1
Physics E1a
Expt 1:
Measuring from a Distance
Fall 2010
Due Thursday, Sept 16, by 6 pm in your lab
TA’s mailbox
Introduction
There are many objects in the universe that simply aren't easy to measure. You can not go
out with a ruler and easily determine the radius of the Earth (although, it can be done!).
Similarly, the size of the Moon is beyond the reach of your meter stick, and even the
heights of the trees in the Yard are hard to sample with even the longest of tape measures.
Since direct measurement isn't always possible, people have found indirect techniques for
getting at various measurements. In this experiment, we will explore how an object's
angular size can be used to determine its physical size, or its distance.
Objectives
The measurements for this experiment will not be performed in the lab. You will conduct
them on your own (or with a partner), on your own time. We call this a “home experi
ment” and hope to accomplish the following:
•
If you have been away from math for a while, this experiment will help you review
the geometry and trigonometry.
•
It will start you off on the right track concerning error analysis — learning to identify
and deal with uncertainties in your measurements.
•
You'll also get some practice in plotting data and extracting information from a graph.
•
And finally, you will discover that it’s possible to measure seemingly difficult things
with simple tools (this is the fun part). It’s actually pretty amazing what one can learn
about our physical world using only the simplest of apparatus, good observations, and
mathematics.
Method
The tool you will make is a quadrant. The quadrant uses the basic principles of surveying:
that light travels in straight lines, and that some lengths and angles of a triangle (or other
shape) can be measured so that unknown lengths, often
not
directly measurable, can be
calculated. The simplest cases are (1) those in which one angle of a triangle is very
“small,” or (2) one angle is 90˚.
By “small” we mean that the angle (measured in
radians) differs from its sine or tangent by so little that, for all practical purposes, these
three quantities can be considered equal — this small angle approximation will be used in
the moon measurement (and many times in this course throughout the year).
Secondly, if
one of the angles is 90˚, we simply apply the rules governing right triangles.
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Order of Tasks:
First make your quadrant (page 10) and learn how to use it by measuring a window. Next
measure the height of the Science Center with this new tool. Then, using only your arm, a
piece of paper, and a ruler, measure the size of the moon. Please don’t leave the moon
measurement until the last minute as the weather and/or phases of the moon may not
cooperate with you. Finally, answer all the bold numbered questions on a separate paper
with a few concise sentences. You will hand in these answers along with a copy of your
graph from the procedure section (there is a checklist for this report on page 8).
Quadrant
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 Fall '11
 WolfgangRueckner
 Physics, mechanics, science center

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