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A spiral staircase winds up to the top of a tower in an old castle. To measure the height of the tower, a rope is attached to the top of the tower and hung down the center of the staircase. However, nothing is available with which to measure the length of the rope. Therefore, at the bottom of the rope a small object is attached so as to form a simple pendulum that just clears the floor. The period of the pendulum is measured to be 8.5 s. What is the height of the tower

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Answer:

 L = 17.94 m

Explanation:

The angular velocity of a simple pendulum is

          w = [tex]\sqrt{ \frac{g}{L} }[/tex]

the angular velocity is related to the period

         w = 2π / T

we substitute

         [tex]\frac{4\pi ^2 }{T^2} = \frac{g}{L}[/tex]

         L = [tex]\frac{g T^2}{4 \pi ^2}[/tex]

let's calculate

         L = 9.8 8.5² / 4π²  

         L = 17.94 m

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