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 official marathon length in 1921. What is the official length of the marathon in miles?
> 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
> (a) Estimate the number of breaths you take in one year. (b) Estimate the volume of air you breathe in during one year.
> 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
> 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
> A computer monitor manufacturer subcontracts its major parts to four vendors: A, B, C, and D. Past records show that vendors A and C provide 30% of the requirements each, vendor B provides 25%, and vendor D provides 15%. In a random sample of 10 parts, 4
> Distinguish between producer’s risk and consumer’s risk. In this context, explain the terms acceptable quality level and limiting quality level. Discuss instances for which one type of risk might be more important than the other.
> Explain the difference between the decision-making procedure using Forms 1 and 2 for variable sampling plans that are designed to estimate the proportion of nonconforming items.
> What are the parameters of a variable sampling plan for which the process average quality is of interest? Explain the working procedure of such a plan when single and double specification limits are given.
> What are the advantages and disadvantages of variable sampling plans over those for attributes?
> Discuss the assumptions made in Deming’s kp rule. When would you use this rule?
> Compare and contrast chain sampling and sequential sampling plans. When are they used?
> Discuss the advantages and disadvantages of sampling.
> Suppose that the dimension of an assembly has to be within certain tolerances. Discuss how tolerances could be set for the components given that the difference between two component dimensions comprises this assembly dimension. Assume that the inherent v
> Suppose that the time to complete a project is the sum of several independent operations. If the means and standard deviations of the independent operations are known, determine the mean and standard deviation of the project completion time. If the opera
> What condition must exist prior to calculating the process capability? Discuss how process capability can be estimated through control charts.
> Discuss the indices for measuring quality costs. Give examples where each might be used.
> Compare the capability indices Cpk, Cpm, and Cpmk and discuss what they measure in the process. When would you use Cpq?
> What are the advantages of having a process spread that is less than the specification spread? What should the value of Cp be in this situation? Could Cpk be here?
> Is it possible for a process to be in control and still produce nonconforming output? Explain. What are some corrective measures under these circumstances?
> What are statistical tolerance limits? Explain how they differ from natural tolerance limits.
> Explain the difference between natural tolerance limits and specification limits. How does a process capability index incorporate both of them? What assumptions are made in constructing the natural tolerance limits?
> Distinguish between gage repeatability and gage reproducibility in the context of measuring unloading times of super tankers.
> Discuss how the precision of a measurement system affects the process potential in the context of measuring unloading times of super tankers. What bounds exist on the observed process potential?
> Discuss the importance of identifying an appropriate distribution of the quality characteristic in process capability analysis. Address this in the context of waiting time for service in a fast-food restaurant during lunch hour.
> Explain the difference between specification limits and control limits. Is there a desired relationship between the two?
> Discuss the role of the customer in influencing the proportion-nonconforming chart. How would the customer be integrated into a total quality systems approach?
> Classify each of the following into the cost categories of prevention, appraisal, internal failure, and external failure: (a) Vendor selection (b) Administrative salaries (c) Downgraded product (d) Setup for inspection (e) Supplier control (f) External c
> Is it possible for a process to be in control and still not meet some desirable standards for the proportion nonconforming? How would one detect such a condition, and what remedial actions would one take?
> Discuss the assumptions that must be satisfied to justify using a p-chart. How are they different from the assumptions required for a c-chart?
> What are the advantages and disadvantages of the standardized p-chart as compared to the regular proportion-nonconforming chart?
> How does changing the sample size affect the center line and the control limits of a p-chart?
> The CEO of a company has been charged with reducing the proportion nonconforming of the product output. Discuss which control charts should be used and where they should be placed.
