Tall buildings are designed to sway in the wind. In a 100-km/h wind, for example

Question

Tall buildings are designed to sway in the wind. In a 100-km/h wind, for example, the top of the 110-story Sears Tower oscillates horizontally with an amplitude of 15 cm. The building oscillates at its natural frequency, which has a period of 7.0 s.

Part A

Assuming SHM, find the maximum horizontal velocity experienced by a Sears employee as she sits working at her desk located on the top floor.

Express your answer to two significant figures and include the appropriate units.

art B

Find the maximum acceleration experienced by a Sears employee as she sits working at her desk located on the top floor.

Express your answer to two significant figures and include the appropriate units.

Part C

Compare the maximum acceleration (as a percentage) with the acceleration due to gravity.

Express your answer using two significant figures.

Explanation / Answer

Vmax = A*w = A*2*pi/T = 0.15*2*pi/7 = 0.135 m/s

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part B

maximum acceleration amax = w^2*A = (2*pi/T)^2*A

amax = (2*pi/7)^2*0.15 = 0.121 m/s^2

====================

part C

amax/g = 0.121/9.8 = 1.23 % <<<<-------------answer

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