# Measuring the Height of a Lighthouse with a Pendulum

• Forceflow
In summary, the visitor to the lighthouse used a simple pendulum with a period of 9.52 s to determine the height of the tower. Using the formula T=2Pi(square root(length/gravity)), the height of the tower was calculated to be 2193.727 meters. However, there was an error in the initial calculation that was later corrected.

#### Forceflow

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 9.52 s. What is the height of the tower?

So, the formula that i used was T=2Pi(square root(length/gravity))
so..that equals 9.52^2=4Pi^2(l/9.81)
-Then, 9.81(9.52^2)/(4Pi^2)=length
So, the answer that i got was 2193.727, but it was wrong.

Forceflow said:
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 9.52 s. What is the height of the tower?

So, the formula that i used was T=2Pi(square root(length/gravity))
so..that equals 9.52^2=4Pi^2(l/9.81)
-Then, 9.81(9.52^2)/(4Pi^2)=length
So, the answer that i got was 2193.727, but it was wrong.
The approach is correct. Check your computation.

ok

ok thanks. I got it right. I did wrong on on the calculator lol.

## 1. How does using a pendulum help measure the height of a lighthouse?

Using a pendulum can help measure the height of a lighthouse because the pendulum's period is affected by gravity, which is dependent on the distance from the center of the Earth. By measuring the period of the pendulum at different heights, we can calculate the height of the lighthouse.

## 2. What equipment is needed to measure the height of a lighthouse with a pendulum?

To measure the height of a lighthouse with a pendulum, you will need a pendulum with a known period, a stopwatch or timer, a measuring tape, and a means of safely hanging the pendulum from the top of the lighthouse.

## 3. What is the process for measuring the height of a lighthouse with a pendulum?

The process for measuring the height of a lighthouse with a pendulum involves timing the period of the pendulum at the top and bottom of the lighthouse, and using the formula T = 2π√(L/g) to calculate the length (L) of the pendulum at each point. The difference between these lengths will give the height of the lighthouse.

## 4. How accurate is this method of measuring the height of a lighthouse?

This method can be quite accurate if proper measurements are taken and calculations are done correctly. However, factors such as air resistance and external forces can affect the accuracy of the results. It is important to repeat the measurements multiple times and take an average to improve accuracy.

## 5. Are there any limitations to using a pendulum to measure the height of a lighthouse?

Yes, there are some limitations to using a pendulum for this measurement. The accuracy can be affected by environmental factors such as wind and temperature. The height of the lighthouse must also be within the range of the pendulum's length. Additionally, this method may not be suitable for measuring the height of lighthouses with irregular shapes or structures.

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