The Falling Balloon Experiment
Students drop a small water balloon from a third-floor window, 10 m above the ground. They measure the fall time three times: 1.42 s, 1.45 s, and 1.41 s. Using g = 9.8 m/s² and ignoring air resistance, the theoretical time for a 10 m free fall is t = √(2h/g). The balloon bursts on impact. A classmate claims the experiment "proves" air resistance is negligible. The teacher asks the group to evaluate this claim and to consider what the spread in measurements indicates.
1. Calculate the theoretical fall time and compare it with the average measured time.
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t = √(2h/g) = √(2 × 10 / 9.8) = √(2.0408) ≈ 1.429 s. Average measured = (1.42 + 1.45 + 1.41) / 3 = 4.28 / 3 ≈ 1.427 s. The measured average (1.427 s) is within about 0.002 s of the theoretical value (1.429 s) - essentially identical at this precision.
2. Does the experiment prove air resistance is negligible? Evaluate the claim critically.
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No. Agreement within ~0.002 s is consistent with negligible air resistance, but it does not prove it. The measurement precision (readings to 0.01 s, spread of 0.04 s) is coarser than the effect being tested, so a small drag effect could hide inside the uncertainty. A water balloon is also not a streamlined object, and a 10 m drop is short. To test the claim properly one would need a taller drop, more trials, and a timing method with finer resolution (e.g., a photogate). The correct statement is: the data are consistent with negligible air resistance at this precision, not that they prove it.
3. What does the spread of the three measurements (1.41–1.45 s) tell you about the reliability of the result?
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The range is 0.04 s, about 2.8% of the mean. This spread reflects random error - reaction time in starting/stopping the stopwatch, slight variation in release height, and human timing. The mean is a better estimate than any single trial, but the uncertainty of the mean is roughly the spread divided by √n, i.e., about 0.04/√3 ≈ 0.023 s (order-of-magnitude). Because the difference between theory and measurement (~0.002 s) is far smaller than this uncertainty, the result is reliable as a confirmation of the free-fall model but cannot resolve small drag effects.