Chapter 4, Problem 94RPP

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)	$\theta (°)$
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 kra /h Thus the takeoff speed predicted by his simple pendulum was 215-220 km /h very close to what the pilot said.

Choose the best force diagram for the pendulum bob as the plane is accelerating down the runway (Figure P4.94).