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physics 2211
MP01: Chapter 1
Due at 5:30pm on Wednesday, September 19, 2007
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Converting Units: The Magic of 1
Learning Goal:
To learn how to change units of physical quantities.
Quantities with physical dimensions like length or time must be measured with respect to a
unit
, a standard for
quantities with this dimension. For example, length can be measured in units of meters or feet, time in seconds or
years, and velocity in meters per second.
When solving problems in physics, it is necessary to use a consistent system of units such as the International
System (abbreviated SI, for the French Système International) or the more cumbersome English system. In the SI
system, which is the preferred system in physics, mass is measured in kilograms, time in seconds, and length in
meters. The necessity of using consistent units in a problem often forces you to convert some units from the given
system into the system that you want to use for the problem.
The key to unit conversion is to multiply (or divide) by a ratio of different units that equals one. This works because
multiplying any quantity by one doesn't change it. To illustrate with length, if you know that
, you
can write
.
To convert inches to centimeters, you can multiply the number of inches times this fraction (since it equals one),
cancel the inch unit in the denominator with the inch unit in the given length, and come up with a value for the length
in centimeters. To convert centimeters to inches, you can divide by this ratio and cancel the centimeters.
For all parts, notice that the units are already written after the answer box; don't try to write them in your answer
also.
Part A
How many centimeters are there in a length 357.7
?
Express your answer in centimeters to three significant figures.
ANSWER:
909
Sometimes you will need to change units twice to get the final unit that you want. Suppose that you know how to
convert from centimeters to inches and from inches to feet. By doing both, in order, you can convert from
centimeters to feet.
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Part B
Suppose that a particular artillery piece has a range
= 1.250
×
10
4
. Find its range in miles. Use the facts that
and
.
Part B.1 Convert yards to feet
Part not displayed
Express your answer in miles to three significant figures.
ANSWER:
1.250
×
10
4
=
7.10
Often speed is given in miles per hour (
), but in physics you will almost always work in SI units. Therefore,
you must convert
to meters per second (
).
Part C
What is the speed of a car going
in SI units? Notice that you will need to change from miles to meters
and from hours to seconds. You can do each conversion separately. Use the facts that
and
.
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 Fall '08
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 Physics, Acceleration, Velocity, Assignment Print View

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