Question:

> Why do scientists plot graphs of their data instead of just listing values?

> What are the first two steps to be followed in solving almost any physics problem?

> Sort the following units into three groups of dimensions and identify the dimensions: fathoms, grams, years, kilometers, miles, months, kilograms, inches, seconds.

> In the following calculations, be sure to use an appropriate number of significant figures. 3.68 × 107 g − 4.759 × 105 g

> What are some of the differences between the SI and the customary U.S. system of units? Why is SI preferred for scientific work?

> List three of the base units used in SI.

> Why is it important to write quantities with the correct number of significant figures?

> Are all the digits listed as “significant figures” definitely known? Might any of the significant digits be less definitely known than others? Explain.

> After which numeral is the decimal point usually placed in scientific notation? What determines the number of numerical digits written in scientific notation?

> What are some of the advantages of scientific notation?

> Once the solution of a problem has been found, what should be done before moving on to solve another problem?

> Why are simplified models used in scientific study if they do not exactly match real conditions?

> Why must words be carefully defined for scientific use?

> Give a few reasons for studying physics.

> Write these numbers in scientific notation: (a) the mass of a blue whale, 170 000 kg (b) the diameter of a helium nucleus, 0.000 000000 000 003 8 m.

> The population of a culture of yeast cells is studied to see the effects of limited resources (food, space) on population growth. (a) Make a graph of the yeast population (measured as the total mass of yeast cells, tabulated below) versus time. Draw a be

> On April 15, 1999, a South Korean cargo plane crashed due to a confusion over units. After takeoff, the first officer was instructed by the Shanghai tower to climb to 1500 m and maintain that altitude. The captain, after reaching 1450 m, twice asked the

> A baby was persistently spitting up after nursing, so the pediatrician prescribed ranitidine syrup to reduce the baby's stomach acid. The prescription called for 0.75 mL to be taken twice a day for a month. The pharmacist printed a label for the bottle o

> (a) How many center-stripe road reflectors, separated by 17.6 yd., are required along a 2.20-mile section of curving mountain roadway? (b) Solve the same problem for a road length of 3.54 km with the markers placed every 16.0 m. Would you prefer to be t

> Astronauts aboard the International Space Station use a massing chair to measure their mass. The chair is attached to a spring and is free to oscillate back and forth. The frequency of the oscillation is measured and is used to calculate the total mass m

> Use dimensional analysis to determine how the period T of a swinging pendulum (the elapsed time for a complete cycle of motion) depends on some, or all, of these properties: the length L of the pendulum, the mass m of the pendulum bob, and the gravitatio

> Three of the fundamental constants of physics are the speed of light, c = 3.0 × 108 m/s, the universal gravitational constant, G = 6.7 × 10−11 m3·kg−1·s−2, and Planck's constant, h = 6.6 × 10−34 kg·m2·s −1. (a) Find a combination of these three constant

> The electric power P drawn from a generator by a lightbulb of resistance R is P = V2/R, where V is the line voltage. The resistance of bulb B is 42% greater than the resistance of bulb A. What is the ratio PB/PA of the power drawn by bulb B to the power

> Without looking up any data, make an order-of-magnitude estimate of the annual consumption of gasoline (in gallons) by passenger cars in the United States. Make reasonable estimates for any quantities you need. Think in terms of average quantities. (1 ga

> The speed of ocean waves depends on their wavelength λ (measured in meters) and the gravitational field strength g (measured in m/s2) in this way: where K is a dimensionless constant. Find the values of the exponents p and q.

> Perform these operations with the appropriate number of significant figures. (a) 3.783 × 106 kg + 1.25 × 108 kg (b) (3.783 × 106 m)/ (3.0 × 10−2 s)

> The weight of an object at the surface of a planet is proportional to the planet's mass and inversely proportional to the square of the radius of the planet. Jupiter's radius is 11 times Earth's, and its mass is 320 times Earth's. An apple weighs 1.0 N o

> A car has a gas tank that holds 12.5 U.S. gal. Using the conversion factors from Appendix B. (a) determine the size of the gas tank in cubic inches. (b) A cubit is an ancient measurement of length that was defined as the distance from the elbow to the t

> Suppose you have a pair of Seven League Boots. These are magic boots that enable you to stride along a distance of 7.0 leagues with each step. (a) If you march along at a military march pace of 120 paces per minute, what is your speed in km/h? (b) Assu

> The average depth of the oceans is about 4 km, and oceans cover about 70% of Earth's surface. Make an order-of-magnitude estimate of the volume of water in the oceans. Do not look up any data. (Use your ingenuity to estimate the radius or circumference o

> One morning you read in the New York Times that a certain billionaire has a net worth of $59 000 000 000. Later that day you see her on the street, and she gives you a $100 bill. What is her net worth now? (Think of significant figures.)

> Kepler's third law of planetary motion says that the square of the period of a planet (T2) is proportional to the cube of the distance of the planet from the Sun (r3). Mars is about twice as far from the Sun as Venus. How does the period of Mars compare

> The weight W of an object is given by W = mg, where m is the object's mass and g is the gravitational field strength. The SI unit of field strength g, expressed in SI base units, is m/s2. What is the SI unit for weight, expressed in base units?

> Two thieves, escaping after a bank robbery, drop a sack of money on the sidewalk. Estimate the mass if the sack contains $1 000 000 in $20 bills.

> In the United States, we often use miles per hour (mi/h) when discussing speed, but the SI unit of speed is m/s. What is the conversion factor for changing m/s to mi/h?

> A furlong is 220 yd.; a fortnight is 14 d. How fast is 1 furlong per fortnight (a) in µm/s? (b) in km/d?

> Rank these measurements of surface area in order of the number of significant figures, from fewest to greatest: (a) 20 145 m2; (b) 1.750 × 103 cm2; (c) 0.000 36 mm2; (d) 8.0 × 10−2 mm2; (e) 0.200 cm2.

> The average speed of a nitrogen molecule in air is proportional to the square root of the temperature in kelvins (K). If the average speed is 475 m/s on a warm summer day (temperature = 300.0 K), what is the average speed on a frigid winter day (250.0 K)

> A sheet of paper has length 27.95 cm, width 8.5 in., and thickness 0.10 mm. What is the volume of a sheet of paper in cubic meters? (Volume = length × width × thickness.)

> The total length of the blood vessels in the body is roughly 100 000 km. Most of this length is due to the capillaries, which have an average diameter of 8 µm. Estimate the total volume of blood in the human body by assuming that all the blood is found i

> The record blue whale in Problem 73 had a mass of 1.9 × 105 kg. Assuming that its average density was 0.85 g/cm3, as has been measured for other blue whales, what was the volume of the whale in cubic meters (m3)? (Average density is mass divided by volum

> A typical virus is a packet of protein and DNA (or RNA) and can be spherical in shape. The influenza A virus is a spherical virus that has a diameter of 85 nm. If the volume of saliva coughed onto you by your friend with the flu is 0.010 cm3 and 10−9 is

> You are given these approximate measurements: (a) the radius of Earth is 6 × 106 m. (b) the length of a human body is 6 ft. (c) a cell's diameter is 2 × 10−6 m. (d) the width of the hemoglobin molecule is 3 × 10−9 m. (e) the distance between two atoms (

> Estimate the number of hairs on the average human head. Consider the number of hairs in an area of 1 cm2 and then consider the area covered by hair on the head.

> It is useful to know when a small number is negligible. Perform the following computations: (a) 186.300 + 0.0030, (b) 186.300 − 0.0030, (c) 186.300 × 0.0030, (d) 186.300/0.0030. (e) For cases (a) and (b), what percent error will result if you ignore

> Estimate the number of automobile repair shops in your city by considering its population, how often an automobile needs repairs, and how many cars each shop can service per day. Then do a web search to see if your estimate has the right order of magnitu

> The weight of a baby measured over the first 10 months is given in the following table. (a) Plot the baby's weight versus age. (b) What was the average monthly weight gain for this baby over the period from birth to 5 months? How do you find this value

> According to Kepler's third law, the orbital period T of a planet is related to the radius R of its orbit by T2 ∝ R3. Jupiter's orbit is larger than Earth's by a factor of 5.19. What is Jupiter's orbital period? (Earth's orbital period is 1 yr.)

> Use dimensional analysis to determine how the linear speed (v in m/s) of a particle traveling in a circle depends on some, or all, of the following properties: r is the radius of the circle; ω is an angular frequency in s−1 with which the particle orbits

> In a physics lab, students measure the sedimentation velocity v of spheres with radius r falling through a fluid. The expected relationship is v = 2r2 g (ρ − ρf)/(9η). (a) How should the students plot the data to test this relationship? (b) How could t

> In a laboratory you measure the decay rate of a sample of radioactive carbon. You write down the following measurements: (a) Plot the decay rate versus time. (b) Plot the natural logarithm of the decay rate versus the time. Explain why the presentation o

> A graph of x versus t4, with x on the vertical axis and t4 on the horizontal axis, is linear. Its slope is 25 m/s4 and its vertical axis intercept is 3 m. Write an equation for x as a function of t.

> You have just performed an experiment in which you measured many values of two quantities, A and B. According to theory, A = cB3 + A0. You want to verify that the values of c and A0 are correct by making a graph of your data that enables you to determine

> An object is moving in the x-direction. A graph of its position (i.e., its x-coordinate) as a function of time is shown. (a) What are the slope and vertical axis intercept? (Be sure to include units.) (b) What physical significance do the slope and int

> A nurse recorded the values shown in the following chart for a patient's temperature. Plot a graph of temperature versus elapsed time. From the graph, find (a) an estimate of the temperature at noon and (b) the slope of the graph. (c) Would you expect

> A patient's temperature was 97.0°F at 8:05 A.M. and 101.0°F at 12:05 P.M. If the temperature changes with respect to elapsed time was linear throughout the day, what would the patient's temperature be at 3:35 P.M.?

> Average-sized cells in the human body are about 10 µm in diameter. How many cells are in the human body? Make an order-of magnitude estimate.

> The quantity of energy Q transferred by heat conduction through an insulating pad in time interval Δt is described by Q/Δt = κA ΔT/d, where κ is the thermal conductivity of the material, A is the face area of the pad (perpendicular to the direction of he

> What is the order of magnitude of the height (in meters) of a 40-story building?

> Estimate the average number of times a human heart beats during its lifetime.

> Estimate the average mass of a person's leg.

> Estimate the volume of a soccer ball in cubic centimeters (cm3).

> What is the approximate distance from your eyes to a book you are reading?

> An object moving at constant speed v around a circle of radius r has an acceleration a directed toward the center of the circle. The SI unit of acceleration is m/s2. (a) Use dimensional analysis to find how a depends on v and r (i.e., find n and m so th

> An expression for buoyant force is FB = ρgV, where FB has dimensions [MLT−2], ρ (density) has dimensions [ML−3], and g (gravitational field strength) has dimensions [LT−2]. (a) What must be the dimensions of V? (b) Which could be the correct interpretat

> One equation involving force states that Fnet = ma, where Fnet is in newtons (N), m is in kg, and a is in m·s−2. Another equation states that F = −kx, where F is in newtons, k is in kg·s−2, and x is in m. (a) Analyze the dimensions of ma and kx to show t

> An equation for potential energy states U = mgy. If U is in joules (J), with m in kg, y in m, and g in m/s2, find the combination of SI base units that is equivalent to joules.

> An average-sized capillary in the human body has a cross-sectional area of about 150 µm2. What is this area in square millimeters (mm2)?

> The quantity of energy Q transferred by heat conduction through an insulating pad in time interval Δt is described by Q/Δt = κA ΔT/d, where κ is the thermal conductivity of the material, A is the face area of the pad (perpendicular to the direction of he

> A snail crawls at a pace of 5.0 cm/min. Express the snail's speed in (a) ft./s and (b) mi/h.

> (a) How many square centimeters are in 1 square foot? (1 in = 2.54 cm.) (b) How many square centimeters are in 1 square meter?

> Express this product in units of km3 with the appropriate number of significant figures:

> A molecule in air is moving at a speed of 459 m/s. How far would the molecule move during 7.00 ms (milliseconds) if it didn't collide with any other molecules?

> Blood flows through the aorta at an average speed of v = 18 cm/s. The aorta is roughly cylindrical with a radius r = 12 mm. The volume rate of blood flow through the aorta is π r2v. Calculate the volume rate of blood flow through the aorta in L/min.

> The intensity of the Sun's radiation that reaches Earth's atmosphere is 1.4 kW/m2 (kW = kilowatt; W = watt). Convert this to W/cm2.

> At the end of 2006 an expert economist predicted a drop in the value of the U.S. dollar against the euro of 10% over the next five years. If the exchange rate was $1.27 to 1 euro on November 5, 2006, and was $1.45 to 1 euro on November 5, 2007, what was

> The first modern Olympics in 1896 had a marathon distance of 40 km. In 1908, for the Olympic marathon in London, the length was changed to 42.195 km to provide the British royal family with a better view of the race. This distance was adopted as the offi

> A nerve impulse travels along a myelinated neuron at 80 m/s. What is this speed in (a) mi/h and (b) cm/ms?

> A beaker contains 255 mL of water. What is the volume of the water in (a) cubic centimeters? (b) cubic meters?

> The quantity of energy Q transferred by heat conduction through an insulating pad in time interval Δt is described by Q/Δt = κA ΔT/d, where κ is the thermal conductivity of the material, A is the face area of the pad (perpendicular to the direction of he

> The length of the river span of the Brooklyn Bridge is 1595.5 ft. The total length of the bridge is 6016 ft. Convert both of these lengths to meters.

> The label on a small soda bottle lists the volume of the drink as 355 mL. Use the conversion factor 1 gal = 128 fl oz. (a) How many fluid ounces are in the bottle? (b) A competitor's drink is labeled 16.0 fl oz. How many milliliters are in that drink?

> A cell membrane is 7.0 nm thick. How thick is it in inches?

> The density of body fat is 0.9 g/cm3. Find the density in kg/m3.

> Solve the following problem and express the answer in meters per second (m/s) with the appropriate number of significant figures: (3.21 m)/ (7.00 ms) =? Hint: Note that ms stands for milliseconds.

> Solve the following problem and express the answer in meters with the appropriate number of significant figures and in scientific notation:

> Given these measurements, identify the number of significant figures and rewrite in standard scientific notation. (a) 0.005 74 kg (b) 2 m (c) 0.450 × 10−2 m (d) 45.0 kg (e) 10.09 × 104 s (f) 0.095 00 × 105 mL

> Rank these measurements in order of the number of significant figures, from least to greatest. (a) 7.68 g (b) 0.420 kg (c) 0.073 m (d) 7.68 × 105 g (e) 4.20 × 103 kg (f) 7.3 × 10−2 m (g) 2.300 × 104 s

> Find the product below and express the answer with units and in scientific notation with the appropriate number of significant figures:

> On Monday, a stock market index goes up 5.00%. On Tuesday, the index goes down 5.00%. What is the net percentage change in the index for the two days? Explain why it is not zero.

> A study finds that the metabolic rate of mammals is proportional to m3/4, where m is total body mass. By what factor does the metabolic rate of a 70 kg human exceed that of a 5.0 kg cat?

> Samantha is 1.50 m tall on her eleventh birthday and 1.65 m tall on her twelfth birthday. By what factor has her height increased? By what percentage?

> A homeowner is told that she must increase the height of her fences 37% if she wants to keep the deer from jumping in to eat the foliage and blossoms. If the current fence is 1.8 m high, how high must the new fence be?

> 55 mi/h is approximately (a) 90 km/h (b) 30 km/h (c) 10 km/h (d) 2 km/h

> By what factor does the volume of a cube increase if the length of the edges is doubled? (a) 16 (b) 8 (c) 4 (d) 2

> One kilometer is approximately (a) 2 miles (b) 1/2 mile (c) 1/10 mile (d) 1/4 mile

> How many significant figures should be written in the product 0.007840 6 m × 9.450 20 m? (a) 3 (b) 4 (c) 5 (d) 6 (e) 7

> Rank the results of the following calculations in order of the number of significant figures, from least to greatest. (a) 6.85 × 10−5 m + 2.7 × 10−7 m (b) 702.35 km + 1897.648 km (c) 5.0 m × 4.302 m (d) (0.040/π) m

> The “scale” of a certain map is 1/10 000. This means the length of, say, a road as represented on the map is 1/10 000 the actual length of the road. What is the ratio of the area of a park as represented on the map to the actual area of the park?

> Refer to Exercise 8-21 and the data shown in Table 8-23. Construct a standardized p-chart and discuss your conclusions. Data from Exercise 8-21: Observations are taken from the output of a company making semiconductors. Table 8-23 shows the sample size