How to Find Gravity by Length & Time
- 1). Take several timings of a pendulum's swing. Start the stopwatch at the top of the pendulum's arc and stop it when it returns to the same point on the same side. Do this five to ten times and write down the times in seconds.
- 2). Find the average for the times by adding them up on the calculator, then dividing the total number of seconds by the number of timings. For example, if you did three timings and wrote down 1, 1.5, and 1.3 seconds, the total is 3.8 seconds. Dividing 3.8 by 3 gives an average value of 1.3 seconds after rounding.
- 3). Find the square of the average time value by pressing the calculator's x^2 key. Write this number down. For this example, the square of 1.3 seconds is 1.69.
- 4). Measure the length of the pendulum from the pivot to the end of the bob using the meter stick. In this example, use .419 meters.
- 5). Key in the number 4 on the calculator, then multiply it by 9.87, the value for pi squared. The formula to find the pendulum's time interval uses 2 times pi, but in rearranging the formula to find the gravitational acceleration, you must square 2 times pi, making 4 times 9.87.
- 6). Multiply the result by the pendulum's length in meters. Divide by the square of the average time in seconds. The final result is Earth's gravitational acceleration in units of meters per second, squared.
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