CH1 -PROBLEMS
1
Helpful conversions
1 in = 2.54 cm = 2.54x10-2 m
1 ft = 30.5 cm = 0.3305 m
1 mi = 5280 ft = 1.61 km
1 light year = 9.46 x 1015 m
Power
10-18
10-15
10-12
10-9
10-6
10-3
10-2
Prefix
attofemtopiconanomicromillicenti-
Abbr.
a
f
p
n

m
c
Power
10-1
101
103
106
109
1012
1015
1018
Prefix
decidekakilomegagigaterapetaexa-
Abbr.
d
da
k
M
G
T
P
E
1. List the steps of the scientific method.
2. How can only seven basic units serve to express any measured quantity?
3. Which of these is a scientific hypothesis? Explain.
a. Atoms are the smallest particles of matter.
b. The universe is surrounded by a second universe, the existence of which cannot be detected by scientists.
c. Albert Einstein was the greatest physicist of the twentieth century.
4. Scientific theories undergo change. Is this a strength or a weakness of science? Explain.
5. There are three _______________ SI units in mechanics and many ________________ units.
6. 1. Which areas of physics deal with the following?
a. how fast things move __________________________________________________________
b. how the shape of a cave affects an echo ____________________________________________
c. which sunglasses are best for cutting the glare on a ski slope ____________________________
d. how the cooling system in a refrigerator works ______________________________________
e. what lightning is _____________________________________________________________
f. how energy is produced by the sun ________________________________________________
7. Physics is the most basic science because
a. underneath biology is chemistry and underneath chemistry is physics.
b. it is about the nature of basic things like forces, energy, and motion.
c. you can better understand science in general if you understand physics.
d. the ideas of physics extend into more complex sciences.
e. All of these
2
8. Why do physicists use models?
a. to explain the complex features of simple phenomena
b. to describe all aspects of a phenomenon
c. to explain the basic features of complex phenomena
d. to describe all of reality
9. Which statement about models is NOT correct?
a. Models describe only part of reality.
b. Models help build hypotheses.
c. Models help guide experimental design.
d. Models manipulate a single variable or factor in an experiment.
10. Complete the following statement: Today, the standard unit of mass is defined in terms of
a. a specified volume of water at 4 °C.
b. a standard platinum-iridium cylinder.
c. a specified number of cesium atoms.
d. a standard platinum bar.
e. the speed of light.
11. The standard of time is based on:
a. the daily rotation of the Earth
b. the frequency of light emitted by Kr86
c. the yearly revolution of the Earth about the
sun
d.
e.
a precision pendulum clock
none of these
12. The standard of length is based on:
a. the distance from the north pole to the equator along a meridian passing through Paris
b. wavelength of light emitted by Hg198
c. wavelength of light emitted by Kr86
d. a precision meter stick in Paris
e. the speed of light
13. In 1866, the U. S. Congress defined the U. S. yard as exactly 3600/3937 international meter. This was done
primarily because:
a. length can be measured more accurately in meters than in yards
b. the meter is more stable than the yard
c. this definition relates the common U. S. length units to a more widely used system
d. there are more wavelengths in a yard than in a meter
e. the members of this Congress were exceptionally intelligent
14. What is a surface area and a volume of a sphere with a radius of 1.7 cm in SI system?
15. Justine and her friends exit the physics classroom and walk 0.81 km to their math class. While walking, Justine's
average step length is 58 cm. How many steps does she take in walking between these two classes?
3
16. 55 mi/h = ? m/s
17. List the symbols for units of length: m, cm, km, mm in order from smallest to largest
18. A square with an edge of exactly 1 cm has an area of (SI-units):
19. Calculate and express the result in scientific notation. The ratio
is (in scientific notation):
20. Which one of the following pairs of units may not be added together, even after the appropriate unit conversions
have been made?
a. grams and milligrams
c. miles and kilometers
e. kilograms and kilometers
b. slugs and kilograms
d. centimeters and yards
21.Calculate the following, and express the answer in scientific notation with the correct number of significant figures:
(0.82 + 0.042 ) x (4.4 x 103) =
22. You are asked to find the area of a room that is 4.56 m long and 5.668 m wide. How many significant figures should
you show in your answer?
23. You are asked to find the volume of a cube that is 2.5 cm high, 2.65 cm wide, and 3.456 cm long. How many
significant figures should you show in your answer?
4
24. A physics text has 1060 pages and is 33.5 millimeters thick between the inside front cover and the inside back
cover. What is the thickness of a page? The answer should be expressed in scientific notation with the correct
number of significant figures.
25. What is 78,900,000,000 expressed in scientific notation?
26. If some measurements agree closely with each other but differ widely from the actual value, these measurements
are
a. neither precise nor accurate.
c. acceptable as a new standard of accuracy.
b. accurate but not precise.
d. precise but not accurate.
27.
Poor precision in scientific measurements may arise from
a. significant figures.
c. scientific notation.
b. human error.
d. both significant figures and scientific notation.
28. These values were obtained as the mass of a bar of metal: 8.83 g; 8.84 g; 8.82 g. The known mass is 10.68 g. The
values are
a. accurate.
c. both accurate and precise.
b. precise.
d. neither accurate nor precise.
29.
A precise measurement is one that
a. contains the correct number of significant figures.
b. contains at least three significant figures.
c. is close to the true value.
d. is as exact as possible.
30. During a short interval of time the velocity v in m/s of an automobile is given by v = at2 + bt3, where the time t is
in seconds. The units of a and b are respectively:
31. Suppose A = BC, where A is expressed in [length]/[mass] and C in [length]/[time]. Then B is expressed in::
32. The mathematical relationship between three physical quantities is given by
and c in
. What is a expressed in?
. If b is expressed in
5
33. Using the units given for the variables in the table, determine which one of the following expressions is correct.
variable
f
L
g
units
1/s
m
m/s2
a.
b.
d.
e.
c.
34. How many significant figures are there in the following measurements?
a. 0.0845 kg
b. 37.00 h
c. 8 630 000.000 mi
d. 0.000 000 0217 g
e. 750 in.
f. 0.5003 s
35.Without calculating the result, find the number of significant figures in the following products and quotients.
a. 0.005032 x 4.0009
c. (3.52 x10–11) x(7.823 x1011)
b. 0.0080750 10.037
36. State the number of significant digits in each measurement.
a. 2804 m
b. 2.84 m
c. 0.0029 m
d. 0.003068 m
e. 4.6 x 105 m
f. 4.06 x 10-5 m
37. Calculate the following products and quotients without using a calculator.
a. (3.0 x105) x(2.0 x103) =
b. (3.0 x105) (2.0 x105) =
c. (3.0 x102) (2.0 x105) =
d. (3.0 x10-2) x(2.0 x105) =
e. (3.0 x10-2) (2.0 x10-5) =
38.
f. (3.0 x10-2) x (2.0 x10-5) =
In Hindu chronology, the longest time measure is a para. One para equals 311 040 000 000 000 years. Calculate
this value in megahours and in nanoseconds. Write your answers in scientific notation.
39. One light-year is the distance light travels in one year. This distance is equal to 9.461 x1015 m. After the sun, the
star nearest to Earth is Alpha Centauri, which is about 4.35 light-years from Earth. Express this distance in
a. megameters.
b. picometers.
6
40. It is estimated that the sun will exhaust all of its energy in about ten billion years. By that time, it will have
radiated about 1.2 x1044 J (joules) of energy. Express this amount of energy in
a. kilojoules.
b. nanojoules.
41. Rewrite the following quantities in scientific notation without prefixes.
a. 3582 gigabytes =
b. 0.0009231 milliwatts =
c. 53657 nanoseconds =
d. 5.32 milligrams =
e. 88900 megahertz =
f. 0.00000083 centimeters =
42. Rewrite the following quantities in units with SI prefixes.
a. 36582472 g =
b. 0.000000452 m =
c. 53236 V =
d. 4.62 x10–3 s =
43. Convert each of the following mass measurements to its equivalent in kilograms.
a. 147 g =
b. 11 Mg =
c. 7.23 g =
d. 478 mg =
44. Rank the following mass measurements from smallest to largest: 11.6 mg, 1021 g, 0.000 006 kg, 0.31 mg.
45. Convert each of the following time measurements to its equivalent in seconds.
a. 58 ns
b. 0.046 Gs
c. 9270 ms
d. 12.3 ks
7
46. Solve the following division problems:
a. 20.2 cm 7.41 s
b. 3.1416 cm 12.4 s
c. 13.78 g 11.3 mg
d. 18.21 g 4.4 cm3
47. Find the value of each of the following quantities.
a.
b.
c.
d.
48. Multiply or divide as indicated using significant digits correctly.
a. (5 x 108 m)(4.2 x 107 m)
b. (1.67 x 10–2 km)(8.5 x 10–6 km)
c. (2.6 x 104 kg)
d. (6.3 x 10–1 m)
(9.4 x 103 m3)
(3.8 x 102 s)
49. Solve the following problems. Write your answers in scientific notation.
a. 6 x 10–8 m2 - 4 x 10–8 m2
b. 3.8 x 10–12 m2 - 1.90 x 0–11 m2
c. 5.8 x 10–7 m2 - 28 x 10–9 m2
d. 4 x 10–3 m + 3 x 10–3 m2
ANSWERS:
1. The steps in the scientific method include making observations and collecting data that lead to a question,
formulating and objectively testing hypotheses by experiments, interpreting results and revising hypotheses if
necessary, and stating conclusions in a form that can be evaluated by others.
2. The basic units can be combined to form units for other quantities.
3. Only (a) is scientific, because there is a test for its wrongness. The statement is not only capable of being proven
wrong, but in fact it has been proven wrong. Statement b) has no test for possible wrongness and is therefore
unscientific- Some pseudoscientists and other pretenders of knowledge will not even consider a test for the
possible wrongness of their statements. Statement (c) is an assertion that has no test for possible wrongness. If
Einstein was not the greatest physicist, how would we know? It is important to note that because the name
Einstein is generally held in high esteem, it is a favorite of pseudoscientists. So we should not be surprised that the
name Einstein, like the names of other prominent and respected figures, is often cited by charlatans who wish to
bring respect to themselves and their point of view.
4. A strength; change can nurture growth.
5. basic , derived.
6. a. mechanics (laws of motion)
b. vibrations and waves (sound or acustics)
c. optics
d. thermodynamics
e. electricity
f. nuclear physics
8
7. E
8.
9.
10.
11.
12.
13.
14.
15.
16.
34.
35.
36.
37.
38.
C
D
B
E
E
C
3.6  10–3 m2
2.1  10–5 m3
1400 = 14x102
25 m/s
a. 3
a. 4
a. 4
a. 6.0 x 108
b. 4
b. 5
b. 3
b. 1.5 x 102
17. mm, cm, m, and km.
18. 10–4 m2
19. 106.
20. B
21.3.8 x 103
22. 3
23. 2
24. 3.16  105 m
25. 7.89 x 1010
26. D
27. B
c. 10
d. 3
c. 3
c. 2
d. 4
c. 1.5 x 10-3 d. 6.0 x 103
28. B
29.D
30.m/s3; m/s4
31. [length]2/[time][mass]
32.
33. C
e. 2
e. 2
e. 1.5 x 103
f.
4
f. 3
f. 6.0 x 10-7
1 para = 311 040 000 000 000 years = 3.11 04 x 1014 years = 2.7247 x 1018 h = 9.8090x1021 s
1 para = 2.7247 x 1018 h = 2.7247 x 1012 x 106 h = 2.7247 x 1012 Mh
1 para = 9.8090x1021 s = 9.8090x1021 x109x10-9 s = 9.8090 x 1030 ns
39. 4.35 light years = 4.12 x 1016 m
4.35 ly = 4.12 x 1010 x 106 m = 4.12 x 1010 M m
4.35 ly = 4.12 x 1016 x 1012 x 10 -12 m = 4.12 x 1028 pm
40. 1.2 x 1044 J = 1.2 x 1041 x 103 J = 1.2 x 1041 kJ
1.2 x 1044 J = 1.2 x 1044 x 109 x 10-9 J = 1.2 x 1053 nJ
41.
a. 3.582x1012 bytes b. 9.2331x10-7 W
d. 5.32 x 10-3 g
e. 8.8900 x 1010 Hz
42. a. 36.582472 Mg
b. 452 nm
c. 5.3657x 10-5 s
f. 8.3 x 10-9 m
c. 53.236 kV
43. a. 147 x 10–3 kg = 1.47 x 10–1 kg
c. 7.23 x 10–6 x 10–3kg = 7.23 x 10–9kg
44.
11.6 mg = 11.6 x 10–3 g
0.000 006 kg = 6 x 10–3 g
0.31 mg, 1021 g, 0.000 006 kg, 11.6 mg
45. a. 5.8 x 10–8 s
46. a. 2.73 cm/s
47. a. 3 x 104 kg/m3
48. a. 2 x 1016 m2
c. 2.8 kg/m3
49. a. 2 x 10–8 m2
c. 5.58 x 10–9 m2
b. 4.6 x 107 s
b. 11 x 106 x 10-3 kg = 1.1 x 104 kg
d. 4.78 x 10–4 kg
1021 g = 1.021 x 10–3 g
0.31 mg = 0.31 x 10–3 g
d. 1.23 x 104 s
c. 9.27 s
b. 0.253 cm/s
b. 3 x 1012 kg/m3
d. 4.62 ms
c. 1.22 x 103
d. 4.1 g/cm3
-12
3
c. 3 x 10 kg/m
d.3 x 10-4 kg/m3
–7
2
b. 1.4 x 10 km
d. 1.7 x 10–3 m/s
b. - 1.52 x 0–11 m2
d. 4 x 10 m + 3 x 10–3 m2
–3