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Professor tests airplane takeoff speed D A Wardle, a professor of physics from the University of Auckland New Zealand tested the takeoff speed of a commercial airliner. The pilot had insisted that the takeoff speed had to be 232 km /h To perform the testing experiment, Wardle used a pendulum attached to stiff cardboard (Figure 4.14) Prior to takeoff, when the plane was stationary, he marked the position of the pendulum bob on the cardboard to provide a vertical reference line (the dashed line in Figure 4.14) During the takeoff, he recorded the position of the bob at 5-s intervals. The results are shown in the table.
The information is taken from the article by D. A Wardle "Measurement of aeroplane takeoff speed and cabin pressure" published in The Physics Teacher, 37, 410-411 (1999).
t( S) |
|
0 | 9.9 |
5 | 14.8 |
10 | 13.8 |
15 | 13.0 |
20 | 12.0 |
25 | 11.4 |
Using these data, Professor Wardle determined the acceleration at takeoff to be greater than g/4. Then he plotted an acceleration-versus-time graph and used it to find the takeoff speed It turned out to be about 201 km /h. He was very satisfied—the day was windy, and the speed of the breeze was about 15-20 km /h Thus the takeoff speed predicted by his simple pendulum was 215-220 km /h very close to what the pilot said.
The professor used which of the following expressions for the pendulum bob acceleration (
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