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Topic 1 1 Topic 1 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 and : 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 and : R = | A - B | = 4 units.
1.2 Vector x-component y-component
- +
- -
+-
1.3 Vector . 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 ! A ! B ! A ! B ! A ! B ! A+ B ! B College Physics 12e Raymond Serway, Chris Vuille, John Hughes ( Solutions Manual All Chapters, 100% Original Verified, A+ Grade) (All Chapters Solutions Manual Supplement files download link at the end of this file) 1 / 4
Topic 1 2 vector 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 ~10
kg (c)~4 000 lb ≈ 2 000 kg or ~10 3 kg 1.6 Let us assume the atoms are solid spheres of diameter 10 - 10
- Then,
the volume of each atom is of the order of 10 - 30 m 3 . (More precisely, volume = .) Therefore, since 1 cm 3 = 10 - 6 m 3 , the number of atoms in the 1 cm 3 solid is on the order of 10 - 6
/ 10 - 30 = 10 24 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 1.10 In the metric system, units differ by powers of ten, so it’s very easy ! B
4 πr 3 /3
−1≤sin θ≤1 and −1≤cos θ≤1 2 / 4
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 / T 2 (b) L 1.4 All three equations are dimensionally incorrect.
1.6 (a) kg × m/s (b) Ft = p 1.8 132 m 2
1.10 3.09 cm/s 1.12 (a) 5.60 ´ 10 2 km = 5.60 ´ 10 5 m = 5.60 ´ 10 7 cm (b) 0.491 2 km = 4.912 ´ 10 4 cm (c) 6.192 km = 6.192 ´ 10 3 m = 6.192 ´ 10 5 cm 3 / 4
Topic 1 4 (d) 2.499 km = 2.499 ´ 10 3 m = 2.499 ´ 10 5 cm 1.14 10.6 km/L 1.16 9.2 nm/s
1.18 2.9 ´ 10
2 m 3
= 2.9 ´ 10
8 cm 3
1.20 2.57 ´ 10
6 m 3
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 ´ 10 8 m/s (b) 2.997 9 ´ 10 8 m/s (c) 2.997 925 ´ 10 8 m/s 1.30 (a) 346 m 2 ± 13 m 3 (b) 66.0 m ± 1.3 m
1.32 ~10
8 steps
1.34 ~10
8
people with colds on any given day 1.36 (a) 4.2 ´ 10 - 18 m 3 (b) ~10 - 1 m 3 (c) ~10 16 cells
1.38 10
- 14 kg 1.40 2.2 m 1.42 8.1 cm 1.44 Δs=r 1 2 +r 2 2 −2r 1 r 2 cos(θ 1 − θ 2
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