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Homework 1
Due: 11:59pm on Sunday, September 12, 2010
Note: You will receive no credit for late submissions. To learn more, read your instructor's Grading Policy [Switch to
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Converting Units
The ability to convert from one system of units to another is important in physics. It is often impractical to measure
quantities in the standard meters, kilograms, and seconds, but the laws of physics that you learn will involve constants
that are defined in these units. Therefore, you may often have to convert your measured quantities into meters,
kilograms, and seconds. The following table lists metric prefixes that come up frequently in physics. Learning these
prefixes will help you in the various exercises. mega ( kilo ( ) centi ( ) milli ( ) )
micro ( ) nano ( ) When doing unit conversions, you need a relation between the two units. For instance, in converting
from millimeters to meters, you need to know that . Once you know this, you need to divide one side by the other to
obtain a ratio of . in the denominator, so that it will cancel the units of the If you are converting from millimeters to
meters, then this is the proper ratio. It has , then you would have quantity that you are converting. For instance, if you
were converting . If you were converting a quantity from meters to millimeters, you would use the reciprocal ratio: . to :
Part A Suppose that you measure a pen to be 10.5 Hint A.1 long. Convert this to meters.
Relating centimeters and meters Hint not displayed
Express your answer in meters.
ANSWER: 10.5 = 0.105 Correct
When converting areas, you must be careful to use the correct ratio. If you were converting from
to
, it might be tempting to use
again. Be careful! Think of
as
. That is to say, think of this as a pair of millimeter units, each of which must be to square meters you would use the
following calculation: .
converted separately. To convert
Notice that the exponent distributes to both the numbers and the units: . Now the will cancel properly: .
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Part B Suppose that, from measurements in a microscope, you determine that a certain bacterium covers an area of
meters. Hint B.1 Find the conversion factor Hint not displayed . Convert this to square
Express your answer in square meters.
ANSWER: 1.50 = 1.50×10−12 Correct
As with areas, you must be careful when converting between volumes. For volumes, you must cancel off three copies of
whatever unit you are converting from. Part C Suppose that you find the volume of all the oceans to be in a reference
book. To find the mass, you can use the density of
water, also found in this reference book, but first you must convert the volume to cubic meters. What is this volume in
cubic meters? Hint C.1 Find the conversion factor Hint not displayed
Express your answer in cubic meters.
ANSWER: = 1.40×1018 Correct
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 Spring '10
 SAUL
 Physics, Work

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