Chapter 1 Systems of Measurement
*1 • Determine the Concept The fundamental physical quantities in the SI system include mass, length, and time. Force, being the product of mass and acceleration, is not a fundamental quantity. (c) is correct. 2 • Picture the Problem We can express and simplify the ratio of m/s to m/s2 to determine thefinal units. Express and simplify the ratio of m/s to m/s2:
m 2 s = m ⋅ s = s and (d ) is correct. m m ⋅s 2 s
3 • Determine the Concept Consulting Table 1-1 we note that the prefix giga means 109. (c ) is correct. 4 • Determine the Concept Consulting Table 1-1 we note that the prefix mega means 106. (d ) is correct. *5 • Determine the Concept Consulting Table 1-1 we note that the prefix picomeans 10−12. (a ) is correct. 6 • Determine the Concept Counting from left to right and ignoring zeros to the left of the first nonzero digit, the last significant figure is the first digit that is in doubt. Applying this criterion, the three zeros after the decimal point are not significant figures, but the last zero is significant. Hence, there are four significant figures in this number.
7 • Determine the Concept Counting from left to right, the last significant figure is the first digit that is in doubt. Applying this criterion, there are six significant figures in this number. (e) is correct. 8 • Determine the Concept The advantage is that the length measure is always with you. The disadvantage is that arm lengths are not uniform; if you wishto purchase a board of ″two arm lengths″ it may be longer or shorter than you wish, or else you may have to physically go to the lumberyard to use your own arm as a measure of length. 9 • (a) True. You cannot add ″apples to oranges″ or a length (distance traveled) to a volume (liters of milk). (b) False. The distance traveled is the product of speed (length/time) multiplied by the time of travel(time). (c) True. Multiplying by any conversion factor is equivalent to multiplying by 1. Doing so does not change the value of a quantity; it changes its units.
Estimation and Approximation
*10 •• Picture the Problem Because θ is small, we can approximate it by θ ≈ D/rm provided that it is in radian measure. We can solve this relationship for the diameter of the moon. Express the moon’sdiameter D in terms of the angle it subtends at the earth θ and the earth-moon distance rm: Find θ in radians:
D = θ rm
θ = 0.524° ×
2π rad = 0.00915 rad 360°
Substitute and evaluate D:
D = (0.00915 rad )(384 Mm )
= 3.51 × 106 m
Systems of Measurement
*11 •• Picture the Problem We’ll assume that the sun is made up entirely of hydrogen. Then we can relate the mass of thesun to the number of hydrogen atoms and the mass of each. Express the mass of the sun MS as the product of the number of hydrogen atoms NH and the mass of each atom MH: Solve for NH:
M S = NHM H
1.99 × 1030 kg = 1.19 × 1057 1.67 × 10 −27 kg
Substitute numerical values and evaluate NH:
12 •• Picture the Problem Let P represent the population of the United States, rthe rate of consumption and N the number of aluminum cans used annually. The population of the United States is roughly 3×108 people. Let’s assume that, on average, each person drinks one can of soft drink every day. The mass of a soft-drink can is approximately 1.8 ×10−2 kg. (a) Express the number of cans N used annually in terms of the daily rate of consumption of soft drinks r and thepopulation P: Substitute numerical values and approximate N:
N = rP∆t
⎛ 1can ⎞ 8 N =⎜ ⎜ person ⋅ d ⎟ 3 × 10 people ⎟ ⎝ ⎠ ⎛ d⎞ × (1 y )⎜ 365.24 ⎟ ⎜ y⎟ ⎝ ⎠
≈ 1011 cans
(b) Express the total mass of aluminum used per year for soft drink cans M as a function of the number of cans consumed and the mass m per can:
M = Nm
Substitute numerical values and evaluate M:...
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