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 9.71 s.
What is the height of the tower? The accel-
eration due to gravity is 9.81 m/s2 .
Answer in units of m
Period = 2*pi*sqrt(L/g)
Solve for L, the pendulum length and tower height.
You expact you to assume the pendulum string is attached near the top of the tower.
idk man
To determine the height of the tower using the period of oscillation of a simple pendulum, we can use the formula:
T = 2π √(L/g)
Where T is the period of oscillation, L is the length of the pendulum, and g is the acceleration due to gravity.
Given:
T = 9.71 s
g = 9.81 m/s^2
We need to rearrange the formula to solve for L:
L = (g * T^2) / (4π^2)
Plugging in the given values:
L = (9.81 * 9.71^2) / (4 * π^2)
L = (9.81 * 94.3541) / (4 * 3.14159)
L = 914.4653411 / 12.566368
L ≈ 72.834
Therefore, the height of the tower is approximately 72.834 meters.
To determine the height of the tower using the given information, we can use the formula for the period of a simple pendulum:
T = 2π√(L / g)
where T is the period of oscillation, L is the length of the pendulum, and g is the acceleration due to gravity.
In this case, the period of oscillation is given as 9.71 s and the acceleration due to gravity is 9.81 m/s^2.
Let's rearrange the formula to solve for L, the length of the pendulum:
L = (T^2 * g) / (4π^2)
Now we can substitute the given values into the formula:
L = (9.71^2 * 9.81) / (4 * π^2)
L ≈ 94.52 m
So, the length of the pendulum is approximately 94.52 meters. Since the pendulum is hung down the spiral staircase in the center of the tower, the length of the pendulum is equal to the height of the tower.
Therefore, the height of the tower is approximately 94.52 meters.