CollegePhysics2e-SSM-Ch01

OpenStax College Physics 2e Student Solutions Manual Chapter 1

OpenStax College Physics 2e Student Solutions Manual Chapter 1 CHAPTER 1: INTRODUCTION: THE NATURE OF SCIENCE AND PHYSICS 1.2 PHYSICAL QUANTITIES AND UNITS 1. The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this? Solution (a) 100 km h × 1000 m 1 km × 1 h 3600 s = 27.77 m / s = 27.8 m / s (b) 100 km h × 1 mi 1.609 km = 62 mi / h 3. Show that 1.0 m / s = 3.6 km / h . Hint: Show the explicit steps involved in converting 1.0 m / s = 3.6 km / h . Solution 1.0 m s = 1.0 m s × 3600 s hr × 1 km 1000 m = 3.6 km / h 5. Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? (Assume that 1 meter equals 3.281 feet.) Solution 115 m× 1 ft 0.3048 m = 377.3 ft = 377 ftlong 377.3 ft × 12 ∈ . 1.0 ft = 4528 ∈ . = 4.53 × 10 3 ∈ .long 85 m× 1 ft 0.3048 m = 278.9 ft = 2.8 × 10 2 ft wide 278.9 ft× 12 ∈ . 1.0 ft = 3346 ∈ . = 3.3 × 10 3 ∈ .wide

OpenStax College Physics 2e Student Solutions Manual Chapter 1 (b) 85.5 km h × 0.6214 mi 1 km = 53.1 mi / h; 94.5 km 1 h × 0.6214 mi 1 km = 58.7 mi / h 53.1 Sothe rangeis ¿ 58.7 mi / h ¿ . 15. (a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats do they have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y? Solution 72.0 beats 1 min × 60.0 min 1.00 h × 24.0 h 1.00 d × 365.25 d 1.00 y × 2.0 y = 7.5738 × 10 7 beats ( a) 7.6 × 10 7 beats (limited by 2.0 y) (b) 7.57 × 10 7 beats (limited by 2.00 y) (c) 7.57 × 10 7 beats (limited by 72.0 beats/min) 17. State how many significant figures are proper in the results of the following calculations: (a) ( 106.7 ) ( 98.2 ) / ( 46.210 ) ( 1.01 ) (b) ( 18.7 ) 2 (c) ( 1.60 × 10 − 19 ) ( 3712 ) . Solution (a) 3 (limited by 98.2 and 1.01) (b) 3 (limited by 18.7) (c) 3 (limited by 1.60) 19. (a) If your speedometer has an uncertainty of 2.0 km / h at a speed of 90 km / h , what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads 60 km / h , what is the range of speeds you could be going?

OpenStax College Physics 2e Student Solutions Manual Chapter 1 Solution (a) % unc = 2.0 km / h 90 km / h × 100% = 2.2% (b) δ v = 2.2% 100% × 60 km / h = 1 km / h So the range is 60 ± 1 km / h or 59 ¿ 61 km / h ¿ . 21. A person measures their heart rate by counting the number of beats in 30 s . If 40 ± 1 beats are counted in 30.0 ± 0.5 s , what is the heart rate and its uncertainty in beats per minute? Solution beats minute = 40 beats 30.0 s × 60.0 s 1.00 min = 80 beats / min. % unc = 1 beat 40 beats × 100% + 0.5 s 30.0 s × 100% = 2.5% + 1.7% = 4.2% = 4% δ A = % unc 100% × A = 4.2% 100% × 80 beats / min = 3.3 beats / min = 3 beats / min The heart rate is 80 ± 3 beats / min. 23. If a marathon runner averages 9.5 mi/h, how long does it take him or her to run a 26.22-mi marathon? Solution 26.22 mi 9.5 mi / h = 2.8 h 25. The sides of a small rectangular box are measured to be 1.80 ± 0.01 cm , 2.05 ± 0.02 cm , and 3.1 ± 0.1 cm long. Calculate its volume and uncertainty in cubic centimeters.

OpenStax College Physics 2e Student Solutions Manual Chapter 1 Solution 1 lifetime× 10 9 s 0.5 lifetime × 1 heartbeat 1 s = 2 × 10 9 heartbeats 31. How many times longer than the mean life of an extremely unstable atomic nucleus is the lifetime of a human? (Hint: The lifetime of an unstable atomic nucleus is on the order of 10 − 22 s .) Solution 2 × 10 31 × ¿ T h T n = 2 × 10 9 s 10 − 22 s = ¿ 33. Approximately how many atoms thick is a cell membrane, assuming all atoms there average about twice the size of a hydrogen atom? Solution d m d a = d m 2 d H = 10 − 8 m ( 2 )( 10 − 10 m / atom ) = 50 atoms 35. (a) Calculate the number of cells in a hummingbird assuming the mass of an average cell is ten times the mass of a bacterium. (b) Making the same assumption, how many cells are there in a human? Solution (a) 10 − 2 kg / hummingbird 10 × 10 − 15 kg / cell = 10 12 cells / hummingbird (b) 10 2 kg / person 10 × 10 − 15 kg / cell = 10 16 cells / person This file is copyright 2022, Rice University. All Rights Reserved.