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(Parte 1 de 2) CHAPTER 1 Systems of Measurement 1* Which of the following is not one of the fundamental physical quantities in the SI system? (a) mass (b) length (c) force (d) time (e) All of the above are fundamental physical quantities. (c) Force is not a fundamental physical quantity; see text. 2 In doing a calculation, you end up with m/s in the numerator and m/s2 in the denominator.

What are your final units? (a) m2/s3 (b) 1/s (c) s3/m2 (d) s (e) m/s (d) (m/s)/(m/s2) = (m/s)(s2/m) = s. 3 Write the following using prefixes listed in Table 1-1 and the abbreviations listed on page EP-1; for example, 10,0 meters = 10 km. (a) 1,0,0 watts, (b) 0.002 gram, (c) 3 10-6 meter, (d) 30,0 seconds. (a) 1 MW (b) 2 mg (c) 3 m (d) 30 ks 4 Write each of the following without using prefixes: (a) 40 mW, (b) 4 ns, (c) 3 MW, (d) 25 km.

(a) 0.0040 W (b) 0.004 s (c) 3,0,0 W (d) 25,0 m 5* Write out the following (which are not SI units) wihout using any abbreviations. For example, 103 meters = 1 kilometer. (a) 10-12 boo, (b) 109 low, (c) 10-6 phone, (d) 10-18 boy, (e) 106 phone, (f) 10-9 goat (g) 1012 bull. (a) 1 picoboo (b) 1 gigalow (c) 1 microphone (d) 1 attoboy (e) 1 megaphone (f) 1 nanogoat (g) 1 terabull 6 In the following equations, the distance x is in meters, the time t is in seconds, and the velocity v is in meters per second. What are the SI units of the constants C1 and C2? (a) x = C1 + C2t (b) x = 1/2C1t2 (c) v2 = 2C1x (a) C1 and C2t must be in meters (d) x = C1 cos C2t (e) e C = vtC-21 (b) C1t2 must be in meters (c) v2 is in m2/s2; so C1x must be in m2/s2 (d) cos C2t is a number; C2t is a number (e) v is in m/s.

C2t is a number. Chapter 1 Systems of Measurement 7 If x is in feet, t is in seconds, and v is in feet per second, what are the units of the constants C1 and C2 in each part of Problem 6? It is only necessary to change the unit of length in each case from m (meter) to ft (foot). Thus, for example, in part (e), we have C1 in ft/s; C2 in s-1. 8 From the original definition of the meter in terms of the distance from the equator to the North Pole, find in meters (a) the circumference of the earth, and (b) the radius of the earth. (c) Convert your answers for (a) and (b) from meters into miles. (a) The Pole–Equator distance is one-fourth of the circumference (b) Use C = 2pR (c) Use the conversion factor (1 mi)/(1.61 km) = 1 C = 4 107 m.

9* The speed of sound in air is 340 m/s. What is the speed of a supersonic plane that travels at twice the speed of sound?

Give your answer in kilometers per hour and miles per hour. Find the speed in m/s 2. Use [1 h/(60 min/h)(60 s/min)] = 1 3. Use (1 mi/1.61 km) = 1 v = 2(340 m/s) = 680 m/s = 0.680 km/s v = (0.680 km/s)/(1 h/3600 s/h) = 2450 km/h v = (2450 km/h)(1 mi/1.61 km) = 1520 mi/h H = (6 12 + 10.5) in = 82.5 in H = (82.5 in)/(1 in/2.54 cm) = 210 cm 1 Complete the following: (a) 100 km/h = mi/h; (b) 60 cm = ___in; (c) 100 yd = ___m. Express H in inches 2. Use (1 in/2.54 cm) = 1 (a) (100 km/h)(1 mi/1.61 km) = 62.1 mi/h; (b) (60 cm)(1 in/2.54 cm) = 23.6 in; (c) (100 yd)/(1 yd/0.9144 m) = 91.4 m. 12 The main span of the Golden Gate Bridge is 4200 feet.

Express this distance in kilometers. (4200 ft)/(1 ft/0.3048 m)(1000 m/1 km) = 1.28 km. 13* Find the conversion factor to convert from miles per hour into kilometers per hour.

Since 1 mi = 1.61 km, (v mi/h) = (v mi/h)(1.61 km/1 mi) = 1.61v km/h. ___ft/s; (d) 60 mi/h = m/s. 15 There are 1.057 quarts in a liter and 4 quarts in a gallon. (a) How many liters are there in a gallon?

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(b) A barrel equals 42 gallons. How many cubic meters are there in a barrel? (a) 1 gal = (1 gal)(4 qt/1 gal)(1 L/1.057 qt) = 3.784 L; (b) 1 ba = (1 ba)(42 ga/1 ba)(3.784 L/1 ga)(1 m3/1000 L) = 0.1589 m3.

Chapter 1 Systems of Measurement 17* A right circular cylinder has a diameter of 6.8 in and a height of 2 ft. What is the volume of the cylinder in (a) cubic feet, (b) cubic meters, (c) liters? Express the diameter in feet 2. The volume of a cylinder is V = (pD2/4)H (b) Use (1 ft/0.3048 m) = 1 (c) Use (1000 L/1 m3) = 1 D = (6.8 in)(1 ft/12 in) = 0.567 ft V = [p(0.567 ft)2/4](2 ft) = 0.505 ft3 V = (0.505 ft3)(0.3048 m/1 ft)3 = 0.0143 m3 V = (0.0143 m3)(1000 L/1 m3) = 14.3 L 18 In the following, x is in meters, t is in seconds, v is in meters per second, and the acceleration a is in meters per. 19 What are the dimensions of the constants in each part of Problem 6? Referring to the results of Problem 6 we see that the dimensions are: 20 The law of radioactive decay is N(t) = N0e-lt, where N0 is the number of radioactive nuclei at t = 0, N(t) is the number remaining at time t, and l is a quantity known as the decay constant. What is the dimension of l?

Since the exponent must be a number, the dimension of l must be 1/T. 21* The SI unit of force, the kilogram-meter per second squared (kg×m/s2) is called the newton (N). Replace the variables by their dimensions 3. Use the SI units for L, M, and T UniUnits of G are m3/kg×s2 2 An object on the end of a string moves in a circle. The force exerted by the string has units of ML/T2 and depends on the mass of the object, its speed, and the radius of the circle. What combination of these variables gives the correct dimensions?

Write the relationship in terms of powers of the variables 2. Insert the appropriate dimensions 3. Solve for the exponents a, b, and c 4. Write the corresponding expression F = mavbrc MLT-2 = Ma(L/T)bLc a = 1; b = 2; b + c = 1, c = -1 F = mv2/r. Replace the variables by their dimensions 27 Kepler’s third law relates the period of a planet to its radius r, the constant G in Newton’s law of gravitation (F = Gm1m2/r2), and the mass of the sun MS.

What combination of these factors gives the correct dimensions for the period of a planet? Write a general expression for the period in terms of the dimensions of the variables 2. Solve for b, c, and a in that order 3. Write the result in terms of r, G, and MS T = LaGbMc; note that G = L3/(MT 2) (see Problem 21) T = La[L3/(MT 2)]bMc = La + 3bMc - bT -2b -2b = 1, b = -1/2; c - b = 0, c = -1/2; a + 3b = 0, a = 3/2. 28 The prefix giga means (a) 103 (b) 106 (c) 109 (d) 1012 (e) 1015 29* The prefix mega means (a) 10-9 (b) 10-6 (c) 10-3 (d) 106 (e) 109 30 The prefix pico means (a) 10-12 (b) 10-6 (c) 10-3 (d) 106 (e)109 31 The number 0.0005130 has _ significant figures. (a) one (b) three (c) four (d) seven (e) eight (c) four; the three zeros after the decimal point are not significant figures, but the last zero is significant.

32 The number 23.0040 has _ significant figures. (a) two (b) three (c) four (d) five (e) six (e) six; all digits including the last zero are significant.

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