Chapter 1

Chapter thumbnail
Infrared Andromeda Galaxy (M31).

Chapter 1 : Measurement and the scientific method. - all with Video Solutions

Problems & Exercises

Section 1.2: Physical Quantities and Units

Problem 2

A car is traveling at a speed of 33 m/s. (a) What is its speed in kilometers per hour? (b) Is it exceeding the 90 km/h speed limit?

View solution

Problem 3

Show that 1.0 m/s=3.6 km/h1.0 \textrm{ m/s} = 3.6 \textrm{ km/h} . Hint: Show the explicitsteps involved in converting 1.0 m/s=3.6 km/h1.0 \textrm{ m/s} = 3.6 \textrm{ km/h}

View solution

Problem 4

American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)

View solution

Problem 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.)

View solution

Problem 7

Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.)

View solution

Problem 9

Tectonic plates are large segments of the Earth's crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?

View solution

Problem 10

(a) Refer to Table 1.3 to determine the average distance between the Earth and the Sun. Then calculate the average speed of the Earth in its orbit in kilometers per second. (b) What is this in meters per second?

View solution

Section 1.3: Accuracy, Precision, and Significant Figures

Problem 11

Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)?

View solution

Problem 13

(a) A car speedometer has a 5.0% uncertainty. What is the range of possible speeds when it reads 90 km/h90\textrm{ km/h}? (b) Convert this range to miles per hour. (1 km=0.6214 mi1 \textrm{ km} = 0.6214 \textrm{ mi})

View solution

Problem 14

An infant's pulse rate is measured to be 130±5 beats/min130 \pm 5 \textrm{ beats/min}. What is the percent uncertainty in this measurement?

View solution

Problem 15

(a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats does he or she have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y?

View solution

Problem 17

State how many significant figures are proper in the results of the following calculations: (a) (106.7)(98.2)(46.210)(1.01)\dfrac{(106.7)(98.2)}{(46.210)(1.01)} (b) (18.7)2(18.7)^2 (c) (1.60×1019)(3712)\left( 1.60 \times 10^{-19} \right) (3712)

View solution

Problem 18

(a) How many significant figures are in the numbers 99 and 100? (b) If the uncertainty in each number is 1, what is the percent uncertainty in each? (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties?

View solution

Problem 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?

View solution

Problem 20

(a) A person's blood pressure is measured to be 120±2 mm Hg120 \pm 2 \textrm{ mm Hg} . What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of 80 mm Hg?

View solution

Problem 21

A person measures his or her heart rate by counting the number of beats in 30 s30 \textrm{ s} . If 40±140 \pm 1 beats are counted in

30.0±0.5 s30.0 \pm 0.5 \textrm{ s}, what is the heart rate and its uncertainty in beats per minute?

View solution

Problem 24

A marathon runner completes a 42.188 km course in 2 h, 30 min, and 12 s. There is an uncertainty of 25 m in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the uncertainty in the elapsed time. (c) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?

View solution

Problem 25

The sides of a small rectangular box are measured to be 1.80±0.01 cm1.80 \pm 0.01 \textrm{ cm} 2.05±0.02 cm2.05 \pm 0.02 \textrm{ cm} 3.1±0.1 cm3.1 \pm 0.1 \textrm{ cm}, long. Calculate its volume and uncertainty in cubic centimeters.

View solution

Problem 26

When non-metric units were used in the United Kingdom, a unit of mass called the pound-mass (lbm) was employed, where 1 lbm = 0.4539 kg . (a) If there is an uncertainty of 0.0001 kg in the pound-mass unit, what is its percent uncertainty? (b) Based on that percent uncertainty, what mass in pound-mass has an uncertainty of 1 kg when converted to kilograms?

View solution

Problem 27

The length and width of a rectangular room are measured to be 3.955±0.005 m3.955 \pm 0.005 \textrm{ m} and 3.050±0.005 m3.050 \pm 0.005 \textrm{ m}. Calculate the area of the room and its uncertainty in square meters.

View solution

Problem 28

A car engine moves a piston with a circular cross section of 7.500±0.002 cm7.500 \pm 0.002 \textrm{ cm} diameter a distance of 3.250±0.001 cm3.250 \pm 0.001 \textrm{ cm} to compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters? (b) Find the uncertainty in this volume.

View solution

Section 1.4: Approximation

Problem 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 1022 s10^{-22} \textrm{ s}.)

View solution

Problem 32

Calculate the approximate number of atoms in a bacterium. Assume that the average mass of an atom in the bacterium is ten times the mass of a hydrogen atom. (Hint: The mass of a hydrogen atom is on the order of 10×1027 kg10\times 10^{-27}\textrm{ kg} and the mass of a bacterium is on the order of 10×1015 kg10\times 10^{-15}\textrm{ kg})

View solution

Problem 33

Approximately how many atoms thick is a cell membrane, assuming all atoms there average about twice the size of a hydrogen atom?

View solution

Problem 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?

View solution

Problem 36

Assuming one nerve impulse must end before another can begin, what is the maximum firing rate of a nerve in impulses per second?

View solution

Test Prep for AP® Courses