How Much Time Does a Shortened Pendulum Clock Lose in 24 Hours?

• bleedblue1234
In summary, the grandfather clock with a pendulum that is 85 centimeters long experienced an error of -1.7 minutes after being repaired with a shortened length of 84.8 centimeters. This is due to the fact that a shorter pendulum leads to a quicker rate and results in a loss of time.
bleedblue1234

Homework Statement

Pendulum clocks are typically made so the period of the pendulum is 1 second or 2 seconds, but they don't have to be. Suppose a grandfather clock uses a pendulum that is 85 centimeters long. The clock is accidentally broken, and when repaired, the length is shorter by 2.0 millimeters. Every 24 hours of correct time, the "repaired" clock will be off how much?

Homework Equations

Tp = 2(pi)sqrt(L/g)

The Attempt at a Solution

So i found the period of the pendulum for both clocks but now I am stuck as to how to find the error...

You have the periods of the 85 and 84.8 cm pendulums.
Whats the percentage difference?
eg If the wrong period is 5% shorter then the clock will be 5% faster and will record 5% more time

.001177... so it will be the percent difference times the number of minutes in a day?

so 1.70 minutes?

verification anyone?

That's correct.
Another better way to do it though (and probably what you will learn) is to look at the order of the equation

In the pendulum equation the length is a sqrt() so the ratio of change in time is sqrt() the ratio of change in length, ie a 4times change in lentgth gives a 2x change in period.

So in this case the change in time is 1-sqrt(84.8/85), which when multiplied by 24*60 gives 1.7
Then a double check, shorter pendulums go fatser, so the 84.8 means a quicker rate and time is lost

1. What causes errors in a pendulum clock?

Errors in a pendulum clock can be caused by a variety of factors such as changes in temperature, humidity, and air pressure. These changes can affect the length of the pendulum, which in turn affects the accuracy of the clock. Other factors that can cause errors include wear and tear on the clock's mechanism, improper maintenance, and external disturbances such as vibrations or movements.

2. How can I fix errors in my pendulum clock?

The first step in fixing errors in a pendulum clock is to identify the cause of the error. If it is due to changes in temperature or humidity, adjusting the length of the pendulum may help. However, if the error is caused by wear and tear or external disturbances, it is best to seek the help of a professional clock repairer. Regular maintenance and cleaning can also prevent errors from occurring in the first place.

3. Can errors in a pendulum clock be prevented?

While some errors in a pendulum clock are inevitable, regular maintenance and cleaning can help prevent errors from occurring. Keeping the clock in a stable environment with consistent temperature and humidity levels can also help maintain its accuracy. It is also important to handle the clock with care and avoid any external disturbances that may affect its accuracy.

4. How accurate are pendulum clocks?

Pendulum clocks are known for their accuracy and were widely used as timekeepers before the invention of more precise timekeeping devices. With proper maintenance and adjustments, a pendulum clock can be accurate to within a few seconds per day. However, external factors such as changes in temperature and humidity can affect their accuracy, so they may need to be adjusted periodically.

5. Can errors in a pendulum clock affect its value?

Yes, errors in a pendulum clock can affect its value. Clock collectors and enthusiasts place a high value on the accuracy and functionality of a clock. If a pendulum clock consistently has errors, it may not be as valuable as one that is well-maintained and accurate. It is important to address any errors in a pendulum clock to maintain its value and functionality.

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