Solutions Manual for College Physics 12th Edition By Raymond Serway (Author), Chris Vuille (Author), John Hughes (Author) | All chapters | Newest version A+

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 -p/2 < q < p/2). Only




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
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 = 4π r 3 /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 q from 0° to 360°, the sine and cosine

functions take the values

−1 ≤ sin θ ≤ 1 and − 1 ≤ cosθ ≤ 1


1.10 In the metric system, units differ by powers of ten, so it’s very easy




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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


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(d) 2.499 km = 2.499 ´ 103 m = 2.499 ´ 105 cm


1.14 10.6 km/L


1.16 9.2 nm/s


1.18 2.9 ´ 102 m3 = 2.9 ´ 108 cm3


1.20 2.57 ´ 106 m3


1.22 (a) 797 (b) 1.1 (c) 17.66


1.24 58


1.26 (a) 22.6 (b) 22.7 (c) 22.6 is more reliable


1.28 (a) 3.00 ´ 108 m/s (b) 2.997 9 ´ 108 m/s


(c) 2.997 925 ´ 108 m/s


1.30 (a) 346 m2 ± 13 m3 (b) 66.0 m ± 1.3 m


1.32 ~108 steps


1.34 ~108 people with colds on any given day


1.36 (a) 4.2 ´ 10-18 m3 (b) ~10-1 m3 (c) ~1016 cells


1.38 10-14 kg


1.40 2.2 m


1.42 8.1 cm


1.44 Δs = r12 + r22 − 2r1r2 cos(θ1 − θ 2 )


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