If the average density of the universe is at least then

Which of the following is not one of the base quantities in the SI system? (a) mass, (b) length, (c) energy, (d) time, (e) All of the above are base quantities.

In doing a calculation, you end up with in the numerator and in the denominator. What are your final units? (a) (b) (c) (d) s, (e)

The prefix giga means (a) (b) (c) (d) (e)

The prefix mega means (a) (b) (c) (d) (e)

Show that there are 30.48 cm per foot. How many centimeters are there in one mile?

The number 0.000 513 0 has ______ significant figures. (a) one, (b) three, (c) four, (d) seven, (e) eight

The number 23.0040 has ______ significant figures. (a) two, (b) three, (c) four, (d) five, (e) six

Force has dimensions of mass times acceleration. Acceleration has dimensions of speed divided by time. Pressure is defined as force divided by area. What are the dimensions of pressure? Express pressure in terms of the SI base units kilogram, meter, and second.

True or false: Two quantities must have the same dimensions in order to be multiplied.

A vector has a negative x component and a positive y component. Its angle measured counterclockwise from the positive x axis is (a) between zero and 90 degrees, (b) between 90 and 180 degrees, (c) more than 180 degrees.

A vector points in the direction. Show graphically at least three choices for a vector such that points in the _y direction. SSM

A vector points in the direction. Show graphically at least three choices for a vector such that points in the direction.

Is it possible for three equal-magnitude vectors to add to zero? If so, sketch a graphical answer. If not, explain why not.

The angle subtended by the moons diameter at a point on Earth is about (Figure 1-18). Use this information and the fact that the moon is about 384 Mm away to find the diameter of the moon. Hint: The angle can be determined from the diameter of the moon and the distance to the moon.

BIOLOGICAL APPLICATION Some good estimates about the human body can be made if it is assumed that we are made mostly of water. The mass of a water molecule is \(29.9 \times 10^{-27}\) kg. If the mass of a person is 60 kg, estimate the number of water molecules in that person.

ENGINEERING APPLICATION In 1989, IBM scientists moved atoms with a scanning tunneling microscope (STM). One of the first STM images seen by the general public was of the letters IBM spelled with xenon atoms on a nickel surface. The letters IBM were 15 xenon atoms across. If the space between the centers of adjacent xenon atoms is 5 nm estimate how many times IBM could be written across this 8.5-inch page.

There is an environmental debate over the use of cloth versus disposable diapers. (a) If we assume that between birth and 2.5 y of age, a child uses 3 diapers per day, estimate the total number of disposable diapers used in the United States per year. (b) Estimate the total landfill volume due to these diapers, assuming that 1000 kg of waste fills about 1 m3 of landfill volume. (c) How many square miles of landfill area at an average height of 10 m is needed for the disposal of diapers each year?

(a) Estimate the number of gallons of gasoline used per day by automobiles in the United States and the total amount of money spent on it. (b) If 19.4 gal of gasoline can be made from one barrel of crude oil, estimate the total number of barrels of oil imported into the United States per year to make gasoline. How many barrels per day is this?

ENGINEERING APPLICATION A megabyte (MB) is a unit of computer memory storage. A CD has a storage capacity of 700 MB and can store approximately 70 min of high-quality music. (a) If a typical song is 5 min long, how many megabytes are required for each song? (b) If a page of printed text takes approximately 5 kilobytes, estimate the number of novels that could be saved on a CD.

Express the following quantities using the prefixes listed in Table 1-1 and the unit abbreviations listed in the table Abbreviations for Units. For example, (a) 1 000 000 watts, (b) 0.002 gram, (c) (d) 30000 seconds

Write each of the following without using prefixes: (a) (b) 4 ns, (c) 3 MW, (d) 25 km.

Write the following (which are not SI units) using prefixes (but not their abbreviations). For example, (a) (b) (c) (d) (e) (f) (g)

In the following equations, the distance x is in meters, the time t is in seconds, and the velocity is in meters per second. What are the SI units of the constants and (a) (b) (c) (d) (e)

If x is in feet, t is in milliseconds, and is in feet per second, what are the units of the constants and in each part of Problem 23?

MULTISTEP From the original definition of the meter in terms of the distance along a meridian from the equator to the North Pole, find in meters (a) the circumference of Earth and (b) the radius of Earth. (c) Convert your answers for (a) and (b) from meters into miles.

The speed of sound in air is What is the speed of a supersonic plane that travels at twice the speed of sound? Give your answer in kilometers per hour and miles per hour.

Abasketball player is 6 ft in tall. What is his height in centimeters?

Complete the following: (a) ______ (b) ______in., (c) ______ m.

The main span of the Golden Gate Bridge is 4200 ft. Express this distance in kilometers.

Find the conversion factor to convert from miles per hour into kilometers per hour.

Complete the following: (a) ______ (b) ______ (c) ______ (d) ______

There are 640 acres in a square mile. How many square meters are there in one acre?

CONTEXT-RICH You are a delivery person for the Fresh Aqua Spring Water Company. Your truck carries 4 pallets. Each pallet carries 60 cases of water. Each case of water has 24 one-liter bottles. The dolly you use to carry the water into the stores has a weight limit of 250 lb. (a) If a milliliter of water has a mass of 1 g, and a kilogram has a weight of 2.2 lb, what is the weight, in pounds, of all the water in your truck? (b) How many full cases of water can you carry on the cart?

A right circular cylinder has a diameter of 6.8 in. and a height of 2 ft. What is the volume of the cylinder in (a) cubic feet, (b) cubic meters, (c) liters?

In the following, x is in meters, t is in seconds, is in meters per second, and the acceleration a is in meters per second squared. Find the SI units of each combination: (a) (b) (c)

What are the dimensions of the constants in each part of Problem 23?

The law of radioactive decay is where is the number of radioactive nuclei at is the number remaining at time t, and is a quantity known as the decay constant. What is the dimension of

The SI unit of force, the kilogram-meter per second squared is called the newton (N). Find the dimensions and the SI units of the constant G in Newtons law of gravitation

The magnitude of the force (F) that a spring exerts when it is stretched a distance x from its unstressed length is governed by Hookes law, (a) What are the dimensions of the force constant, k? (b) What are the dimensions and SI units of the quantity

Show that the product of mass, acceleration, and speed has the dimensions of power.

The momentum of an object is the product of its velocity and mass. Show that momentum has the dimensions of force multiplied by time.

What combination of force and one other physical quantity has the dimensions of power?

When an object falls through air, there is a drag force that depends on the product of the cross sectional area of the object and the square of its velocity, that is, \(F_{\mathrm{air}}=C A v^{2}\), where C is a constant. Determine the dimensions of C.

Keplers third law relates the period of a planet to its orbital radius r, the constant G in Newtons law of gravitation and the mass of the Sun What combination of these factors gives the correct dimensions for the period of a planet?

Express as a decimal number without using powers of 10 notation: (a) (b) (c) (d)

Write the following in scientific notation: (a) ______ km, (b) ______MW, (c) ______s, (d) ______ mm.

Calculate the following, round off to the correct number of significant figures, and express your result in scientific notation: (a) (b) (c) (d)

Calculate the following, round off to the correct number of significant figures, and express your result in scientific notation: (a) (b) (c) (d)

BIOLOGICAL APPLICATION A cell membrane has a thickness of 7.0 nm. How many cell membranes would it take to make a stack 1.0 in. high?

ENGINEERING APPLICATION A circular hole of radius \(8.470 \times 10^{-1} \ \mathrm {cm}\) must be cut into the front panel of a display unit. The tolerance is \(1.0 \times 10^{-3} \ \mathrm {cm}\) , which means the actual hole cannot differ by more than this quantity from the desired radius. If the actual hole is larger than the desired radius by the allowed tolerance, what is the difference between the actual area and the desired area of the hole?

ENGINEERING APPLICATION A square peg must be made to fit through a square hole. If you have a square peg that has an edge length of and the square hole has an edge length of (a) what is the area of the space available when the peg is in the hole? (b) If the peg is made rectangular by removing of material from one side, what is the area available now?

MULTISTEP A vector that is 7.0 units long and a vector that is 5.5 units long are added. Their sum is a vector 10.0 units long. (a) Show graphically at least one way that the vectors can be added. (b) Using your sketch in Part (a), determine the angle between the original two vectors.

Determine the x and y components of the following three vectors in the plane. (a) A10-m displacement vector that makes an angle of clockwise from the direction. (b) A velocity vector that makes an angle of counterclockwise from the direction. (c) A40-lb force vector that makes an angle of 120 counterclockwise from the _y direction. SSM

Rewrite the following vectors in terms of their magnitude and angle (counterclockwise from the direction). (a) A displacement vector with an x component of and a y component of (b) A velocity vector with an x component of and a y component of (c) A force vector with a magnitude of 50 lb that is in the third quadrant with an x component whose magnitude is 40 lb.

CONCEPTUAL You walk 100 m in a straight line on a horizontal plane. If this walk took you 50 m east, what are your possible north or south movements? What are the possible angles that your walk made with respect to due east?

ESTIMATION The final destination of your journey is 300 m due east of your starting point. The first leg of this journey is the walk described in Problem 55, and the second leg in also a walk along a single straight-line path. Estimate graphically the length and heading for the second leg of your journey.

Given the following vectors: and (a) Find the vector in unit vector notation, such that (b) Express your answer in Part (a) in terms of magnitude and angle with the direction.

Given the following force vectors: is 25 lb at an angle of clockwise from the axis, and is 42 lb at an angle of clockwise from the axis. (a) Make a sketch and visually estimate the magnitude and angle of the vector such that results in a vector with a magnitude of 35 lb pointing in the direction. (b) Repeat the calculation in Part (a) using the method of components and compare your result to the estimate in (a).

Calculate the unit vector (in terms of and ) in the direction opposite to the direction of each of vectors , and in Problem 57.

Unit vectors and are directed east and north, respectively. Calculate the unit vector (in terms of and ) in the following directions. (a) northeast, (b) clockwise from the axis, (c) southwest.

The Apollo trips to the moon in the 1960s and 1970s typically took 3 days to travel the Earthmoon distance once they left Earth orbit. Estimate the spacecrafts average speed in kilometers per hour, miles per hour, and meters per second.

On many of the roads in Canada the speed limit is What is this speed limit in miles per hour?

If you could count $1.00 per second, how many years would it take to count 1.00 billion dollars?

(a) The speed of light in vacuum is Use this fact to find the number of kilometers in a mile. (b) The weight of of water is 62.4 lb, and 1.00 ft _ 30.5 cm. Use this information and the fact that of water has a mass of 1.00 g to find the weight in pounds of a 1.00-kg mass.

The mass of one uranium atom is How many uranium atoms are there in 8.0 g of pure uranium?

During a thunderstorm, a total of 1.4 in. of rain falls. How much water falls on one acre of land? Express your answer in (a) cubic inches, (b) cubic feet, (c) cubic meters, and (d) kilograms. Note that the density of water is 1000 kg>m3.

An iron nucleus has a radius of and a mass of (a) What is its mass per unit volume in (b) If Earth had the same mass per unit volume, what would be its radius? (The mass of Earth is )

ENGINEERING APPLICATION The Canadian Norman Wells Oil Pipeline extends from Norman Wells, Northwest Territories, to Zama, Alberta. The -m-long pipeline has an inside diameter of 12 in. and can be supplied with oil at (a) What is the volume of oil in the pipeline if it is full at some instant in time? (b) How long would it take to fill the pipeline with oil if it is initially empty?

The astronomical unit (AU) is defined as the mean centerto- center distance from Earth to the Sun, namely The parsec is the radius of a circle for which a central angle of 1 s intercepts an arc of length 1 AU. The light-year is the distance that light travels in 1 y. (a) How many parsecs are there in one astronomical unit? (b) How many meters are in a parsec? (c) How many meters in a light-year? (d) How many astronomical units in a lightyear? (e) How many light-years in a parsec?

If the average density of the universe is at least then the universe will eventually stop expanding and begin contracting. (a) How many electrons are needed in each cubic meter to produce the critical density? (b) How many protons per cubic meter would produce the critical density?

CONTEXT-RICH, ENGINEERING APPLICATION, SPREADSHEET You are an astronaut doing physics experiments on the moon. You are interested in the experimental relationship between distance fallen, y, and time elapsed, t, of falling objects dropped from rest. You have taken some data for a falling penny, which is represented in the table below. (a) y (m) 10 20 30 40 50 (b) t (s) 3.5 5.2 6.0 7.3 7.9 You expect that a general relationship between distance y and time t is where B and C are constants to be determined experimentally. To accomplish this, create a log-log plot of the data: (a) graph vs. with the ordinate variable and the abscissa variable. (b) Show that if you take the log of each side of your expected relationship, you get (c) By comparing this linear relationship to the graph of the data, estimate the values of B and C. (d) If you drop a penny, how long should it take to fall 1.0 m? (e) In the next chapter, we will show that the expected relationship between y and tis where a is the acceleration of the object. What is the acceleration of objects dropped on the moon?

SPREADSHEET A particular companys stock prices vary with the market and with the companys type of business, and can be very unpredictable, but people often try to look for mathematical patterns where they may not belong. Corning is a materials-engineering company located in upstate New York. Below is a table of the price of Corning stock on August 3, for every 5 years from 1981 to 2001. Assume that the price follows a power law: price where t is expressed in years. (a) Evaluate the constants B and C (see methods suggested for the previous problem). (b) According to the power law, what should the price of Corning stock have been on August 3, 2000? (It was actually $82.83!) (a) Price (dollars) 2.10 4.19 9.14 10.82 16.85 (b) Years since 1980 1 6 11 16 21

ENGINEERING APPLICATION The Super-Kamiokande neutrino detector in Japan is a large transparent cylinder filled with ultra-pure water. The height of the cylinder is 41.4 m and the diameter 5.4 _ 10_15 m is 39.3 m. Calculate the mass of the water in the cylinder. Does this match the claim posted on the official Super-K Web site that the detector uses 50,000 tons of water?

CONTEXT-RICH You and a friend are out hiking across a large flat plain and decide to determine the height of a distant mountain peak, and also the horizontal distance from you to the peak (Figure 1-19). In order to do this, you stand in one spot and determine that the sightline to the top of the peak is inclined at above the horizontal. You also make note of the heading to the peak at that point: east of north. You stand at the original position, and your friend hikes due west for 1.5 km. He then sights the peak and determines that its sightline has a heading of east of north. How far is the mountain from your position, and how high is its summit above your position?

SPREADSHEET The table below gives the periods T and orbit radii r for the motions of four satellites orbiting a dense, heavy asteroid. (a) These data can be fitted by the formula Find the values of the constants C and n. (b) Afifth satellite is discovered to have a period of 6.20 y. Find the radius for the orbit of this satellite, which fits the same formula. (a) Period T, y 0.44 1.61 3.88 7.89 (b) Radius r, Gm 0.088 0.208 0.374 0.600

MULTISTEP The period T of a simple pendulum depends on the length L of the pendulum and the acceleration of gravity g (dimensions ). (a) Find a simple combination of L and g that has the dimensions of time. (b) Check the dependence of the period T on the length L by measuring the period (time for a complete swing back and forth) of a pendulum for two different values of L. (c) The correct formula relating T to L and g involves a constant that is a multiple of , and cannot be obtained by the dimensional analysis of Part (a). It can be found by experiment as in Part (b) if g is known. Using the value and your experimental results from Part (b), find the formula relating T to L and g.

A sled at rest is suddenly pulled in three horizontal directions at the same time but it goes nowhere. Paul pulls to the northeast with a force of 50 lb. Johnny pulls at an angle of south of due west with a force of 65 lb. Connie pulls with a force to be determined. (a) Express the boys two forces in terms of the usual unit vectors. (b) Determine the third force (from Connie), expressing it first in component form and then as a magnitude and angle (direction).

You spot a plane that is 1.50 km north, 2.5 km east, and at an altitude 5.0 km above your position. (a) How far from you is the plane? (b) At what angle from due north (in the horizontal plane) are you looking? (c) Determine the planes position vector (from your location) in terms of the unit vectors, letting be toward the east direction, be toward the north direction, and be in vertically upward. (d) At what elevation angle (above the horizontal plane of Earth) is the airplane?