What is the height of the tower in the following case?
A visitor to a lighthouse wishes to determine the height of the tower. The visitor ties a spool of thread to a small rock to make a simple pendulum, then hangs the pendulum down a spiral staircase in the center of the tower. The period of oscillation is 9.18 s. The acceleration due to gravity is 9.81 m/s^2 .
To determined the height of the tower a pendulum is created by tying a rock to a thread and hanging it from the ceiling of the tower. The period of the pendulum us found to be 9.18 s.
The period of a pendulum is given by T = 2*pi*sqrt(L/g) where L is the length of the pendulum and g is the gravitational attraction where it is being oscillated.
Substituting the values given:
9.18 = 2*pi*sqrt(L/9.81)
=> 9.18/(2*pi) = sqrt (L/9.81)
=> L = 9.81*9.18^2/4*pi^2
=> L = 20.94 m
The height of the tower is equal to 20.94 m