SOLUTION
MANUAL
FOR
COLLEGE
PHYSICS
TH
12 E
.
,Solutions Manual for College Physics 12th Edition by Serway
Topic 1 1
Topic 1
Complete Chapters
Units, Trigonometry, and Vectors
QUICK QUIZZES
1.1 Choice (c). The largest possible magnitude of the resultant occurs when
the two vectors are in the same direction. In this case, the magnitude of
the resultant is the sum of the magnitudes of A and B : R = A + B = 20
units. The smallest possible magnitude of the resultant occurs when the
two vectors are in opposite directions, and the magnitude is the
difference of the magnitudes of A and B : R = | A − B | = 4 units.
1.2
Vector x-component y-component
A − +
B + −
A+B − −
1.3 Vector B . The range of the inverse tangent function includes only the first
and fourth quadrants (i.e., angles in the range −/2 /2). Only
.
,Topic 1 2
vector B has an orientation in this range.
ANSWERS TO EVEN NUMBERED CONCEPTUAL QUESTIONS
1.2 Atomic clocks are based on the electromagnetic waves that atoms
emit. Also, pulsars are highly regular astronomical clocks.
1.4 (a) ~0.5 lb ≈ 0.25 kg or ~10−1 kg
(b) 4 lb ≈ 0.25 kg or ~100 kg
(c) ~4 000 lb ≈ 2 000 kg or ~103 kg
1.6 Let us assume the atoms are solid spheres of diameter 10−10 m. Then,
the volume of each atom is of the order of 10 −30 m3 . (More precisely,
volume = 4 r3 /3 .) Therefore, since 1 cm3 = 10− 6 m3 , the number of
atoms in the 1 cm3 solid is on the order of 10 − − 30 = 1024 atoms. A
more precise calculation would require knowledge of the density of
the solid and the mass of each atom. However, our estimate agrees
with the more precise calculation to within a factor of 10.
1.8 Choice (d). For an angle from 0 to 360, the sine and cosine
functions take the values
−1 sin 1 and − 1 cos 1
1.10 In the metric system, units differ by powers of ten, so it’s very easy
.
, Topic 1 3
and accurate to convert from one unit to another.
1.12 Both answers (d) and (e) could be physically meaningful. Answers (a),
(b), and (c) must be meaningless since quantities can be added or
subtracted only if they have the same dimensions.
1.14 The correct answer is (a). The second measurement is more precise
but, given the number of reported significant figures, each
measurement is consistent with the other.
1.16 The components of a vector will be equal in magnitude if the vector
lies at a 45 angle with the two axes along which the components lie.
ANSWERS TO EVEN NUMBERED PROBLEMS
1.2 (a) L / T2 (b) L
1.4 All three equations are dimensionally incorrect.
1.6 (a) kg m/s (b) Ft = p
1.8 132 m2
1.10 3.09 cm s
1.12 (a) 5.60 102 km = 5.60 105 m = 5.60 107 cm
(b) 0.491 2 km = 4.912 104 cm
(c) 6.192 km = 6.192 103 m = 6.192 105 cm
.
MANUAL
FOR
COLLEGE
PHYSICS
TH
12 E
.
,Solutions Manual for College Physics 12th Edition by Serway
Topic 1 1
Topic 1
Complete Chapters
Units, Trigonometry, and Vectors
QUICK QUIZZES
1.1 Choice (c). The largest possible magnitude of the resultant occurs when
the two vectors are in the same direction. In this case, the magnitude of
the resultant is the sum of the magnitudes of A and B : R = A + B = 20
units. The smallest possible magnitude of the resultant occurs when the
two vectors are in opposite directions, and the magnitude is the
difference of the magnitudes of A and B : R = | A − B | = 4 units.
1.2
Vector x-component y-component
A − +
B + −
A+B − −
1.3 Vector B . The range of the inverse tangent function includes only the first
and fourth quadrants (i.e., angles in the range −/2 /2). Only
.
,Topic 1 2
vector B has an orientation in this range.
ANSWERS TO EVEN NUMBERED CONCEPTUAL QUESTIONS
1.2 Atomic clocks are based on the electromagnetic waves that atoms
emit. Also, pulsars are highly regular astronomical clocks.
1.4 (a) ~0.5 lb ≈ 0.25 kg or ~10−1 kg
(b) 4 lb ≈ 0.25 kg or ~100 kg
(c) ~4 000 lb ≈ 2 000 kg or ~103 kg
1.6 Let us assume the atoms are solid spheres of diameter 10−10 m. Then,
the volume of each atom is of the order of 10 −30 m3 . (More precisely,
volume = 4 r3 /3 .) Therefore, since 1 cm3 = 10− 6 m3 , the number of
atoms in the 1 cm3 solid is on the order of 10 − − 30 = 1024 atoms. A
more precise calculation would require knowledge of the density of
the solid and the mass of each atom. However, our estimate agrees
with the more precise calculation to within a factor of 10.
1.8 Choice (d). For an angle from 0 to 360, the sine and cosine
functions take the values
−1 sin 1 and − 1 cos 1
1.10 In the metric system, units differ by powers of ten, so it’s very easy
.
, Topic 1 3
and accurate to convert from one unit to another.
1.12 Both answers (d) and (e) could be physically meaningful. Answers (a),
(b), and (c) must be meaningless since quantities can be added or
subtracted only if they have the same dimensions.
1.14 The correct answer is (a). The second measurement is more precise
but, given the number of reported significant figures, each
measurement is consistent with the other.
1.16 The components of a vector will be equal in magnitude if the vector
lies at a 45 angle with the two axes along which the components lie.
ANSWERS TO EVEN NUMBERED PROBLEMS
1.2 (a) L / T2 (b) L
1.4 All three equations are dimensionally incorrect.
1.6 (a) kg m/s (b) Ft = p
1.8 132 m2
1.10 3.09 cm s
1.12 (a) 5.60 102 km = 5.60 105 m = 5.60 107 cm
(b) 0.491 2 km = 4.912 104 cm
(c) 6.192 km = 6.192 103 m = 6.192 105 cm
.
