HW1 - Homeworkset1 Solutions Chapter1: 2

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Homework set 1 Solutions Chapter 1: 2 In doing a calculation, you end up with m/s in the numerator and m/s 2 in the denominator. What are your final units? ( a ) m 2 /s 3 , ( b ) 1/s, ( c ) s 3 /m 2 , ( d ) s, ( e ) m/s. Picture the Problem We can express and simplify the ratio of m/s to m/s 2 to determine the final units. Express and simplify the ratio of m/s to m/s 2 : s s m s m s m s m 2 2 = = and ) ( d is correct. 4 The prefix mega means ( a ) 10 –9 , ( b ) 10 –6 , ( c ) 10 –3 , ( d ) 10 6 , ( e ) 10 9 . Determine the Concept Consulting Table 1 1 we note that the prefix mega means 10 6 . ) ( d is correct. 17 •• There is an environmental debate over the use of cloth versus disposable diapers. ( a ) If we assume that between birth and 2.5 y of age, a child uses 3 diapers per day, estimate the total number of disposable diapers used in the United States per year. ( b ) Estimate the total landfill volume due to these diapers, assuming that 1000 kg of waste fills about 1 m 3 of landfill volume. ( c ) How many square miles of landfill area at an average height of 10 m is needed for the disposal of diapers each year? Picture the Problem We’ll assume a population of 300 million (fairly accurate as of September, 2002) and a life expectancy of 76 y. We’ll also assume that a diaper has a volume of about half a liter. In ( c ) we’ll 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: nD N = 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: ild diapers/ch 10 3 y 5 . 2 y d 24 . 365 d diapers 3 3 × × × = D
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Use the assumed life expectancy to estimate the number of children n in diapers: () children 10 children 10 300 y 76 y 5 . 2 7 6 × = n Substitute to obtain: ( ) diapers 10 3 ild diapers/ch 10 3 children 10 10 3 7 × × × = N ( b ) Express the required landfill volume V in terms of the volume of diapers to be buried: diaper one NV V = Substitute numerical values and evaluate V : 3 7 3 3 10 m 10 2 L m 10 diaper L 5 . 0 diapers 10 3 × × × = V ( c ) Express the required volume in terms of the volume of a rectangular parallelepiped: Ah V = h V A = Substitute numerical values evaluate A : 2 6 3 7 m 10 2 m 10 m 10 2 × = × = A Use a conversion factor to express this area in square miles: 2 2 2 6 2 2 2 6 mi 8 . 0 m km 10 km 2.590 mi 1 m 10 2 × × × = A 36 What are the dimensions of the constants in each part of Problem 23? Picture the Problem We can use the facts that each term in an equation must have the same dimensions and that the arguments of a trigonometric or exponential function must be dimensionless to determine the dimensions of the constants.
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HW1 - Homeworkset1 Solutions Chapter1: 2

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