Teaching Physics with the Physics Suite Edward F. Redish

# Alternative Homework Assignment: Tower of Pisa

One of the great folk legends in Physics is that of Galileo in the 16thcentury dropping a wood ball and an iron ball from the top of the LeaningTower of Pisa to refute an Aristotelian belief that heavier objects fallfaster. Although historical research indicates that this event probablynever took place, the Tower itself is an interesting and famous work ofarchitecture. It has a lean that is increasing slowly over the years asa result of the ground under one side settling faster than the ground onthe other side. The following photograph of the tower was taken from anadvertisement found in a 1994 airline magazine. Note that the photo ofman talking on the telephone to the right is not part of the original photograph.

 (a) Examine the photograph. Take the measurements in centimentersthat are needed to find a scale factor that enables you to estimate thelength of the Tower in meters (i.e. its height if it were standing up straight.)Use only evidence in the photograph. No other data are allowed. Then estimatethe tower length in meters. (b) According to data published in Sir Bannester Fletcher's A Historyof Architecture (U. of London Athlone Press, 1975, p. 470) the diameterof the lower part of the Tower is 16.0 m. Using this data find anotherscale factor for estimating the length of the tower, and then re-estimatethe length of the tower using this new scale factor. (c) Which of the scale factors (a) or (b) do you think will give thebest estimate of the length of the Tower? Explain the reasons for youranswer. (d) Using the scale factor you found in part (b) what is the lengthTower without the Belfry or narrow top segment. (i.e. just consider thebottom 7 stories.) (e) Based on data also reported by Fletcher the top of the wide partof the Tower (with the narrow top segment omitted) overhangs the bottomby 4.2 meters as of 1975. Question: Is the lean of the tower exaggeratedin the photo used in the ad? Are the little people in front of the towerdubbed in? Discuss this question and provide appropriate calculations and/ormeasurements to support your opinions.

These problems written and collected by P. Laws. These problems maybe freely used in classrooms. They may be copied and cited in publishedwork if the Activity-Based Physics (ABP) Alternative Homework Assignments(AHAs) are mentioned and source cited.

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