Maria Jose fez um comentário

ÓTIMO MATERIAL

• 0 aprovações

2958 pág.

Pré-visualização50 páginas

1 Chapter 1 Systems of Measurement Conceptual Problems *1 \u2022 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. correct. is )(c 2 \u2022 Picture the Problem We can express and simplify the ratio of m/s to m/s2 to determine the final units. Express and simplify the ratio of m/s to m/s2: s sm sm s m s m 2 2 =\u22c5 \u22c5= and correct. is )(d 3 \u2022 Determine the Concept Consulting Table 1-1 we note that the prefix giga means 109. correct. is )(c 4 \u2022 Determine the Concept Consulting Table 1-1 we note that the prefix mega means 106. correct. is )(d *5 \u2022 Determine the Concept Consulting Table 1-1 we note that the prefix pico means 10\u221212. correct. is )(a 6 \u2022 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. correct. is )(c Chapter 1 2 7 \u2022 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. correct. is )(e 8 \u2022 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 wish to purchase a board of \u2033two arm lengths\u2033 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 \u2022 (a) True. You cannot add \u2033apples to oranges\u2033 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 \u2022\u2022 Picture the Problem Because \u3b8 is small, we can approximate it by \u3b8 \u2248 D/rm provided that it is in radian measure. We can solve this relationship for the diameter of the moon. Express the moon\u2019s diameter D in terms of the angle it subtends at the earth \u3b8 and the earth-moon distance rm: mrD \u3b8= Find \u3b8 in radians: rad00915.0 360 rad2524.0 =°×°= \u3c0\u3b8 Substitute and evaluate D: ( )( ) m1051.3 Mm384rad0.00915 6×= =D Systems of Measurement 3 *11 \u2022\u2022 Picture the Problem We\u2019ll assume that the sun is made up entirely of hydrogen. Then we can relate the mass of the sun 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: HHS MNM = Solve for NH: H S H M MN = Substitute numerical values and evaluate NH: 57 27 30 H 1019.1kg101.67 kg101.99 ×=× ×= \u2212N 12 \u2022\u2022 Picture the Problem Let P represent the population of the United States, r the rate of consumption and N the number of aluminum cans used annually. The population of the United States is roughly 3×108 people. Let\u2019s 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\u22122 kg. (a) Express the number of cans N used annually in terms of the daily rate of consumption of soft drinks r and the population P: trPN \u2206= Substitute numerical values and approximate N: ( ) ( ) cans10 y d24.365y1 people103 dperson can1 11 8 \u2248 \u239f\u239f\u23a0 \u239e\u239c\u239c\u239d \u239b× ×\u239f\u239f\u23a0 \u239e\u239c\u239c\u239d \u239b \u22c5=N (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: NmM = Chapter 1 4 Substitute numerical values and evaluate M: ( )( ) kg/y102 kg/can108.1cans/y10 9 211 ×\u2248 ×= \u2212M (c) Express the value of the aluminum as the product of M and the value at recycling centers: ( ) ( )( ) dollars/ybillion 2 y/102$ kg/y102kg/1$ kg/1$ Value 9 9 = ×= ×= = M 13 \u2022\u2022 Picture the Problem We can estimate the number of words in Encyclopedia Britannica by counting the number of volumes, estimating the average number of pages per volume, estimating the number of words per page, and finding the product of these measurements and estimates. Doing so in Encyclopedia Britannica leads to an estimate of approximately 200 million for the number of words. If we assume an average word length of five letters, then our estimate of the number of letters in Encyclopedia Britannica becomes 109. (a) Relate the area available for one letter s2 and the number of letters N to be written on the pinhead to the area of the pinhead: 22 4 dNs \u3c0= where d is the diameter of the pinhead. Solve for s to obtain: N ds 4 2\u3c0= Substitute numerical values and evaluate s: ( ) ( ) m10104 in cm54.2in 8 9 2 16 1 \u2212\u2248 \u23a5\u23a6 \u23a4\u23a2\u23a3 \u23a1 \u239f\u23a0 \u239e\u239c\u239d \u239b = \u3c0 s (b) Express the number of atoms per letter n in terms of s and the atomic spacing in a metal datomic: atomicd sn = Substitute numerical values and evaluate n: atoms20 atoms/m105 m10 10 8 \u2248×= \u2212 \u2212 n *14 \u2022\u2022 Picture the Problem The population of the United States is roughly 3 × 108 people. Assuming that the average family has four people, with an average of two cars per Systems of Measurement 5 family, there are about 1.5 × 108 cars in the United States. If we double that number to include trucks, cabs, etc., we have 3 × 108 vehicles. Let\u2019s assume that each vehicle uses, on average, about 12 gallons of gasoline per week. (a) Find the daily consumption of gasoline G: ( )( ) gal/d106 gal/d2vehicles103 8 8 ×= ×=G Assuming a price per gallon P = $1.50, find the daily cost C of gasoline: ( )( ) dollars/dbillion $1d/109$ gal/50.1$gal/d106 8 8 \u2248×= ×== GPC (b) Relate the number of barrels N of crude oil required annually to the yearly consumption of gasoline Y and the number of gallons of gasoline n that can be made from one barrel of crude oil: n tG n YN \u2206== Substitute numerical values and estimate N: ( ) ( ) barrels/y10 gal/barrel 19.4 d/y24.365gal/d106 10 8 \u2248 ×=N 15 \u2022\u2022 Picture the Problem We\u2019ll assume a population of 300 million (fairly accurate as of September, 2002) and a life expectancy of 76 y. We\u2019ll also assume that a diaper has a volume of about half a liter. In (c) we\u2019ll assume the disposal site is a rectangular hole in the ground and use the formula for the volume of such an opening to estimate the surface area required. (a) Express the total number N of disposable diapers used in the United States per year in terms of the number of children n in diapers and the number of diapers D used by each child in 2.5 y: nDN = Use the daily consumption, the number of days in a year, and the estimated length of time a child is in diapers to estimate the number of diapers D required per child: ilddiapers/ch103 y5.2 y d24.365 d diapers3 3×\u2248 ××=D Chapter 1 6 Use the assumed life expectancy to estimate the number of children n in diapers: ( ) children10 children10300 y76 y5.2 7 6 \u2248 ×\u239f\u239f\u23a0

Maria Jose fez um comentário

ÓTIMO MATERIAL

• 0 aprovações