## The Anatomy of Black Holes - Page 18

ANALYSIS

From your tape you can see that the mass falls further during each time interval. When you subtract each of the distances, AB, BC, CD, ... from the previous distance, you find that the increase in distance fallen is a constant. That is, each difference BC - AB = CD - BC = DE - CD = gt^{2}. This quantity is the increase in the distance fallen in each successive 10 dot interval and is an acceleration.

From your data table make a table of calculated values of AB, BC, CD, DE, etc. In the next column of your table of calculated values, place values of BC - AB, CD - BC, and so on. These values should be reasonably constant. WHY? Average these values. This represents the constant increase in distance during each time interval. To find the time, divide 10 by the frequency of the tuning fork. Each blank space between dots represents one vibration of the tuning fork, and you counted 10 spaces or 10 vibrations between letters.

To calculate g divide the average distance by the time squared. If you used cm your answer should be 980 cm/s^{2}. Calculate your percent error. It should be less than 10%. You might want to repeat the experiment if your percent error is greater than 12%.

List some sources of error in this experiment. What errors would be introduced by using a tuning fork whose vibrations are slower than about 100 Hz? higher than about 400 Hz?

PROCEDURE - Part B

The best pendulum to use is one whose bob is a metal sphere hung by a fine thread. However, acceptable results can be obtained with a hooked laboratory mass or a washer and any kind of string or thread.

Obtain about one meter of string and a pendulum bob. Attach the string to a suitable stand (a ring stand, for example) and then attach the string to the pendulum bob. The pendulum should be able to swing freely without hitting anything. Measure the length, L, of the pendulum from its point of attachment to the middle of the bob. Set the pendulum swinging with small swings (not more than 10 degrees from the vertical.) Time at least 20 complete round trips. Repeat the timing of 20 complete swings until you are confident that you have a reproducible result. By timing many round trips instead of just one you make the error in starting and stopping the stopwatch a smaller fraction of the total time being measured.