Conversion Factors
Refer again to Fig. 11. Suppose that you want to know the area A in square inches rather than in square meters. To derive this answer, you must know how many square inches comprise one square meter. There are about 1,550 square inches in one square meter. Thus we can restate the formula for Fig. 11 as follows: Let b represent the length (in meters) of the base of a rectangle, and let h represent the height (in meters) measured perpendicular to the base. Then the area A (in square inches) of the rectangle is
A = 1,550 bh
Look again at Fig. 12. Suppose that you want to know the area in square inches when the base length and the height are expressed in feet. There are exactly 144 square inches in one square foot, so we can restate the formula for Fig. 12 this way: Let b represent the length (in feet) of the base of a triangle, and let h represent the height (in feet) measured perpendicular to the base. Then the area A (in square inches) of the triangle is
A = 144 bh /2
= (144/2) bh
= 72 bh
Give Fig. 13 another look. Suppose that you want to know how far the car has traveled in miles when its speed is given in feet per second and the time is given in hours. To figure this out, you must know the relationship between miles per hour and feet per second. To convert feet per second approximately to miles per hour, it is necessary to multiply by 0.6818. Then the units will be consistent with each other: The distance will be in miles, the speed will be in miles per hour, and the time will be in hours. The formula for Fig. 13 can be rewritten: Suppose that a car travels at a constant speed s (in feet per second) down a straight highway (see Fig. 13). Let t be a certain length of time (in hours). Then the distance d (in miles) that the car travels in that length of time is given by
d = 0.6818 st
You can derive these conversion factors easily. All you need to know is the number of inches in a meter, the number of inches in a foot, the number of feet in a mile, and the number of seconds in an hour. As an exercise, you might want to go through the arithmetic for yourself. Maybe you’ll want to derive the factors to greater precision than is given here.
Conversion factors are not always straightforward. Fortunately, databases abound in which conversion factors of all kinds are listed in tabular form. You don’t have to memorize a lot of data. You can simply look up the conversion factors you need. The Internet is a great source of this kind of information. At the time of this writing, a comprehensive conversion database for physical units was available at the following location on the Web:
http://www.physics.nist.gov/Pubs/SP 811/ appenB 8. html
If you’ve used the Web very much, you know that uniform resource locators (URLs) are always changing. If the preceding URL does not guide you to conversion factors, point your browser to the National Institute of Standards and Technology (NIST) home page and search the site for tables of conversion factors:
Practice problems for these concepts can be found at: Equations, Formulas, And Vectors for Physics Practice Test
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