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Physics Study Guide | Techniques for Accuracy and Precision

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Techniques of Good Measurement

To assure accuracy and precision, instruments also have to be used correctly. Measurements have to be made carefully if they are to be as precise as the instrument allows. One common source of error comes from the angle at which an instrument is read. Scales should be read with one’s eye directly above the measure, as shown in Figure 1-13a. If the scale is read from an angle, as shown in Figure 1-13b, you will get a different, and less accurate, value. The difference in the readings is caused by parallax, which is the apparent shift in the position of an object when it is viewed from different angles. To experiment with parallax, place your pen on a ruler and read the scale with your eye directly over the tip, then read the scale with your head shifted far to one side.
 

Figure 1-13 By positioning the scale head on (a), your results will be more accurate than if you read your measurements at an angle (b). How far did parallax shift the measurement in b?

 

The Global Positioning System, or GPS, offers an illustration of accuracy and precision in measurement. The GPS consists of 24 satellites with transmitters in orbit and numerous receivers on Earth. The satellites send signals with the time, measured by highly accurate atomic clocks. The receiver uses the information from at least four satellites to determine latitude, longitude, and elevation. (The clocks in the receivers are not as accurate as those on the satellites.)

Receivers have different levels of precision. A device in an automobile might give your position to within a few meters. Devices used by geophysicists, as in Figure 1-14, can measure movements of millimeters in Earth’s crust.

The GPS was developed by the United States Department of Defense. It uses atomic clocks, developed to test Einstein’s theories of relativity and gravity. The GPS eventually was made available for civilian use. GPS signals now are provided worldwide free of charge and are used in navigation on land, at sea, and in the air, for mapping and surveying, by telecommunications and satellite networks, and for scientific research into earthquakes and plate tectonics.

Figure 1-14 A series of expeditions succeeded in placing a GPS receiver on top of Mount Everest. This improved the accuracy of the altitude measurement: Everest’s peak is 8850 m, not 8848 m, above sea level.

 

APPLYING PHYSICS

Distance to the Moon
For over 25 years, scientists have been accurately measuring the distance to the Moon by shining lasers through telescopes.

The laser beam reflects off reflectors placed on the surface of the Moon by Apollo astronauts. They have determined that the average distance between the centers of Earth and the Moon is 385,000 km, and it is known with an accuracy of better than one part in 10 billion.

Using this laser technique, scientists also have discovered that the Moon is receding from Earth at about 3.8 cm/yr.

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