Solved: A watch manufacturer claims that its watches gain

How many significant figures do each of the following numbers have: (a) 214, (b) 81.60, (c) 7.03, (d) 0.03, (e) 0.0086, ( ) 3236, and (g) 8700?

Write the following numbers in powers of 10 notation: (a) 1.156, (b) 21.8, (c) 0.0068, (d) 328.65, (e) 0.219, and ( ) 444

(I) Write out the following numbers in full with the correct number of zeros: (a) \(8.69 \times 10^4\), (b) \(9.1 \times 10^3\), (c) \(8.8 \times 10^{-1}\), (d) \(4.76 \times 10^2\), and (e) \(3.62 \times 10^{-5}\).

The age of the universe is thought to be about 14 billion years. Assuming two significant figures, write this in powers of 10 in (a) years, (b) seconds

What is the percent uncertainty in the measurement 5.4860.25 m?

Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 s, due to human reaction time at the start and stop moments. What is the percent uncertainty of a hand-timed measurement of (a) 5.5 s, (b) 55 s, (c) 5.5 min?

Add A9.2 * 103 sB + A8.3 * 104 sB + A0.008 * 106 sB.

Multiply by taking into account significant figures.

What, approximately, is the percent uncertainty for a measurement given as

What, roughly, is the percent uncertainty in the volume of a spherical beach ball of radius

What is the area, and its approximate uncertainty, of a circle of radius

Write the following as full (decimal) numbers without prefixes on the units: (a) 286.6 mm, (b) (c) 760 mg, (d) 62.1 ps, (e) 22.5 nm, ( ) 2.50 gigavolts

Express the following using the prefixes of Table 14: (a) (b) (c) (d) and

One hectare is defined as One acre is How many acres are in one hectare?

The Sun, on average, is 93 million miles from Earth. How many meters is this? Express (a) using powers of 10, and (b) using a metric prefix (km).

Express the following sum with the correct number of significant figures:

A typical atom has a diameter of about (a) What is this in inches? (b) Approximately how many atoms are along a 1.0-cm line, assuming they just touch?

Determine the conversion factor between (a) and (b) and and

A light-year is the distance light travels in one year (at speed (a) How many meters are there in 1.00 light-year? (b) An astronomical unit (AU) is the average distance from the Sun to Earth, How many AU are there in 1.00 light-year?

(II) How much longer (percentage) is a one-mile race than a 1500-m race (“the metric mile”)?

American football uses a field that is 100.0 yd long, whereas a soccer field is 100.0 m long. Which field is longer, and by how much (give yards, meters, and percent)?

(a) How many seconds are there in 1.00 year? (b) How many nanoseconds are there in 1.00 year? (c) How many years are there in 1.00 second?

Use Table 13 to estimate the total number of protons or neutrons in (a) a bacterium, (b) a DNA molecule, (c) the human body, (d) our Galaxy.

A standard baseball has a circumference of approximately 23 cm. If a baseball had the same mass per unit volume (see Tables in Section 15) as a neutron or a proton, about what would its mass be?

(I) Estimate the order of magnitude (power of 10) of: (a) 2800, (b) \(86.30 \times 10^3\), (c) 0.0076, and (d) \(15.0 \times 10^8\).

Estimate how many hours it would take to run (at ) across the U.S. from New York to California

Estimate the number of liters of water a human drinks in a lifetime

Estimate how long it would take one person to mow a football field using an ordinary home lawn mower (Fig. 115). (State your assumption, such as the mower moves with a speed, and has a 0.5-m width.)

Estimate how long it would take one person to mow a football field using an ordinary home lawn mower (Fig. 115). (State your assumption, such as the mower moves with a speed, and has a 0.5-m width.)

Estimate the number of gallons of gasoline consumed by the total of all automobile drivers in the U.S., per year.

Estimate the number of dentists (a) in San Francisco and (b) in your town or city

You are in a hot air balloon, 200 m above the flat Texas plains. You look out toward the horizon. How far out can you seethat is, how far is your horizon? The Earths radius is about 6400 km.

I agree to hire you for 30 days. You can decide between two methods of payment: either (1) $1000 a day, or (2) one penny on the first day, two pennies on the second day and continue to double your daily pay each day up to day 30. Use quick estimation to make your decision, and justify it

Many sailboats are docked at a marina 4.4 km away on the opposite side of a lake. You stare at one of the sailboats because, when you are lying flat at the waters edge, you can just see its deck but none of the side of the sailboat. You then go to that sailboat on the other side of the lake and measure that the deck is 1.5 m above the level of the water. Using Fig. 116, where estimate the radius R of the Earth

You are lying on a beach, your eyes 20 cm above the sand. Just as the Sun sets, fully disappearing over the horizon, you immediately jump up, your eyes now 150 cm above the sand, and you can again just see the top of the Sun. If you count the number of seconds until the Sun fully disappears again, you can estimate the Earths radius. But for this Problem, use the known radius of the Earth to calculate the time t.

What are the dimensions of density, which is mass per volume?

The speed of an object is given by the equation where refers to time. (a) What are the dimensions of A and B? (b) What are the SI units for the constants A and B?

Three students derive the following equations in which x refers to distance traveled, the speed, a the acceleration the time, and the subscript zero means a quantity at time . Here are their equations: (a) (b) and (c) Which of these could possibly be correct according to a dimensional check, and why?

The smallest meaningful measure of length is called the Planck length, and is defined in terms of three fundamental constants in nature: the speed of light the gravitational constant and Plancks constant The Planck length is given by the following combination of these three constants: Show that the dimensions of are length [L], and find the order of magnitude of [Recent theories (Chapters 32 and 33) suggest that the smallest particles (quarks, leptons) are strings with lengths on the order of the Planck length, These theories also suggest that the Big Bang, with which the universe is believed to have begun, started from an initial size on the order of the Planck length.]

Global positioning satellites (GPS) can be used to determine your position with great accuracy. If one of the satellites is 20,000 km from you, and you want to know your position to what percent uncertainty in the distance is required? How many significant figures are needed in the distance?

Computer chips (Fig. 117) are etched on circular silicon wafers of thickness 0.300 mm that are sliced from a solid cylindrical silicon crystal of length 25 cm. If each wafer can hold 400 chips, what is the maximum number of chips that can be produced from one entire cylinder?

A typical adult human lung contains about 300 million tiny cavities called alveoli. Estimate the average diameter of a single alveolus.

If you used only a keyboard to enter data, how many years would it take to fill up the hard drive in a computer that can store 1.0terabytes of data? Assume 40-hour work weeks, and that you can type 180 characters per minute, and that one byte is one keyboard character.

An average family of four uses roughly 1200 L (about 300 gallons) of water per day How much depth would a lake lose per year if it covered an area of with uniform depth and supplied a local town with a population of 40,000 people? Consider only population uses, and neglect evaporation, rain, creeks and rivers.

Estimate the number of jelly beans in the jar of Fig. 118.

How big is a ton? That is, what is the volume of something that weighs a ton? To be specific, estimate the diameter of a 1-ton rock, but first make a wild guess: will it be 1 ft across, 3 ft, or the size of a car? [Hint: Rock has mass per volume about 3 times that of water, which is 1 kg per liter or 62 lb per cubic foot.

A certain compact disc (CD) contains 783.216 megabytes of digital information. Each byte consists of exactly 8 bits. When played, a CD player reads the CDs information at a constant rate of 1.4 megabits per second. How many minutes does it take the player to read the entire CD?

Hold a pencil in front of your eye at a position where its blunt end just blocks out the Moon (Fig. 119). Make appropriate measurements to estimate the diameter of the Moon, given that the EarthMoon distance is 3.8 * 105 km

A storm dumps 1.0 cm of rain on a city 6 km wide and 8 km long in a 2-h period. How many metric tons of water fell on the city? ( of water has a mass of ) How many gallons of water was this?

Estimate how many days it would take to walk around the Earth, assuming 12 h walking per day at 4 kmh.

One liter of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the oil slick. Assume the oil molecules have a diameter of 2 * 1010 m

A watch manufacturer claims that its watches gain or lose no more than 8 seconds in a year. How accurate are these watches, expressed as a percentage?

An angstrom (symbol ) is a unit of length, defined as which is on the order of the diameter of an atom. (a) How many nanometers are in 1.0 angstrom? (b) How many femtometers or fermis (the common unit of length in nuclear physics) are in 1.0 angstrom? (c) How many angstroms are in 1.0 m? (d) How many angstroms are in 1.0 light-year (see Problem 19)?

Jim stands beside a wide river and wonders how wide it is. He spots a large rock on the bank directly across from him. He then walks upstream 65 strides and judges that the angle between him and the rock, which he can still see, is now at an angle of 30 downstream (Fig. 120). Jim measures his stride to be about 0.8 m long. Estimate the width of the river.

Determine the percent uncertainty in and in when

If you walked north along one of Earths lines of longitude until you had changed latitude by 1 minute of arc (there are 60 minutes per degree), how far would you have walked (in miles)? This distance is a nautical mile

Make a rough estimate of the volume of your body (in ).

The following formula estimates an average persons lung capacity V (in liters, where ): where H and A are the persons height (in meters) and age (in years), respectively. In this formula, what are the units of the numbers 4.1, 0.018, and 2.7?

One mole of atoms consists of individual atoms. If a mole of atoms were spread uniformly over the Earths surface, how many atoms would there be per square meter?

The density of an object is defined as its mass divided by its volume. Suppose a rocks mass and volume are measured to be 6 g and To the correct number of significant figures, determine the rocks density (mass volume).

Recent findings in astrophysics suggest that the observable universe can be modeled as a sphere of radius light-years with an average total mass density of about Only about 4% of total mass is due to ordinary matter (such as protons, neutrons, and electrons). Estimate how much ordinary matter (in kg) there is in the observable universe. (For the light-year, see Problem 19.)

How many are in ? (a) 10. (b) 100. (c) 1000. (d) 10,000. (e) 100,000. (f) 1,000,000.

The area of a rectangle 4.5 cm by 3.25 cm is correctly given by

Problem 1EB All three have three significant figures; the number of decimal places is (a) 2, (b) 3, (c) 4.

Problem 1EC (a) 2.58 X 10-2, 3; (b)4.23 X 104, 3(Probably); (c) 3.4450 X 102 , 5.

Problem 1ED Return to the first Chapter-Opening Question, page 1, and answer it again now. Try to explain why you may have answered differently the first time.

Problem 1EE Would a driver traveling 15 m/s at in a 35 mi/h zone be exceeding the speed limit? Why or why not?

Return to the second Chapter-Opening Question, page 1, and answer it again now. Try to explain why you may have answered differently the first time.

Problem 1MCQ A student’s weight displayed on a digital scale is 117.2 lb. This would suggest her weight is (a) within 1% of 117.2 lb. (b) exactly 117.2 lb. (c) somewhere between 117.18 and 117.22 lb. (d) somewhere between 117.0 and 117.4 lb.

Problem 1P (I) How many significant figures do each of the following numbers have: (a) 214, (b) 81.60, (c) 7.03, (d) 0.03, (e) 0.0086, (f) 3236, and (g) 8700?

Problem 1Q What are the merits and drawbacks of using a person’s foot as a standard? Consider both (a) a particular person’s foot, and (b) any person’s foot. Keep in mind that it is advantageous that fundamental standards be accessible (easy to compare to), invariable (do not change), indestructible, and reproducible.

Problem 1SL Galileo is to Aristotle as Copernicus is to Ptolemy. See Section 1–1 and explain this analogy.

Problem 2COQ Suppose you wanted to actually measure the radius of the Earth, at least roughly, rather than taking other people’s word for what it is. Which response below describes the best approach? (a) Use an extremely long measuring tape. (b) It is only possible by flying high enough to see the actual curvature of the Earth. (c) Use a standard measuring tape, a step ladder, and a large smooth lake. (d) Use a laser and a mirror on the Moon or on a satellite. (e) Give up; it is impossible using ordinary means.

Problem 2MCQ Four students use different instruments to measure the length of the same pen. Which measurement implies the greatest precision? (a) 160.0mm. (b) 16.0 cm. (c) 0.160 m. (d) 0.00016 km. (e) Need more information.

Problem 2P (I) Write the following numbers in powers of 10 notation: (a) 1.156, (b) 21.8, (c) 0.0068, (d) 328.65, (e) 0.219, and (f) 444.

Problem 2Q What is wrong with this road sign: Memphis 7 mi (11.263 km)?

Problem 2SL How many wavelengths of orange krypton-86 light (Section 1–5) would fit into the thickness of one page of this book?

Problem 3MCQ The number 0.0078 has how many significant figures? (a) 1. (b) 2. (c) 3. (d) 4.

(I) Write out the following numbers in full with the correct number of zeros: and

Why is it incorrect to think that the more digits you include in your answer, the more accurate it is?

Problem 3SL Using the French Academy of Sciences’ original definition of the meter, determine Earth’s circumference and radius in those meters.

Problem 4MCQ How many significant figures does 1.362 +25.2 have? (a) 2. (b) 3. (c) 4. (d) 5.

Problem 4P (II) The age of the universe is thought to be about 14 billion years. Assuming two significant figures, write this in powers of 10 in (a) years, (b) seconds.

Problem 4Q For an answer to be complete, the units need to be specified. Why?

Problem 4SL Estimate the ratio (order of magnitude) of the mass of a human to the mass of a DNA molecule.

Problem 5MCQ Accuracy represents (a) repeatability of a measurement, using a given instrument. (b) how close a measurement is to the true value. (c) an ideal number of measurements to make. (d) how poorly an instrument is operating.

II) What is the percent uncertainty in the measurement \(5.48\pm0.25\mathrm{\ m}\)? Equation Transcription: Text Transcription: 5.48 +/- 0.25 m

Problem 5Q You measure the radius of a wheel to be 4.16 cm. If you multiply by 2 to get the diameter, should you write the result as 8 cm or as 8.32 cm? Justify your answer.

Problem 5SL To the correct number of significant figures, use the information inside the front cover of this book to determine the ratio of (a) the surface area of Earth compared to the surface area of the Moon; (b) the volume of Earth compared to the volume of the Moon.

To convert from \(f t^{2} \text { to } y d^{2}\), you should (a) multiply by 3. (b) multiply by 1/ 3. (c) multiply by 9. (d) multiply by 1/ 9. (e) multiply by 6. (f) multiply by 1/ 6. Equation Transcription: Text Transcription: ft^2 to yd^2

Problem 6P (II) Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 s, due to human reaction time at the start and stop moments. What is the percent uncertainty of a hand-timed measurement of (a) 5.5 s, (b) 55 s, (c) 5.5 min?

Problem 6Q Express the sine of 30.0° with the correct number of significant figures.

Problem 7MCQ Which is not true about an order-of-magnitude estimation? (a) It gives you a rough idea of the answer. (b) It can be done by keeping only one significant figure. (c) It can be used to check if an exact calculation is reasonable. (d) It may require making some reasonable assumptions in order to calculate the answer. (e) It will always be accurate to at least two significant figures.

Add

Problem 7Q List assumptions useful to estimate the number of car mechanics in (a) San Francisco, (b) your hometown, and then make the estimates.

\(\left[L^{2}\right]\) represents the dimensions for which of the following? (a) \(\mathrm{cm}^{2}\). (b) square feet. (c) \(m^{2}\). (d) All of the above. Equation Transcription: Text Transcription: [L^2] cm^2 m^2

Problem 8P (II) Multiply by 3.079 X 102 m by 0.068 X 10-1 m, taking into account significant figures.

(II) What, approximately, is the percent uncertainty for a measurement given as ?

(III) What, roughly, is the percent uncertainty in the volume of a spherical beach ball of radius \(r=0.84 \pm 0.04 \mathrm{\ m}\)? Equation Transcription: Text Transcription: r= 0.84 ± 0.04 m

What is the area, and its approximate uncertainty, of a circle of radius ?

Express the following using the prefixes of Table 1–4: (a) (b) (c) (d) and (e)

(I) Write the following as full (decimal) numbers without prefixes on the units: (a) , (b) \(85\ \mu V\), (c) , (d) gigavolts. Equation Transcription: Text Transcription: 85 mu V

One hectare is defined as One acre is How many acres are in one hectare?

Problem 15P (II) The Sun, on average, is 93 million miles from Earth. How many meters is this? Express (a) using powers of 10, and (b) using a metric prefix (km).

Problem 15Q Can the diver of Fig. 8–28 do a somersault without having any initial rotation when she leaves the board? Explain.

Problem 16P (II) A turntable of radius R1 is turned by a circular rubber roller of radius R2 in contact with it at their outer edges. What is the ratio of their angular velocities, w1/w2

Problem 16P (II) A turntable of radius R1 is turned by a circular rubber roller of radius R2 in contact with it at their outer edges. What is the ratio of their angular velocities, w1/w2

A typical atom has a diameter of about (a) What is this in inches? (b) Approximately how many atoms are along a 1.0-cm line, assuming they just touch?

Problem 18P (II) Determine the conversion factor between (a) km/h and mi/h (b) m/s and ft/s and (c) km/h and m/s.

A light-year is the distance light travels in one year (at (a) How many meters are there in 1.00 light-year? (b) An astronomical unit (AU) is the average distance from the Sun to Earth, How many AU are there in 1.00 light-year?

Problem 20P (II) How much longer (percentage) is a one-mile race than a 1500-m race (“the metric mile”)?

Problem 21P (II) American football uses a field that is 100.0 yd long, whereas a soccer field is 100.0 m long. Which field is longer, and by how much (give yards, meters, and percent)?

Problem 22P (II) (a) How many seconds are there in 1.00 year? (b) How many nanoseconds are there in 1.00 year? (c) How many years are there in 1.00 second?

(II) Use Table 1–3 to estimate the total number of protons or neutrons in (a) a bacterium, (b) a DNA molecule, (c) the human body, (d) our Galaxy.

(III) A standard baseball has a circumference of approximately 23 cm. If a baseball had the same mass per unit volume (see Tables in Section 1–5) as a neutron or a proton, about what would its mass be?

(I) Estimate the order of magnitude (power of 10) of: (a) , (b) (c) and (d)

(II) Estimate how many books can be shelved in a college library with \(3500 \mathrm{~m}^{2}\) of floor space. Assume 8 shelves high, having books on both sides, with corridors 1.5 m wide. Assume books are about the size of this one, on average. Equation Transcription: Text Transcription: 3500 m^2

Problem 27P (II) Estimate how many hours it would take to run (at 10 km/h ) across the U.S. from New York to California.

Problem 28P (II) Estimate the number of liters of water a human drinks in a lifetime.

(II) Estimate how long it would take one person to mow a football field using an ordinary home lawn mower (Fig. 1–15). (State your assumption, such as the mower moves with a speed, and has a 0.5-m width.)

Problem 30P (II) Estimate the number of gallons of gasoline consumed by the total of all automobile drivers in the U.S., per year.

(II) Estimate the number of dentists (a) in San Francisco and (b) in your town or city.

Problem 32P (III) You are in a hot air balloon, 200 m above the flat Texas plains. You look out toward the horizon. How far out can you see—that is, how far is your horizon? The Earth’s radius is about 6400 km.

Problem 33P (III) I agree to hire you for 30 days. You can decide between two methods of payment: either (1) $1000 a day, or (2) one penny on the first day, two pennies on the second day and continue to double your daily pay each day up to day 30. Use quick estimation to make your decision, and justify it.

(III) Many sailboats are docked at a marina 4.4 km away on the opposite side of a lake. You stare at one of the sailboats because, when you are lying flat at the water’s edge, you can just see its deck but none of the side of the sailboat. You then go to that sailboat on the other side of the lake and measure that the deck is 1.5 m above the level of the water. Using Fig. 1–16, where \(h=1.5 \mathrm{\ m}\), estimate the radius of the Earth. FIGURE 1-16 Problem 34. You see a sailboat across a lake (not to scale). is the radius of the Earth. Because of the curvature of the Earth, the water “bulges out” between you and the boat. Equation Transcription: Text Transcription: h=1.5 m

Problem 35P (III) You are lying on a beach, your eyes 20 cm above the sand. Just as the Sun sets, fully disappearing over the horizon, you immediately jump up, your eyes now 150 cm above the sand, and you can again just see the top of the Sun. If you count the number of seconds ( =t) until the Sun fully disappears again, you can estimate the Earth’s radius. But for this Problem, use the known radius of the Earth to calculate the time t.

Problem 36P (I) What are the dimensions of density, which is mass per volume?

(II) The speed v of an object is given by the equation \(v=A t^{3}-B t\) where t refers to time. (a) What are the dimensions of A and B? (b) What are the SI units for the constants A and B?

Three students derive the following equations in which x refers to distance traveled, v the speed, a the acceleration t the time, and the subscript zero (0) means a quantity at time t =0 . Here are their equations: (a) (b) and (c) . Which of these could possibly be correct according to a dimensional check, and why?

Global positioning satellites (GPS) can be used to determine your position with great accuracy. If one of the satellites is 20,000 km from you, and you want to know your position to \(\pm\ 2\ \mathrm m\), what percent uncertainty in the distance is required? How many significant figures are needed in the distance? Equation Transcription: Text Transcription: +/- 2 m

(III) The smallest meaningful measure of length is called the Planck length, and is defined in terms of three fundamental constants in nature: the speed of light \(c=3.00 \times 10^{8} \mathrm{\ m} / \mathrm{s}\) the gravitational constant \(G=6.67\times10^{11}\mathrm{\ m}^3/\mathrm{kg}\cdot\mathrm{s}^2\), and Planck's constant \(h=6.63\times10^{-34}\mathrm{\ kg}\cdot\mathrm{m}^2/\mathrm{s}\). The Planck length \(\ell_{\mathrm{p}}\) is given by the following combination of these three constants: \(\ell_{\mathrm{P}}=\sqrt{\frac{G h}{c^{3}}}\). Show that the dimensions of \(\ell_{\mathrm{p}}\) are length , and find the order of magnitude of \(\ell_{\mathrm{p}}\). [Recent theories (Chapters 32 and 33 ) suggest that the smallest particles (quarks, leptons) are "strings" with lengths on the order of the Planck length, \(10^{-35}\ \mathrm m\). These theories also suggest that the "Big Bang, with which the universe is believed to have begun, started from an initial size on the order of the Planck length.] Equation Transcription: ?P ?P ?P ?P Text Transcription: c=3.00 x 10^{8} m/s G=6.67 x 10^{11} m{3}/{kg} cdot {s}^{2} h=6.63 x 10^{-34} kg \cdot{m}^{2}/{s} ell_{p} ell_{P}=sqrt {Gh}over{c^{3}} ell_{p} ell_{p} 10^{-35} m

Computer chips (Fig. 1–17) are etched on circular silicon wafers of thickness 0.300 mm that are sliced from a solid cylindrical silicon crystal of length 25 cm. If each wafer can hold 400 chips, what is the maximum number of chips that can be produced from one entire cylinder? FIGURE 1-17 Problem 41. The wafer held by the hand is shown below, enlarged and illuminated by colored light. Visible are rows of integrated circuits (chips).

Problem 42GP A typical adult human lung contains about 300 million tiny cavities called alveoli. Estimate the average diameter of a single alveolus.

If you used only a keyboard to enter data, how many years would it take to fill up the hard drive in a computer that can store 1.0 terabytes of data? Assume 40-hour work weeks, and that you can type 180 characters per minute, and that one byte is one keyboard character.

An average family of four uses roughly 1200 L (about 300 gallons) of water per day ( ) How much depth would a lake lose per year if it covered an area of with uniform depth and supplied a local town with a population of 40,000 people? Consider only population uses, and neglect evaporation, rain, creeks and rivers.

Problem 46GP How big is a ton? That is, what is the volume of something that weighs a ton? To be specific, estimate the diameter of a 1-ton rock, but first make a wild guess: will it be 1 ft across, 3 ft, or the size of a car? [Hint: Rock has mass per volume about 3 times that of water, which is 1 kg per liter (103 cm3)or 62 lb per cubic foot.]

Estimate the number of jelly beans in the jar of Fig. 1–18. FIGURE 1-18 Problem 45. Estimate the number of jelly beans in the jar.

A certain compact disc (CD) contains 783.216 megabytes of digital information. Each byte consists of exactly 8 bits. When played, a CD player reads the CD’s information at a constant rate of 1.4 megabits per second. How many minutes does it take the player to read the entire CD?

Hold a pencil in front of your eye at a position where its blunt end just blocks out the Moon (Fig. 1–19). Make appropriate measurements to estimate the diameter of the Moon, given that the Earth–Moon distance is \(3.8\times10^5\mathrm{\ km}\). FIGURE 1-19 Problem 48. How big is the Moon? Equation Transcription: Text Transcription: 3.8x10^{5} km

A storm dumps 1.0 cm of rain on a city 6 km wide and 8 km long in a 2-h period. How many metric tons (1 metric ton = ) of water fell on the city? ( of water has a mass of ) How many gallons of water was this?

Estimate how many days it would take to walk around the Earth, assuming 12 h walking per day at 4km/h.

One liter ( )of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the oil slick. Assume the oil molecules have a diameter of

A watch manufacturer claims that its watches gain or lose no more than 8 seconds in a year. How accurate are these watches, expressed as a percentage?

An angstrom (symbol Å) is a unit of length, defined as which is on the order of the diameter of an atom. (a) How many nanometers are in 1.0 angstrom? (b) How many femtometers or fermis (the common unit of length in nuclear physics) are in 1.0 angstrom? (c) How many angstroms are in 1.0 m? (d) How many angstroms are in 1.0 light-year (see Problem 19)?

Jim stands beside a wide river and wonders how wide it is. He spots a large rock on the bank directly across from him. He then walks upstream 65 strides and judges that the angle between him and the rock, which he can still see, is now at an angle of \(30^{\circ}\) downstream (Fig. 1–20). Jim measures his stride to be about 0.8 m long. Estimate the width of the river. FIGURE 1-20 Problem 54. Equation Transcription: Text Transcription: 30deg 30deg

Determine the percent uncertainty in \(\theta\), and in \(\sin \theta\), when \((a)\ \theta=15.0^{\circ} \pm 0.5^{\circ}\), \((b)\ \theta=75.0^{\circ} \pm 0.5^{\circ}\). Equation Transcription: Text Transcription: \theta \sin\ \theta (a) =15.0deg +/- 0.5deg (b) =75.0deg +/- 0.5deg

Problem 56G If you walked north along one of Earth’s lines of longitude until you had changed latitude by 1 minute of arc (there are 60 minutes per degree), how far would you have walked (in miles)? This distance is a nautical mile.

Make a rough estimate of the volume of your body (in \(m^3\)).

The following formula estimates an average person’s lung capacity V (in liters, where ): V = 4.1 H - 0.018 A - 2.7, where H and A are the person’s height (in meters) and age (in years), respectively. In this formula, what are the units of the numbers 4.1, 0.018, and 2.7?

One mole of atoms consists of individual atoms. If a mole of atoms were spread uniformly over the Earth’s surface, how many atoms would there be per square meter?

The density of an object is defined as its mass divided by its volume. Suppose a rock’s mass and volume are measured to be To the correct number of significant figures, determine the rock’s density (mass volume).

Recent findings in astrophysics suggest that the observable universe can be modeled as a sphere of radius \(R=13.7 \times 10^{9}\) light-years \(=13.0 \times 10^{25}\) m with an average total mass density of about \(1\times10^{-26}\mathrm{\ kg}/\mathrm{m}^3\). Only about 4% of total mass is due to “ordinary” matter (such as protons, neutrons, and electrons). Estimate how much ordinary matter (in kg) there is in the observable universe. (For the light-year, see Problem 19.) Equation Transcription: Text Transcription: R=13.7x10^9 =13.0x10^25 1x10^{-26} kg/m^3

How many significant figures do each of the following numbers have: (a) 214, (b) 81.60, (c) 7.03, (d) 0.03, (e) 0.0086, ( ) 3236, and (g) 8700?

Write the following numbers in powers of 10 notation: (a) 1.156, (b) 21.8, (c) 0.0068, (d) 328.65, (e) 0.219, and ( ) 444

Write out the following numbers in full with the correct number of zeros:

The age of the universe is thought to be about 14 billion years. Assuming two significant figures, write this in powers of 10 in (a) years, (b) seconds

What is the percent uncertainty in the measurement 5.4860.25 m

Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 s, due to human reaction time at the start and stop moments. What is the percent uncertainty of a hand-timed measurement of (a) 5.5 s, (b) 55 s, (c) 5.5 min

Add A9.2 * 103 sB + A8.3 * 104 sB + A0.008 * 106 sB.

Multiply by taking into account significant figures.

What, approximately, is the percent uncertainty for a measurement given as

What, roughly, is the percent uncertainty in the volume of a spherical beach ball of radius

What is the area, and its approximate uncertainty, of a circle of radius

Write the following as full (decimal) numbers without prefixes on the units: (a) 286.6 mm, (b) (c) 760 mg, (d) 62.1 ps, (e) 22.5 nm, ( ) 2.50 gigavolts

Express the following using the prefixes of Table 14: (a) (b) (c) (d) and

One hectare is defined as One acre is How many acres are in one hectare?

The Sun, on average, is 93 million miles from Earth. How many meters is this? Express (a) using powers of 10, and (b) using a metric prefix (km).

Express the following sum with the correct number of significant figures:

A typical atom has a diameter of about (a) What is this in inches? (b) Approximately how many atoms are along a 1.0-cm line, assuming they just touch

Determine the conversion factor between (a) and (b) and and

A light-year is the distance light travels in one year (at speed (a) How many meters are there in 1.00 light-year? (b) An astronomical unit (AU) is the average distance from the Sun to Earth, How many AU are there in 1.00 light-year?

How much longer (percentage) is a one-mile race than a 1500-m race (the metric mile)?

American football uses a field that is 100.0 yd long, whereas a soccer field is 100.0 m long. Which field is longer, and by how much (give yards, meters, and percent)?

(II) (a) How many seconds are there in 1.00 year? (b) How many nanoseconds are there in 1.00 year? (c) How many years are there in 1.00 second?

(II) Use Table 13 to estimate the total number of protons or neutrons in (a) a bacterium, (b) a DNA molecule, (c) the human body, (d) our Galaxy

(III) A standard baseball has a circumference of approximately 23 cm. If a baseball had the same mass per unit volume (see Tables in Section 15) as a neutron or a proton, about what would its mass be?

Estimate the order of magnitude (power of 10) of: (a) 2800, (B) 86.30X10, (C) 0.0076, AND (D) 15.0 X 10

Estimate how many hours it would take to run (at ) across the U.S. from New York to California

Estimate the number of liters of water a human drinks in a lifetime

Estimate how long it would take one person to mow a football field using an ordinary home lawn mower (Fig. 115). (State your assumption, such as the mower moves with a speed, and has a 0.5-m width.)

Estimate how long it would take one person to mow a football field using an ordinary home lawn mower (Fig. 115). (State your assumption, such as the mower moves with a speed, and has a 0.5-m width.)

Estimate the number of gallons of gasoline consumed by the total of all automobile drivers in the U.S., per year.

Estimate the number of dentists (a) in San Francisco and (b) in your town or city

You are in a hot air balloon, 200 m above the flat Texas plains. You look out toward the horizon. How far out can you seethat is, how far is your horizon? The Earths radius is about 6400 km.

I agree to hire you for 30 days. You can decide between two methods of payment: either (1) $1000 a day, or (2) one penny on the first day, two pennies on the second day and continue to double your daily pay each day up to day 30. Use quick estimation to make your decision, and justify it

(III) Many sailboats are docked at a marina 4.4 km away on the opposite side of a lake. You stare at one of the sailboats because, when you are lying flat at the water’s edge, you can just see its deck but none of the side of the sailboat. You then go to that sailboat on the other side of the lake and measure that the deck is 1.5 m above the level of the water. Using Fig. 1–16, where h = 1.5 m, estimate the radius R of the Earth. FIGURE 1;16 Problem 34. You see a sailboat across a lake (not to scale). R is the radius of the Earth. Because of the curvature of the Earth, the water “bulges out” between you and the boat.

You are lying on a beach, your eyes 20 cm above the sand. Just as the Sun sets, fully disappearing over the horizon, you immediately jump up, your eyes now 150 cm above the sand, and you can again just see the top of the Sun. If you count the number of seconds until the Sun fully disappears again, you can estimate the Earths radius. But for this Problem, use the known radius of the Earth to calculate the time t.

What are the dimensions of density, which is mass per volume?

The speed of an object is given by the equation where refers to time. (a) What are the dimensions of A and B? (b) What are the SI units for the constants A and B?

Three students derive the following equations in which x refers to distance traveled, the speed, a the acceleration the time, and the subscript zero means a quantity at time . Here are their equations: (a) (b) and (c) Which of these could possibly be correct according to a dimensional check, and why?

The smallest meaningful measure of length is called the Planck length, and is defined in terms of three fundamental constants in nature: the speed of light the gravitational constant and Plancks constant The Planck length is given by the following combination of these three constants: Show that the dimensions of are length [L], and find the order of magnitude of [Recent theories (Chapters 32 and 33) suggest that the smallest particles (quarks, leptons) are strings with lengths on the order of the Planck length, These theories also suggest that the Big Bang, with which the universe is believed to have begun, started from an initial size on the order of the Planck length.]

Global positioning satellites (GPS) can be used to determine your position with great accuracy. If one of the satellites is 20,000 km from you, and you want to know your position to what percent uncertainty in the distance is required? How many significant figures are needed in the distance?

Computer chips (Fig. 117) are etched on circular silicon wafers of thickness 0.300 mm that are sliced from a solid cylindrical silicon crystal of length 25 cm. If each wafer can hold 400 chips, what is the maximum number of chips that can be produced from one entire cylinder?

A typical adult human lung contains about 300 million tiny cavities called alveoli. Estimate the average diameter of a single alveolus.

If you used only a keyboard to enter data, how many years would it take to fill up the hard drive in a computer that can store 1.0terabytes of data? Assume 40-hour work weeks, and that you can type 180 characters per minute, and that one byte is one keyboard character.

An average family of four uses roughly 1200 L (about 300 gallons) of water per day How much depth would a lake lose per year if it covered an area of with uniform depth and supplied a local town with a population of 40,000 people? Consider only population uses, and neglect evaporation, rain, creeks and rivers.

Estimate the number of jelly beans in the jar of Fig. 118.

How big is a ton? That is, what is the volume of something that weighs a ton? To be specific, estimate the diameter of a 1-ton rock, but first make a wild guess: will it be 1 ft across, 3 ft, or the size of a car? [Hint: Rock has mass per volume about 3 times that of water, which is 1 kg per liter or 62 lb per cubic foot.

A certain compact disc (CD) contains 783.216 megabytes of digital information. Each byte consists of exactly 8 bits. When played, a CD player reads the CDs information at a constant rate of 1.4 megabits per second. How many minutes does it take the player to read the entire CD?

Hold a pencil in front of your eye at a position where its blunt end just blocks out the Moon (Fig. 119). Make appropriate measurements to estimate the diameter of the Moon, given that the EarthMoon distance is 3.8 * 105 km

A storm dumps 1.0 cm of rain on a city 6 km wide and 8 km long in a 2-h period. How many metric tons of water fell on the city? ( of water has a mass of ) How many gallons of water was this?

Estimate how many days it would take to walk around the Earth, assuming 12 h walking per day at 4 kmh.

One liter (\(1000 cm^3\)) of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the oil slick. Assume the oil molecules have a diameter of \(2 \times 10^{-10}\ m\).

A watch manufacturer claims that its watches gain or lose no more than 8 seconds in a year. How accurate are these watches, expressed as a percentage?

An angstrom (symbol ) is a unit of length, defined as which is on the order of the diameter of an atom. (a) How many nanometers are in 1.0 angstrom? (b) How many femtometers or fermis (the common unit of length in nuclear physics) are in 1.0 angstrom? (c) How many angstroms are in 1.0 m? (d) How many angstroms are in 1.0 light-year (see Problem 19)?

Jim stands beside a wide river and wonders how wide it is. He spots a large rock on the bank directly across from him. He then walks upstream 65 strides and judges that the angle between him and the rock, which he can still see, is now at an angle of 30 downstream (Fig. 120). Jim measures his stride to be about 0.8 m long. Estimate the width of the river.

Determine the percent uncertainty in and in when

If you walked north along one of Earths lines of longitude until you had changed latitude by 1 minute of arc (there are 60 minutes per degree), how far would you have walked (in miles)? This distance is a nautical mile

Make a rough estimate of the volume of your body (in ).

The following formula estimates an average persons lung capacity V (in liters, where1 L -10 CM): where H and A are the persons height (in meters) and age (in years), respectively. In this formula, what are the units of the numbers 4.1, 0.018, and 2.7?

One mole of atoms consists of individual atoms. If a mole of atoms were spread uniformly over the Earths surface, how many atoms would there be per square meter?

The density of an object is defined as its mass divided by its volume. Suppose a rocks mass and volume are measured to be 6 g and To the correct number of significant figures, determine the rocks density (mass volume).

Recent findings in astrophysics suggest that the observable universe can be modeled as a sphere of radius light-years with an average total mass density of about Only about 4% of total mass is due to ordinary matter (such as protons, neutrons, and electrons). Estimate how much ordinary matter (in kg) there is in the observable universe. (For the light-year, see Problem 19.)