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Chapter_1_09

# Chapter_1_09 - Chapter 1 Problems 1.1 The micrometer is...

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Chapter 1 Problems 1.1 The micrometer is often called the micron. (a) How man microns make up 1 km? (b) What fraction of a centimeter equals 1 μ m ? (c) How many microns are in 1.0 yard We begin by calculating 1 km in microns d = 1.0 km 1000 m 1 km 1 micron 1 × 10 6 m = 1 × 10 9 microns Now calculate a distance of 1 micron in cm. d = 1 micron 1 × 10 6 m 1 micron 100 cm 1 m = 1 × 10 4 cm Finally we compute a distance of 1 yard in microns. d = 1 yd 3 ft 1 yd 0.3048 m 1 ft 1 micron 1 × 10 6 m = 9.144 × 10 5 microns 1.3 Horses are to race over a certain English meadow for a distance of 4 furlongs. What is the race distance in units of (a) rods and (b) chains? (1 furlong = 201.168m, 1 rod - 5.0292 m and 1 chain = 20.117) d = 4 furlongs 201.168 m 1 furlong = 8.04672 × 10 2 m d = 8.04672 × 10 2 m 1 rod 5.0292 m = 160 rods d = 8.04672 × 10 2 m 1 chain 20.117 = 40 chains 1.5 The Earth is approximately a sphere of radius 6.37 x 10 6 m. (a) What is is its circumference in kilometers? (b) What is its surface area in square kilometers? (c) What is its volume in cubic kilometers? To do all three sections of this problem, we can first convert the radius to kilometers. r = 6.37 × 10 6 m 1 km 1000 m = 6.37 × 10 3 km

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(a) The formula for circumference can be found in most calculus books (and in Appendix E of your Physics text). We will assume that we are finding the circumference of the equator. c = 2 π r = 2 π 6.37 × 10 3 km = 4.002 × 10 4 km (b) The surface area of a sphere is: a = 4 π r 2 = 4 π (6.37 × 10 3 km ) 2 = 5.099 × 10 8 km 2 (c) The volume of a sphere is: v = 4 3 π r 3 = 4 3 π (6.37 × 10 3 km ) 3 = 1.083 × 10 12 km 3 1.7 Antarctica is roughly semicircular, with a radius of 2000 km. The average thickness of its ice cover is 3000m. How many cubic centimeters of ice does Antarctica contain? (Ignore the curvature of the earth) r=2000m 3000m We find the volume in cubic meters first and then convert. Volume = ( Area of half circle ) ( depth ) = π r 2 2 d = π (2000 × 10 3 m ) 2 2 3000 m = 1.885 × 10 16 m 3 = 1.885 × 10 16 m 3 ( 100 cm 1 m ) 3 = 1.885 × 10 22 cm 3 1.9 Hydraulic engineers often use, as a unit of volume of water, the acre-foot, defined a the volume of water that will cover 1 acre of land to a depth of 1 ft. A severe thunderstorm dumps 2.0 inches of rain in 30 min. on a town of area 26 km 2 . What volume of water in acre-feet, fell on the town? We first convert the depth to feet and the area to acres.
d = 2.0 in 1 ft 12 in = 0.1667 ft a = 26 km 2 ( 1000 m 1 km ) 2 2.471 acres 10 4 m 2 = 6.4245 × 10 3 acres Volume = a d = 6.4245 × 10 3 acres 0.1667 ft = 1.071 × 10 3 acre ft 1.18 Because Earth’s rotation is gradually slowing, the length of each day increases: The day at the end of the 1.0 century is 1.0 ms longer than the day at the start of the century.

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Chapter_1_09 - Chapter 1 Problems 1.1 The micrometer is...

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