Motion Detectors do not provide the best measurement of the acceleration due to gravity. If that is your goal, we recommend using a Photogate and a Picket Fence. There are a few factors that make the Motion Detector less-than-perfect for this type of measurement:
- The exact time of the measurement is not controlled. The exact time of measurement is the instant when the ultrasound bounces off the object. This occurs a time, x, after the ultra sound is produced. We know the exact time at which the sound is produced, but x varies with the distance measured. Tiny errors in time measurements cause large errors in acceleration measurements. This timing error is minor for objects undergoing small accelerations, but in freefall the acceleration is large.
- The distance resolution of the Motion Detector is about 3 mm. Tiny errors in distance measurements cause fairly large errors in acceleration measurements. Mostly this results in noisy time series for freefall accelerations.
We performed this experiment with a Motion Detector to see what values we would obtain. We tossed a racquetball and then a basketball using the Motion Detector. Using a quadratic fit, we analyzed the entire parabola, the first half of the parabola, and the second half of the parabola. Here are the results:
- Basketball (m/s2): 9.648 (entire), 9.748 (first half), 9.430 (second half)
- Racquetball (m/s2): 9.724 (entire), 9.902 (first half), 9.686 (second half)
The racquetball has less air resistance, so it gives slightly higher numbers. Keep in mind when selecting a portion of your graph to analyze that the program looks at a few data points on either side of the range you select. So you need to keep well up into your parabola when selecting your range.
Note the business about fitting the two different halves of the toss. This can lead to an interesting physics lesson in itself. On the way up, gravity and air resistance are working in the same direction, and on the way down, gravity and air resistance are working in opposite directions. This provides a way of estimating air resistance by studying the differences in the two different values.
If your only goal is to get 9.8 m/s2 for acceleration due to gravity, we recommend you use a Photogate and a Picket Fence.