Measuring gravitational acceleration

A friend and I measured gravitational acceleration in the stairwell of an apartment building. A good setting, for at the highest point you had 23 meters of freefall for dropping objects. We had a bag of balls along for a good sample size.

We dropped balls 62 times from various heights, and both my friend and I timed them. The data showed clearly that the falling time is sub-linear with respect to height. Assuming constant acceleration, my measurements gave 8.5 m/s² and my friend’s gave 8.9, i.e. a value 10%–15% smaller than the true value.

The setup isn’t very forgiving of systematic errors: a consistent 0.1s measurement error led to about a 1 m/s² change in the gravitational acceleration. Sound indeed takes almost that 0.1s to travel 23 meters, and air resistance is probably already noticeable over that distance as well. In any case, not a bad result for half an hour of dropping.

We also learned that when you drop a ball from the eighth floor, it makes a satisfying, loud thud when it hits the floor. Future research could investigate how well the sound carries into the neighbors’ apartments.