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Chapter 1: Problem 28

The micrometer \((1 \mu \mathrm{m})\) is often called the micron. (a) How many microns make up \(1.0 \mathrm{~km}\) ? (b) What fraction of a centimeter equals \(1.0 \mu \mathrm{m}\) ? (c) How many microns are in \(1.0 \mathrm{yd}\) ?

Short Answer

Expert verified
1.0 km = 1,000,000,000 碌m, 1.0 碌m = 0.0001 cm, 1.0 yd = 914,400 碌m

Step by step solution

01

Convert kilometers to microns

To convert kilometers to microns, start with the fact that there are 1000 meters in a kilometer and 1,000,000 microns in a meter. Therefore, multiply the number of kilometers by the conversion factors: 1 km = 1 km 脳 1000 m/km 脳 1,000,000 碌m/m = 1,000,000,000 碌m
02

Convert micrometers to centimeters

Next, convert micrometers to centimeters by recognizing that there are 10,000 micrometers in a centimeter. Therefore, one micrometer is: 1 碌m = 1 碌m / 10,000 碌m/cm = 0.0001 cm
03

Convert yards to microns

Convert yards to microns by recognizing that there are 0.9144 meters in a yard. Then convert the meters to microns: 1 yd = 0.9144 m 0.9144 m = 0.9144 m 脳 1,000,000 碌m/m = 914,400 碌m

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

micrometers
A micrometer, often referred to as a micron, is a unit of length in the metric system. It is denoted by the symbol \( \mu m \) and is equivalent to one-millionth of a meter. Understanding micrometers is important for dealing with very small measurements, such as those in biology and electronics. For example, the size of bacteria and other microorganisms is often measured in micrometers. When converting units, remember that 1 meter equals 1,000,000 micrometers. This conversion factor is critical when scaling measurements up or down in other units of length.
metric system
The metric system is an internationally adopted system of measurement based on powers of ten. It simplifies conversions, as each unit is related to the others by factors of ten. For example, 1 kilometer is 1,000 meters, and 1 meter is 1,000 millimeters. The main units for measuring length in the metric system are meters, centimeters, and millimeters. Understanding the metric system helps in making quick and accurate conversions. For instance, to convert kilometers to micrometers, recognize that there are 1,000 meters in a kilometer and 1,000,000 micrometers in a meter, leading to 1 kilometer equaling 1,000,000,000 micrometers.
length conversion
Length conversion is a process of changing a measurement from one unit to another. This often requires knowing the relationships between different units. For example, to convert from micrometers to centimeters, one must know that there are 10,000 micrometers in a centimeter. Thus, 1 micrometer equals 0.0001 centimeters. Conversion factors are ratios that express how many of one unit are equivalent to another. In practical problems, like converting yards to micrometers, start by converting yards to meters (1 yard equals 0.9144 meters) and then meters to micrometers (1 meter equals 1,000,000 micrometers). This ensures accurate and reliable results in various applications.

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Most popular questions from this chapter

Throughout your physics course, your instructor will expect you to be careful with the units in your calculations. Yet, some students tend to neglect them and just trust that they always work out properly. Maybe this real-world example will keep you from such a sloppy habit. On July 23, 1983 , Air Canada Flight 143 was being readied for its long trip from Montreal to Edmonton when the flight crew asked the ground crew to determine how much fuel was already onboard the airplane. The flight crew knew that they needed to begin the trip with \(22300 \mathrm{~kg}\) of fuel. They knew that amount in kilograms because Canada had recently switched to the metric system: previously fuel had been measured in pounds. The ground crew could measure the onboard fuel only in liters, which they reported as \(7682 \mathrm{~L}\). Thus, to determine how much fuel was onboard and how much additional fuel must be added, the flight crew asked the ground crew for the conversion factor from liters to kilograms of fuel. The response was \(1.77\), which the flight crew used \((1.77 \mathrm{~kg}\) corresponds to \(1 \mathrm{~L}\) ). (a) How many kilograms of fuel did the flight crew think they had? (In this problem, take all the given data as being exact.) (b) How many liters did they ask to be added to the airplane?

During the summers at high latitudes, ghostly, silver-blue clouds occasionally appear after sunset when common clouds are in Earth's shadow and are no longer visible. The ghostly clouds have been called noctilucent clouds (NLC), which means "luminous night clouds," but now are often called mesospheric clouds, after the mesosphere, the name of the atmosphere at the altitude of the clouds These clouds were first seen in June 1885 , after dust and water from the massive 1883 volcanic explosion of Krakatoa Island (near Java in the Southeast Pacific) reached the high altitudes in the Northern Hemisphere. In the low temperatures of the mesosphere, the water collected and froze on the volcanic dust (and perhaps on comet and meteor dust already present there) to form the particles that made up the first clouds. Since then, mesospheric clouds have generally increased in occurrence and brightness, probably because of the increased production of methane by industries, rice paddies, landfills, and livestock flatulence. The methane works its way into the upper atmosphere, undergoes chemical changes, and results in an increase of water molecules there, and also in bits of ice for the mesospheric clouds. If mesospheric clouds are spotted 38 min after sunset and then quickly dim, what is their altitude if they are directly over the observer?

Earth is approximately a sphere of radius \(6.37 \times\) \(10^{6} \mathrm{~m}\). What are (a) its circumference in kilometers, (b) its surface area in square kilometers, and (c) its volume in cubic kilometers?

A typical sugar cube has an edge length of \(1 \mathrm{~cm}\). If you had a cubical box that contained a mole of sugar cubes, what would its edge length be? (One mole \(=6.02 \times 10^{23}\) units.)

Here are two related problems - one precise, one an estimation. (a) A sculptor builds model for a statue 0 . a terrapin to replace Testudo." She discov. ers that to cast her small scale model she needs \(2 \mathrm{~kg}\) of bronze When she is done, she finds that she can give it two coats of finish. ing polyurethane varnish using exactly one small can of varnish. The final statue is supposed to be 5 times as large as the model in cach dimension. How much bronze will she need? How much varnish should she buy? (Hint: If this seems difficult, you might start by writing a simpler question that is easier to work on before tackling this one.) (b) The human brain has 1000 times the surface area of a mouse's brain. The human brain is convoluted, the mouse's is not. How much of this factor is due just to size (the human brain is bigger)? How sensitive is your result to your estimations of the approximate dimensions of a human brain and a mouse brain?
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