A visitors 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 9.67 s.
What is the height of the tower? The acceleration due to gravity is 9.81 m/s^2
Answer in units of m
To determine the height of the tower using the information given, we can utilize the equation for the period of a simple pendulum:
T = 2π√(L/g)
Where:
T = period of oscillation (given as 9.67 s)
L = length of the pendulum
g = acceleration due to gravity (given as 9.81 m/s^2)
First, let's rearrange the equation to solve for L:
L = (T^2 * g) / (4π^2)
Now, we can substitute the known values into the equation:
L = (9.67 s)^2 * 9.81 m/s^2 / (4 * π^2)
L ≈ 93.50 m
Therefore, the height of the tower is approximately 93.50 meters.