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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

An old manuscript reveals that a landowner in the time of King Arthur held \(3.00\) acres of plowed land plus a livestock area of \(25.0\) perches by \(4.00\) perches. What was the total area in (a) the old unit of roods and (b) the more modern unit of square meters? Here, 1 acre is an area of 40 perches by 4 perches, 1 rood is 40 perches by 1 perch, and 1 perch is \(16.5 \mathrm{ft}\).

A fortnight is a charming English measure of time equal to \(2.0\) weeks (the word is a contraction of "fourteen nights"). That is a nice amount of time in pleasant company but perhaps a painful string of microseconds in unpleasant company. How many microseconds are in a fortnight?

Discuss the question: "Is 500 feet big or small?" Before you do so, carry out the following estimates. (a) You are on the top floor of a 500 -ft-tall building. A fire breaks out in the building and the elevator stops working. You have to walk down to the ground floor. Estimate how long this would take you. (Your stairwell is on the other side of the building from the fire.) (b) You are hiking the Appalachian Trail on a beautiful fall morning as part of a \(10 \mathrm{mi}\) hike with a group of friends. You are walking along a well-tended, level part of the trail. Estimate how long it would take you to walk \(500 \mathrm{ft}\). (c) You are driving on the New Jersey Turnpike at \(65 \mathrm{mi} / \mathrm{hr}\). You pass a sign that says "Lane ends 500 feet." How much time do you have in order to changelanes?

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?

Fermi Physicist Enrico Fermi once pointed out that a standard lecture period (50 min) is close to 1 microcentury. (a) How long is a microcentury in minutes? (b) Using percentage difference \(=\left(\frac{\text { actual }-\text { approximation }}{\text { actual }}\right) 100\) find the percentage difference from Fermi's approximation.
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