Milk is often sold by the gallon in plastic containers,

Can dimensional analysis determine whether the area of a circle is \(\pi r^{2}\) or \(2 \pi r^{2}\)? Explain.

Problem 2CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) If a distance d has units of meters, and a time T has units of seconds, does the quantity T + d make sense physically? What about the quantity d/T? Explain in both cases.

Problem 56PP Suppose a snowy cricket is chirping when the temperature is 65.0 degrees Fahrenheit. How many oscillations does the radiation from a cesium-133 atom complete between successive chirps? A. 7.98 × 107 B. 3.68 × 108 C. 4.78 × 109 D. 9.58 × 109

Problem 2P The Thickness of Hair A human hair has a thickness of about 70 µ m. What is this in (a) meters and (b) kilometers?

Problem 1P Spiderman The movie Spider man brought in $114,000,000 in its opening weekend. Express this amount in (a) gigadollars and (b) teradollars.

Problem 3CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) Is it possible for two quantities to (a) have the same units but different dimensions or (b) have the same dimensions but different units? Explain.

Problem 3P The speed of light in a vacuum is approximately 0.3 Gm/s. Express the speed of light in meters per second.

Problem 4CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) Give an order-of-magnitude estimate for the time in seconds of the following: (a) a year; (b) a baseball game; (c) a heartbeat; (d) the age of the Earth; (e) the age of a person.

Problem 4P A Fast Computer IBM has a computer it calls the Blue Gene/L that can do 136.8 tera calculations per second. How-many calculations can it do in a microsecond?

Problem 5CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) Give an order-of-magnitude estimate for the length in meters of the following: (a) a person; (b) a fly; (c) a car; (d) a 747 airplane; (e) an interstate freeway stretching coast-to-coast.

CE Which of the following equations are dimensionally consistent? (a) \(x=vt\), (b) \(x=\frac{1}{2}at^2\), (c) \(t=(2x/a)^{1/2}\). ________________ Equation Transcription: Text Transcription: x=vt x=frac{1}{2}at^2 t=(2x/a)^{1/2}

CE Which of the following quantities have the dimensions of a distance? (a) \(x=vt\), (b) \(\frac{1}{2}at^2\), (c) \(2at\), (d) \(v^2/a\). ________________ Equation Transcription: Text Transcription: x=vt frac{1}{2}at^2 2at v^2/a

CE Which of the following quantities have the dimensions of a speed? (a) \(\frac{1}{2}at^2\), (b) \(at\), (c) \((2x/a)^{1/2}\), (d) \((2ax)^{1/2}\). ________________ Equation Transcription: Text Transcription: frac{1}{2}at^2 at (2x/a)^{1/2} (2ax)^{1/2}

Problem 8P Velocity is related to acceleration and distance by the following expression: v2 = 2axp. Find the power p that makes this equation dimensionally consistent.

Problem 9P Acceleration is related to distance and time by the following expression: a = 2xtp. Find the power p that makes this equation dimensionally consistent.

Problem 10P Show that the equation v = v0 + at is dimensionally consistent. Note that v and v0 are velocities and that a is an acceleration.

Problem 11P Newton’s second law (to be discussed in Chapter 5) states that acceleration is proportional to the force acting on an object and is inversely proportional to the object’s mass. What are the dimensions of force?

The time required for one complete oscillation of a mass on a spring of force constant is \(T=2\pi \sqrt{\frac{m}{k}}\) Find the dimensions must have for this equation to be dimensionally correct. ________________ Equation Transcription: Text Transcription: T=2{pi}sqrt{frac{m}{k}}

Problem 13P The first several digits of ? are known to be ? = 314159265358979…. What is ? to (a) three significant figures, (b) five significant figures, and (c) seven significant figures?

Problem 14P The speed of light to five significant figures is 2.9979 x 108 m/s. What is the speed of light to three significant figures?

Problem 15P A parking lot is 144.3 m long and 47.66 m wide. What is the perimeter of the lot?

Problem 16P On a fishing trip you catch a 2.35-lb bass., a 12,1-lb rock cod, and a 12.13-lb salmon. What is the total weight of your catch?

Problem 17P How many significant figures are there in (a) 0.000054 and (b) 3.001 x 108?

Problem 19P Mantis Shrimp Peacock mantis shrimps (Odantodactylus scyllarus) feed largely on snails. They shatter the shells of their prey by delivering a sharp blow with their front legs, which have been observed to reach peak speeds of 23 m/s. What is this speed in (a) feet per second and (b) miles per hour?

Problem 21P The Ark of the Covenant is described as a chest of acacia wood 2.5 cubits in length and 1.5 cubits in width and height. Given that a cubit is equivalent to 17.7 in., find the volume of the ark in cubic feet.

Problem 18P What is the area of a circle of radius (a) 14.37 m and (b)3.8 m?

Problem 22P How long does it take for radiation from a cesium-133 atom to complete 1.5 million cycles?

Angel Falls Water going over Angel Falls, in Venezuela, the world’s highest waterfall, drops through a distance of 3212 ft. What is this distance in km?

Problem 20P (a) The largest building in the world by volume is the Boeing 747 plant in Everett, Washington. Tt measures approximately 631 m long, 707 yards wide, and 110 ft high. What is its volume in cubic feet? (b) Convert your result from part (a) to cubic meters.

Problem 24P An electronic advertising sign repeats a message every 7 seconds, day and night, for a week. How many times did the message appear on the sign?

Problem 25P BIO Blue Whales The blue whale (Balaenoptera musculus) is thought to be the largest animal ever to inhabit the Earth. The longest recorded blue whale had a length of 108 ft. What is this length in meters?

Problem 26P The Star of Africa The Star of Africa, a diamond in the royal scepter of the British crown jewels, has a mass of 530.2 carats, where 1 carat = 0.20 g. Given that 1 kg has an approximate weight of 2.21 lb, what is the weight of this diamond in pounds?

Problem 27P Many highways have a speed limit of 55 mi/h. (a) Is this speed greater than, less than, or equal to 55 km/h? Explain. (b) Find the speed limit in km/h that corresponds to 55 mi/h.

Problem 28P What is the speed in miles per hour of a beam of light traveling at 3.00 x 108 m/s?

Problem 29P Woodpecker Impact When red-headed woodpeckers (Melenerpes erythrocephalus) strike the trunk of a tree, they can experience an acceleration ten times greater than the acceleration of gravity, or about 98, 1 m/s2. What is this acceleration in ft/s2?

Problem 35P The acceleration of gravity is approximately 9.81 m/s2 (depending on your location). What is the acceleration of gravity in feet per second squared?

Problem 32P Suppose 1.0 cubic meter of oil is spilled into the ocean. Find the area of the resulting slick, assuming that it is one molecule thick, and that the molecule occupies a cube 0.50 ? m. on a side.

Problem 30P A Jiffy The American physical chemist Gilbert Newton Lewis (1875–1946) proposed a unit of time called the “jiffy.”According to Lewis, 1 jiffy = the time it takes light to travel one centimeter, (a) If you perform a task in a jiffy, how long has it taken in seconds? (b) How many jiffya are in one minute? (Use the fact that the speed of light is approximately 2.9979 x 108 m/s.)

Problem 33P (a) A standard sheet of paper measures 8 1/2 by 11 inches. Find the area of one such sheet of paper in m2, (b) A second sheet of paper is half as long and half as wide as the one described in part (a). By what factor is its area less than the area found in part (a)?

Problem 34P Squid Nerve Impulses Nerve impulses in giant axons of the squid can travel with a speed of 20.0 m/s. How fast is this in (a) ft/s and (b) mi/h?

Problem 31P The Mutchkin and the Noggin (a) A mutchkin is a Scottish unit of liquid measure equal to 0.42 L. How many mutchkins are required to fill a container that measures one foot on a side? (b) A noggin is a volume equal to 0.28 mutchkin. What is the conversion factor between noggins and gallons?

Give a ballpark estimate of the number of seats in a typical major league ballpark.

Problem 37P Milk is often sold by the gallon in plastic containers, (a) Estimate the number of gallons of milk that are purchased in the United States the year, (b) What approximate weight of plastic does this represent?

Problem 39P You’ve just won the $12 million cash lottery, and you go to pick up the prize. What is the approximate weight of the cash if you request payment in (a) quarters or (b) dollar bills?

CE Which of the following equations are dimensionally consistent? (a) \(v=at\), (b) \(v=\frac{1}{2}at^2\), (c) \(t=a/v\), (d) \(v^2=2ax\). ________________ Equation Transcription: Text Transcription: v=at v=frac{1}{2}at^2 t=a/v v^2=2ax

Problem 38P New York is roughly 3000 miles from Seattle. When it is 10:00 A.M. in Seattle, it is 1:00 P.M. in New York. Using this information, estimate (a) the rotational speed of the surface of Earth, (b) the circumference of Earth, and (c) the radius of Earth.

Problem 42GP Photosynthesis The light that plants absorb to perform photosynthesis has a wavelength that peaks near 675 run. Express this distance in (a) millimeters and (b) inches.

Problem 41GP Which of the following quantities have the dimensions of an acceleration? (a) xt2, (b) v2/x, (c) x/t2, (d)v/t.

Glacial Speed On June 9,1983 , the lower part of the Variegated Glacier in Alaska was observed to be moving at a rate of 210 feet per day. What is this speed in meters per second?

Problem 44GP BIO Mosquito Courtship Male mosquitoes in the mood for mating find female mosquitoes of their own species by listening for the characteristic “buzzing” frequency of the female’s wing beats. This frequency is about 605 wing beats per second, (a) How many wing beats occur in one minute? (b) How many cycles of oscillation does the radiation from a cesium-133 atom complete during one mosquito wing beat?

Problem 45GP Ten and Ten When Coast Guard para rescue jumpers leap from a helicopter to save a person in the water, they like to jump when the helicopter is flying “ten and ten,” which means it is 10 feet above the water and moving forward with a speed of 10 knots. What is “ten and ten” in SI units? (A knot is one nautical mile per hour, where a nautical mile is 1.852 km.)

Problem 46GP A Porsche sports car can accelerate at 14m/s2, (a) Is this acceleration greater than, less than, or equal to 14 ft/s2? Explain, (b) Determine the acceleration of a Forsche in ft/s2. (c) Determine its acceleration in km/h2.

BIO Human Nerve Fibers Type A nerve fibers in humans can conduct nerve impulses at speeds up to 140 m/s. (a) How fast are the nerve impulses in miles per hour? (b) How far (in meters) can the impulses travel in 5.0 ms?

Problem 48GP Brain Growth The mass of a newborn baby’s brain has been found to increase by about 1.6 mg per minute, (a) How much does the brain’s mass increase in one day? (b) How long does it take for the brain’s mass to increase by 0.0075 kg?

Problem 49GP The Huygens Probe NASA’s Cassini mission to Saturn released a probe on December 25, 2004, that landed on the Saturnian moon Titan on January 14, 2005. The probe, which was named Huygens, was released with a gentle relative speed of 31 cm/5, As Huygens moved away from the main spacecraft, it rotated at a rate of seven revolutions per minute, (a) How many revolutions had Huygens completed when it was 150 yards from the mother ship? (b) How far did Huygens move away from the mother ship during the revolution? Give your answer in feet.

Problem 50GP Acceleration is related to velocity and time by the following expression: a = vp tq. Find the powers p and q that make this equation dimensionally consistent.

The period of a simple pendulum is the amount of time required for it to undergo one complete oscillation. If the length of the pendulum is and the acceleration of gravity is , then is given by \(T=2 \pi L^{p}g^{q}\) Find the powers and required for dimensional consistency. ________________ Equation Transcription: Text Transcription: T=2{pi}L^{p}g^{q}

Problem 52GP Driving along a crowded freeway, you notice that it takes a time t to go from one mile marker to the next. When you increase your speed by 7.9 mi/h, the time to go one mile decreases by 13 s. What was your original speed?

Which plot in Figure 1–2 represents the chirping rate of the snowy tree cricket? A B C D E

Problem 54PP If the temperature is 43 degrees Fahrenheit, how long does it take for the cricket to chirp 12 times? A. 12s B. 24s C. 43s D. 52s

Problem 55PP Your pet cricket chirps 112 times in one minute (60.0 a). What is the temperature in degrees Fahrenheit? A. 41.9 B. 47.0 C. 64.3 D. 74.7