0 102 km40.0 km/htotal time1.0 102 km60.0 km/h4.2 h2.0 102 km4.2 hdtso v48 km/h80. Find the uniform acceleration that causes a cars velocity to change from 32 m/sto 96 m/s in an 8.0-s period

University of Florida - PHY - 2050

Chapter 3 continued(0.0 m/s)2(2)(49 m/s2)(325 m0.0 m)180 m/s89. A car moves at 12 m/s and coasts up a hill with a uniform accelerationof 1.6 m/s2.a. What is its displacement after 6.0 s?df12at2fvit f(12 m/s)(6.0 s)1( 1.6 m/s2)(6.0 s)2243

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Chapter 3 continuedvf2vi22adf where avi2vfg2gdf(2.0 m/s)2(2)(9.80 m/s2)(2.5 m)7.3 m/s101. If you throw the ball in the previous problem up instead of down, how fast willit be moving when it hits the sidewalk?Choose the same coordinate system.

University of Florida - PHY - 2050

Chapter 3 continued111. The velocity of a car changes over an 8.0-stime period, as shown in Table 3-6.1bh2d1(5.0 s)(20.0 m/s2Table 3-6Velocity v. TimeTime (s)0.01.02.03.04.05.06.07.08.0(8.0 sVelocity (m/s)0.04.08.012.016.020.0

University of Florida - PHY - 2050

Chapter 3 continued1( 3.00 m/s2)(12.0 s)22432 m216 m216 mLocal:dfdivitf100 matf2(11.0 m/s)(12.0 s)0232 mOn this basis, no collision will occur.b. The calculations that you made do not allow for the possibility that a collision might take

University of Florida - PHY - 2050

CHAPTER4Forces in One Dimension3. A cable pulls a crate at a constant speedacross a horizontal surface. The surface provides a force that resists the crates motion.Practice Problems4.1Force and Motionpages 8795Systempage 89For each of the follo

University of Florida - PHY - 2050

Chapter 4 continuedpage 10019. On Earth, a scale shows that you weigh585 N.a. What is your mass?Accelerating downward,so a2.00 m/s2FscaleFnetFgmamgm(aThe scale reads 585 N. Since there isno acceleration, your weight equalsthe downward forc

University of Florida - PHY - 2050

Chapter 4 continuedPractice Problems4.3Interaction Forcespages 10210731. A suitcase sits on a stationary airport luggagecart, as in Figure 4-13. Draw a free-bodydiagram for each object and specifically indicate any interaction pairs between the two

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Chapter 4 continued43. Suppose that the acceleration of an object iszero. Does this mean that there are noforces acting on it? Give an example supporting your answer. (4.2)No, it only means the forces acting on itare balanced and the net force is zer

University of Florida - PHY - 2050

Chapter 4 continued60. Skating Joyce and Efua are skating. Joycepushes Efua, whose mass is 40.0-kg, with aforce of 5.0 N. What is Efuas resultingacceleration?FmaaFm65. Three objects are dropped simultaneouslyfrom the top of a tall building: a s

University of Florida - PHY - 2050

Chapter 4 continuedLevel 278. Male lions and human sprinters can bothaccelerate at about 10.0 m/s2. If a typicallion weighs 170 kg and a typical sprinterweighs 75 kg, what is the difference in theforce exerted on the ground during a racebetween the

University of Florida - PHY - 2050

Chapter 4 continued88. A student stands on a bathroom scale in anelevator at rest on the 64th floor of a building. The scale reads 836 N.a. As the elevator moves up, the scale reading increases to 936 N. Find the acceleration of the elevator.FnetFgF

University of Florida - PHY - 2050

Chapter 4 continuedSolve equation 2 for T:For mA, mAaTFor mB, mBaFEarths mass on 3.0-kg blockm3.0-kg blockam3.0-kg blockgm3.0-kg block(g2.4 m/s2)mAa37 NThinking CriticallymBamBgmB(gmBamB)aTherefore aa. Create a pictorial model.a)mAg(

University of Florida - PHY - 2050

Chapter 4 continuedAnswers will vary. Newtons first law ofmotion involves an object whose netforces are zero. If the object is at rest, itremains at rest; if it is in motion, it willcontinue to move in the same directionat a constant velocity. Only

University of Florida - PHY - 2050

Chapter 5 continuedpage 125Solve problems 510 algebraically. You may also choose to solve some of them graphically tocheck your answers.5. Sudhir walks 0.40 km in a direction 60.0 west of north, then goes 0.50 km duewest. What is his displacement?Id

University of Florida - PHY - 2050

Chapter 5 continuedFfsFN5.8 N0.58FfFNs1.0 101 NFf, afterFfmgk, afterFN(0.06)(1.0 101 N)102 N(105 kg)(9.80 m/s2)0.099119. Mr. Ames is dragging a box full of booksfrom his office to his car. The box andbooks together have a combined weigh

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Chapter 5 continued34. Scott and Becca are moving a folding tableout of the sunlight. A cup of lemonade,with a mass of 0.44 kg, is on the table. Scottlifts his end of the table before Becca does,and as a result, the table makes an angle of15.0 with

University of Florida - PHY - 2050

Chapter 5 continued52. Explain the method that you would use tosubtract two vectors graphically. (5.1)Chapter AssessmentConcept Mappingpage 14047. Complete the concept map below by labeling the circles with sine, cosine, or tangent toindicate wheth

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Chapter 5 continued76. Tennis When stretching a tennis netbetween two posts, it is relatively easy topull one end of the net hard enough toremove most of the slack, but you need awinch to take the last bit of slack out ofthe net to make the top almo

University of Florida - PHY - 2050

Chapter 5 continued88. Space Exploration A descent vehicle landing on Mars has a vertical velocity towardthe surface of Mars of 5.5 m/s. At the sametime, it has a horizontal velocity of 3.5 m/s.a. At what speed does the vehicle movealong its descent

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Chapter 5 continuedSolution by components. The sum ofthe components must equal zero, soFAyFgso FAy123 NFA sin 60.0FAysin 60.07.50 102 Nsin 60.0866 NAlso, FBFA0, soFAFA cos 60.0(866 N)(cos 60.0)433 N, right98. A street lamp weighs 150 N

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Chapter 5 continuedmg(sincos )k(20.0 kg)(9.80 m/s2)(sin 30.0(0.40)(cos 30.0)166 Nb. If Sisyphus pushes the boulder at a velocity of 0.25 m/s and it takes him8.0 h to reach the top of the mountain, what is the mythical mountainsvertical height?h

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Chapter 5 continuedCumulative Reviewpage 144111. Add or subtract as indicated and state theanswer with the correct number of significant digits. (Chapter 1)a. 85.26 g4.7 g90.0 gb. 1.07 km0.608 km1.68 kmc. 186.4 kg57.83 kg128.6 kgd. 60.08 s1

University of Florida - PHY - 2050

CHAPTER6Motion in Two DimensionsPractice Problems6.1Projectile Motionpages 147152page 1501. A stone is thrown horizontally at a speedof 5.0 m/s from the top of a cliff that is78.4 m high.a. How long does it take the stone to reachthe bottom of

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Chapter 6 continuedThe faster ball is in the air a shorter time, and thus gains a smallervertical velocity.8. Free-Body Diagram An ice cube slides without friction across a table at aconstant velocity. It slides off the table and lands on the floor. D

University of Florida - PHY - 2050

Chapter 6 continuedso, vw/g(7.3 kg)(2.5 m/s)20.75 mvb/g0.5 m/s61 N25. An airplane flies due north at 150 km/h relativeto the air. There is a wind blowing at 75 km/hto the east relative to the ground. What is theplanes speed relative to the groun

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Chapter 6 continuedMastering Conceptspage 16433. Consider the trajectory of the cannonball shown in Figure 6-11. (6.1)BACDEsFigure 6-11Up is positive, down is negative.a. Where is the magnitude of the vertical-velocity component largest?The g

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Chapter 6 continued49. Car Racing The curves on a race track arebanked to make it easier for cars to goaround the curves at high speeds. Draw afree-body diagram of a car on a bankedcurve. From the motion diagram, find thedirection of the acceleratio

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Chapter 6 continuedtxvi cosAnd yiso t0, so1gt t2vy i012gt , but y2vy it12gt20 or vy i0From above1xg2vi cosv0 sin i0iMultiplying by vi cos i gives1vi2(sin i)(cos i)gx 02so vigxi)(cos(2)(sini)(9.80 m/s2)(14.0 m)(2)(

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Chapter 6 continued1.5 103 m4.0 m/s 2.0 m/svtan 1 b/air1.5 103 m4.0 m/s 2.0 m/svair1.0 103 s15 m/stan 16.5 m/sOdina wins.67 from the horizon toward the westLevel 270. Crossing a River You row a boat, such asthe one in Figure 6-16, perpendi

University of Florida - PHY - 2050

Chapter 6 continuedso vrg tan(0.80 m)(9.80 m/s2)(tan 14.0)1.4 m/s81. A baseball is hit directly in line with an outfielder at an angle of 35.0 above thehorizontal with an initial velocity of 22.0 m/s. The outfielder starts running as soonas the bal

University of Florida - PHY - 2050

Chapter 6 continuedc21c2cc22c24c588. Analyze and Conclude A ball on a lightstring moves in a vertical circle. Analyze anddescribe the motion of this system. Be sureto consider the effects of gravity and tension. Is this system in uniform ci

University of Florida - PHY - 2050

Chapter 7 continuedrs 3 2TMrMTs6.70 103 km 3(27.3 days)23.90 105 km3.78 10 3 days26.15 10 2 days88.6 minb. How far above Earths surface is this satellite?hrsrE6.70 106 m6.38 106 m3.2 105 m3.2 102 km5. Using the data in the previous prob

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Chapter 7 continuedSection ReviewUsing the Law of Universal of Gravitationpages 1791857.2page 18515. Gravitational Fields The Moon is 3.9 105 km from Earths center and1.5 108 km from the Suns center. The masses of Earth and the Sun are6.0 1024 kg

University of Florida - PHY - 2050

Chapter 7 continued25. Is the area swept out per unit of time byEarth moving around the Sun equal tothe area swept out per unit of time by Marsmoving around the Sun? (7.1)No. The equality of the area swept outper unit of time applies to each planet

University of Florida - PHY - 2050

Chapter 7 continuedthe surface of Earth, 35,700 km aboveEarths equator. Explain how it can stay inexactly the same position day after day.What would happen if it were closer?Farther out? Hint: Draw a pictorial model.The satellite is positioned as cl

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Chapter 7 continuedFf, so FfJmbgButFfGmbmJmbgrJ2FfGmJgrJ2(40.0 N)(6.67 10 11 N m2/kg2)(1.90 1027 kg)(9.80 m/s2)(7.15 107 m)2101 N67. Mimas, one of Saturns moons, has an orbital radius of 1.87 108 m and anorbital period of about 23.0 h. Use

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Chapter 7 continuedIf the weight is1, the distance is22(6.38 106 m)r9.02 106 m2(rE) or9.02 106 m6.38 106 m2.64 106 m2.64 103 km78. Two satellites of equal mass are put into orbit 30.0 m apart. The gravitational forcebetween them is 2.0 10 7

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Chapter 7 continuedMixed Reviewpages 193194Level 188. Use the information for Earth in Table 7-1 on page 173 to calculate the mass ofthe Sun, using Newtons version of Keplers third law.42 3r,GmT242 3r andGso mT 24 2 r3G T2m246.67 1011

University of Florida - PHY - 2050

Chapter 7 continuedTo find g on Mars, the following calculation is used.6.37 1023 kg, and RMarsmMarsSo, gMars3.61 m/s2(12 m/s)2(0.50)(3.61 m/s2)Therefore, RR3.43 106 m8.0 101 m96. Apollo 11 On July 19, 1969, Apollo 11s revolution around the Mo

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Chapter 7 continuedFscale on JaredFEarths mass on JaredFEarths mass on JaredgaagFEarths mass on Jared 1Fscale on JaredFEarths mass on Jaredag1716 N11.75 m/s29.80 m/s2608 N103. Potato Bug A 1.0-g potato bug is walking around the outer ri

University of Florida - PHY - 2050

CHAPTER8Rotational MotionBecause the radius of the wheel isreduced from 35.4 cm to 24 cm, theangular acceleration will beincreased.Practice ProblemsDescribing RotationalMotionpages 1972008.11page 2001. What is the angular displacement of eac

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Chapter 8 continuedFgrchain( 35.0 N)(0.0770 m)2.70 N mThus, a torque of2.70 N m must be exerted to balance this torque.18. Two baskets of fruit hang from strings going aroundpulleys of different diameters, as shown inFigure 8-6. What is the mass

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Chapter 8 continuedSection Review8.2Rotational Dynamicspages 201210page 21030. Torque Vijesh enters a revolving door thatis not moving. Explain where and howVijesh should push to produce a torquewith the least amount of force.To produce a torque

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Chapter 8 continued44. Locating the Center of Mass Describehow you would find the center of mass ofthis textbook.Obtain a piece of string and attach asmall weight to it. Suspend the stringand the weight from one corner of thebook. Draw a line along

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Chapter 8 continuedMastering Problems8.1 Describing Rotational Motionpages 223224Level 172. A wheel is rotated so that a point on theedge moves through 1.50 m. The radiusof the wheel is 2.50 m, as shown inFigure 8-21. Through what angle (in radian

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Chapter 8 continueda. What is the resulting angular velocity of the top?vffrrod3.0 m/s1(0.0080 m)27.5 102 rad/sb. What force was exerted on the string?Frrod sinandThus, Frrod sinFIIIrrod sint1mrdisk22rrod sinmrdisk22 trrod sin(i

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Chapter 8 continued92. The basketball in the previous problemstops rolling after traveling 12 m.dtva. If its acceleration was constant, whatwas its angular acceleration?v f2vi22ad2.00 m/svi22dso aThus,(2.50 m)(1.25 s)vi22rdarc. What

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Chapter 8 continued104. Analyze and Conclude A pivoted lamppole is shown in Figure 8-31. The poleweighs 27 N, and the lamp weighs 64 N.The total tension, then, isFTyFTsin 105FpolerpoleFlamprlamprrope sin 105Ropey(27 N)64 Nx0.33 m0.44 mLa