Embedded Files
How do we know how far away the sun is without stretching a tape measure across millions of miles? How do we know the mass of an electron when we can’t even see one? Since ancient times, people have found ways to measure indirectly what they could not measure directly. In your project for this chapter, you will construct an instrument similar to those used by ancient astronomers and travelers.You will use your device to measure heights you cannot easily reach.You will see how mathematics can extend your power to measure things far beyond your physical grasp.
Task 1: Building
Use the diagram at the right to build a clinometer, an angle-measuring device similar to instruments used by
navigators for hundreds of years. You will need a protractor, string, tape, a piece of heavy cardboard, a small weight, and a plastic straw.
To use the clinometer, look through the straw at the object you want to measure (the top of a building, for example). Have someone else read the angle marked by the hanging string.
Why is the angle measured indicated by the string on the protractor the same as measure of angle 1? (Hint: The string is always perpendicular to the horizon.)
Task 2: Measuring
Use your clinometer to measure the angle of elevation to an object such as the roof of your school or the top of the flagpole.Then, determine how far away you are from the object that you measured. Use what you've learned about trigonometry to find the height of the object. Besure to add your own height to the height you find!
Task 3: Comparing
Repeat the previous activity, but this time work in groups to estimate the height of a single object on your school grounds. Have each person in your group measure the angle of elevation from a different distance. Then compare results within the group. Write a brief report explaining the variations in your estimates of the object's height. Decide as a group on a single estimate of the object's height, and defend your choice.
Task 4: Researching
Find the star Polaris in the evening sky. Use your clinometer to measure the angle of elevation to Polaris. The angle that you measure should be approximately equal to your latitude. Use a map to find your latitude. How accurate was your estimate?
Task 5: Finishing the Project
Create a display on indirect measurement. Include the device you built and
suggestions for improving it. Also include all measurements, calculations,
diagrams, and explanations from the activities in the project as well as
additional measurements you made on your own.
Reflect and Revise
Ask a classmate to review your project with you.Together, check that your
diagrams and explanations are clear, complete, and accurate. Have you
explained why your suggestions for changing the device you built will
improve it? Have you made measurements in addition to those called
for in the activities? Revise your work as needed.
Extending the Project
Research various navigation devices, including those invented long ago, such
as the sextant or the astrolabe, and modern ones, such as GPS (Global
Positioning Satellites). Explain how each navigation device works.
Page updated
Google Sites
Report abuse