CONTENTS
Chapter 1: Introduction, Measurement, Estimating ....................................................... 1
Chapter 2: Describing Motion: Kinematics in One Dimension .................................. 18
Chapter 3: Kinematics in Two or Three Dimensions; Vectors ................................... 56
Chapter 4: Dynamics: Newton’s Laws of Motion ....................................................... 96
Chapter 5: Using Newton’s Laws: Friction, Circular Motion, Drag Forces ............. 134
Chapter 6: Gravitation and Newton’s Synthesis....................................................... 183
Chapter 7: Work and Energy.................................................................................... 218
Chapter 8: Conservation of Energy .......................................................................... 247
Chapter 9: Linear Momentum .................................................................................. 290
Chapter 10: Rotational Motion................................................................................. 332
Chapter 11: Angular Momentum; General Rotation ................................................ 373
Chapter 12: Static Equilibrium; Elasticity and Fracture ........................................... 412
Chapter 13: Fluids .................................................................................................... 456
Chapter 14: Oscillations ........................................................................................... 490
Chapter 15: Wave Motion ........................................................................................ 528
Chapter 16: Sound.................................................................................................... 560
Chapter 17: Temperature, Thermal Expansion, and the Ideal Gas Law ................... 592
Chapter 18: Kinetic Theory of Gases ....................................................................... 620
Chapter 19: Heat and the First Law of Thermodynamics ......................................... 647
Chapter 20: Second Law of Thermodynamics ......................................................... 683
,CHAPTER 1: Introduction, Measurement, Estimating
Responses to Questions
1. (a) A particular person’s foot. Merits: reproducible. Drawbacks: not accessible to the general
public; not invariable (could change size with age, time of day, etc.); not indestructible.
(b) Any person’s foot. Merits: accessible. Drawbacks: not reproducible (different people have
different size feet); not invariable (could change size with age, time of day, etc.); not
indestructible.
Neither of these options would make a good standard.
2. The distance in miles is given to one significant figure, and the distance in kilometers is given to five
significant figures! The value in kilometers indicates more precision than really exists or than is
meaningful. The last digit represents a distance on the same order of magnitude as a car’s length!
The sign should perhaps read “7.0 mi (11 km),” where each value has the same number of
significant figures, or “7 mi (11 km),” where each value has about the same % uncertainty.
3. The number of digits you present in your answer should represent the precision with which you
know a measurement; it says very little about the accuracy of the measurement. For example, if you
measure the length of a table to great precision, but with a measuring instrument that is not
calibrated correctly, you will not measure accurately. Accuracy is a measure of how close a
measurement is to the true value.
4. If you measure the length of an object and you report that it is “4,” you haven’t given enough
information for your answer to be useful. There is a large difference between an object that is 4
meters long and one that is 4 km long. Units are necessary to give meaning to a numerical answer.
5. You should report a result of 8.32 cm. Your measurement had three significant figures. When you
multiply by 2, you are really multiplying by the integer 2, which is an exact value. The number of
significant figures is determined by the measurement.
6. The correct number of significant figures is three: sin 30.0º = 0.500.
7. Useful assumptions include the population of the city, the fraction of people who own cars, the
average number of visits to a mechanic that each car makes in a year, the average number of weeks a
mechanic works in a year, and the average number of cars each mechanic can see in a week.
(a) There are about 800,000 people in San Francisco. Assume that half of them have cars. If each of
these 400,000 cars needs servicing twice a year, then there are 800,000 visits to mechanics in a
year. If mechanics typically work 50 weeks a year, then about 16,000 cars would need to be
seen each week. Assume that on average, a mechanic can work on 4 cars per day, or 20 cars a
week. The final estimate, then, is 800 car mechanics in San Francisco.
(b) Answers will vary. But following the same reasoning, the estimate is 1/1000 of the population.
,Chapter 1 Introduction, Measurement, Estimating
Responses to MisConceptual Questions
1. (c) As stated in the text, scientific laws are descriptive – they are meant to describe how nature
behaves. Since our understanding of nature evolves, so do the laws of physics, when evidence
can convince the community of physicists. The laws of physics are not permanent, and are not
subject to political treaties. In fact, there have been major changes in the laws of physics since
1900 – particularly due to relativity and quantum mechanics. The laws of physics apply in
chemistry and other scientific fields, since those areas of study are based on physics. Finally,
the laws of physics are man-made, not a part of nature. They are our “best description” of
nature as we currently understand it. As stated in the text, “Laws are not lying there in nature,
waiting to be discovered.”
2. (e) The first product is 142.08 m, which is only accurate to the 10’s place, since 37 m/s has only
two significant figures. The second product is 74.73 m, which is only accurate to the 1’s place,
since 5.3 s has only two significant figures. Thus the sum of the two terms can only be accurate
to the 10’s place. 142.08 + 74.73 = 216.81, which to the 10’s place is 220 m.
3. (a) The total number of digits present does not determine the precision, as the leading zeros in (c)
and (d) are only place holders. Rewriting all the measurements in units of meters shows that (a)
implies a precision of 0.0001m, (b) and (c) both imply a precision of 0.001 m, and (d) implies a
precision of 0.01 m. Note that since the period is shown, the trailing zeros are significant. If all
the measurements are expressed in meters, (a) has 4 significant figures, (b) and (c) each have 3
significant figures, and (d) has 2 significant figures.
4. (b) The leading zeros are not significant. Rewriting this number in scientific notation, 7.8 103 ,
shows that it only has two significant digits.
5. (b) When you add or subtract numbers, the final answer should contain no more decimal places
than the number with the fewest decimal places. Since 25.2 has one decimal place, the answer
must be rounded to one decimal place, or to 26.6. Thus the answer has 3 significant figures.
6. (b) The word “accuracy” is often misused. If a student repeats a measurement multiple times and
obtains the same answer each time, it is often assumed to be accurate. In fact, students are
frequently given an “ideal” number of times to repeat the experiment for “accuracy.” However,
systematic errors may cause each measurement to be inaccurate. A poorly working instrument
may also limit the accuracy of your measurement.
7. (a) Quoting the textbook, “precision” refers to the repeatability of the measurement using a given
instrument. Precision and accuracy are often confused. “Accuracy” is defined by answer (b).
8. (d) This addresses misconceptions about squared units and about which factor should be in the
numerator of the conversion. This error can be avoided by treating the units as algebraic
symbols that must be cancelled out.
9. (e) When making estimates, the estimator may frequently believe that their answers are more
significant than they actually are. This question helps the estimator realize what an order-of-
magnitude estimation is NOT supposed to accomplish.
10. (d) This addresses the fact that the generic unit symbol, like [L], does not indicate a specific system
of units.
, Physics for Scientists & Engineers wͅith Modern Physics, 5e, Global Edition Instructor Solutions Manual
Solutions to Problems
1. (a) 777 3 significant figures
(b) 81.60 4 significant figures
(c) 7.03 3 significant figures
(d) 0.03 1 significant figure
(e) 0.0086 2 significant figures
(f) 6465 4 significant figures
(g) 8700 2 significant figures
(a) 5.859 5.859 10
0
2.
(b) 21.8 2.1810
1
3
(c) 0.0068 6.810
328.65 3.2865 10
2
(d)
1
(e) 0.219 2.19 10
444 4.44 10
2
(f)
3. (a) 8.69 105 869, 000
(b) 9.1103 9100
(c) 2.5 101 0.25
(d) 4.76 102 476
(e) 3.62 105 0.0000362
0.35 m
4. % uncertainty 100% 11%
3.25 m
0.2 s
5. (a) % uncertainty 100% 4.444% 4%
4.5s
0.2 s
(b) % uncertainty 100% 0.4444% 0.4%
45s
(c) The time of 4.5 minutes is 270 seconds.
0.2 s
% uncertainty 100% 0.0741% 0.07%
270 s
Chapter 1: Introduction, Measurement, Estimating ....................................................... 1
Chapter 2: Describing Motion: Kinematics in One Dimension .................................. 18
Chapter 3: Kinematics in Two or Three Dimensions; Vectors ................................... 56
Chapter 4: Dynamics: Newton’s Laws of Motion ....................................................... 96
Chapter 5: Using Newton’s Laws: Friction, Circular Motion, Drag Forces ............. 134
Chapter 6: Gravitation and Newton’s Synthesis....................................................... 183
Chapter 7: Work and Energy.................................................................................... 218
Chapter 8: Conservation of Energy .......................................................................... 247
Chapter 9: Linear Momentum .................................................................................. 290
Chapter 10: Rotational Motion................................................................................. 332
Chapter 11: Angular Momentum; General Rotation ................................................ 373
Chapter 12: Static Equilibrium; Elasticity and Fracture ........................................... 412
Chapter 13: Fluids .................................................................................................... 456
Chapter 14: Oscillations ........................................................................................... 490
Chapter 15: Wave Motion ........................................................................................ 528
Chapter 16: Sound.................................................................................................... 560
Chapter 17: Temperature, Thermal Expansion, and the Ideal Gas Law ................... 592
Chapter 18: Kinetic Theory of Gases ....................................................................... 620
Chapter 19: Heat and the First Law of Thermodynamics ......................................... 647
Chapter 20: Second Law of Thermodynamics ......................................................... 683
,CHAPTER 1: Introduction, Measurement, Estimating
Responses to Questions
1. (a) A particular person’s foot. Merits: reproducible. Drawbacks: not accessible to the general
public; not invariable (could change size with age, time of day, etc.); not indestructible.
(b) Any person’s foot. Merits: accessible. Drawbacks: not reproducible (different people have
different size feet); not invariable (could change size with age, time of day, etc.); not
indestructible.
Neither of these options would make a good standard.
2. The distance in miles is given to one significant figure, and the distance in kilometers is given to five
significant figures! The value in kilometers indicates more precision than really exists or than is
meaningful. The last digit represents a distance on the same order of magnitude as a car’s length!
The sign should perhaps read “7.0 mi (11 km),” where each value has the same number of
significant figures, or “7 mi (11 km),” where each value has about the same % uncertainty.
3. The number of digits you present in your answer should represent the precision with which you
know a measurement; it says very little about the accuracy of the measurement. For example, if you
measure the length of a table to great precision, but with a measuring instrument that is not
calibrated correctly, you will not measure accurately. Accuracy is a measure of how close a
measurement is to the true value.
4. If you measure the length of an object and you report that it is “4,” you haven’t given enough
information for your answer to be useful. There is a large difference between an object that is 4
meters long and one that is 4 km long. Units are necessary to give meaning to a numerical answer.
5. You should report a result of 8.32 cm. Your measurement had three significant figures. When you
multiply by 2, you are really multiplying by the integer 2, which is an exact value. The number of
significant figures is determined by the measurement.
6. The correct number of significant figures is three: sin 30.0º = 0.500.
7. Useful assumptions include the population of the city, the fraction of people who own cars, the
average number of visits to a mechanic that each car makes in a year, the average number of weeks a
mechanic works in a year, and the average number of cars each mechanic can see in a week.
(a) There are about 800,000 people in San Francisco. Assume that half of them have cars. If each of
these 400,000 cars needs servicing twice a year, then there are 800,000 visits to mechanics in a
year. If mechanics typically work 50 weeks a year, then about 16,000 cars would need to be
seen each week. Assume that on average, a mechanic can work on 4 cars per day, or 20 cars a
week. The final estimate, then, is 800 car mechanics in San Francisco.
(b) Answers will vary. But following the same reasoning, the estimate is 1/1000 of the population.
,Chapter 1 Introduction, Measurement, Estimating
Responses to MisConceptual Questions
1. (c) As stated in the text, scientific laws are descriptive – they are meant to describe how nature
behaves. Since our understanding of nature evolves, so do the laws of physics, when evidence
can convince the community of physicists. The laws of physics are not permanent, and are not
subject to political treaties. In fact, there have been major changes in the laws of physics since
1900 – particularly due to relativity and quantum mechanics. The laws of physics apply in
chemistry and other scientific fields, since those areas of study are based on physics. Finally,
the laws of physics are man-made, not a part of nature. They are our “best description” of
nature as we currently understand it. As stated in the text, “Laws are not lying there in nature,
waiting to be discovered.”
2. (e) The first product is 142.08 m, which is only accurate to the 10’s place, since 37 m/s has only
two significant figures. The second product is 74.73 m, which is only accurate to the 1’s place,
since 5.3 s has only two significant figures. Thus the sum of the two terms can only be accurate
to the 10’s place. 142.08 + 74.73 = 216.81, which to the 10’s place is 220 m.
3. (a) The total number of digits present does not determine the precision, as the leading zeros in (c)
and (d) are only place holders. Rewriting all the measurements in units of meters shows that (a)
implies a precision of 0.0001m, (b) and (c) both imply a precision of 0.001 m, and (d) implies a
precision of 0.01 m. Note that since the period is shown, the trailing zeros are significant. If all
the measurements are expressed in meters, (a) has 4 significant figures, (b) and (c) each have 3
significant figures, and (d) has 2 significant figures.
4. (b) The leading zeros are not significant. Rewriting this number in scientific notation, 7.8 103 ,
shows that it only has two significant digits.
5. (b) When you add or subtract numbers, the final answer should contain no more decimal places
than the number with the fewest decimal places. Since 25.2 has one decimal place, the answer
must be rounded to one decimal place, or to 26.6. Thus the answer has 3 significant figures.
6. (b) The word “accuracy” is often misused. If a student repeats a measurement multiple times and
obtains the same answer each time, it is often assumed to be accurate. In fact, students are
frequently given an “ideal” number of times to repeat the experiment for “accuracy.” However,
systematic errors may cause each measurement to be inaccurate. A poorly working instrument
may also limit the accuracy of your measurement.
7. (a) Quoting the textbook, “precision” refers to the repeatability of the measurement using a given
instrument. Precision and accuracy are often confused. “Accuracy” is defined by answer (b).
8. (d) This addresses misconceptions about squared units and about which factor should be in the
numerator of the conversion. This error can be avoided by treating the units as algebraic
symbols that must be cancelled out.
9. (e) When making estimates, the estimator may frequently believe that their answers are more
significant than they actually are. This question helps the estimator realize what an order-of-
magnitude estimation is NOT supposed to accomplish.
10. (d) This addresses the fact that the generic unit symbol, like [L], does not indicate a specific system
of units.
, Physics for Scientists & Engineers wͅith Modern Physics, 5e, Global Edition Instructor Solutions Manual
Solutions to Problems
1. (a) 777 3 significant figures
(b) 81.60 4 significant figures
(c) 7.03 3 significant figures
(d) 0.03 1 significant figure
(e) 0.0086 2 significant figures
(f) 6465 4 significant figures
(g) 8700 2 significant figures
(a) 5.859 5.859 10
0
2.
(b) 21.8 2.1810
1
3
(c) 0.0068 6.810
328.65 3.2865 10
2
(d)
1
(e) 0.219 2.19 10
444 4.44 10
2
(f)
3. (a) 8.69 105 869, 000
(b) 9.1103 9100
(c) 2.5 101 0.25
(d) 4.76 102 476
(e) 3.62 105 0.0000362
0.35 m
4. % uncertainty 100% 11%
3.25 m
0.2 s
5. (a) % uncertainty 100% 4.444% 4%
4.5s
0.2 s
(b) % uncertainty 100% 0.4444% 0.4%
45s
(c) The time of 4.5 minutes is 270 seconds.
0.2 s
% uncertainty 100% 0.0741% 0.07%
270 s
