# Find how far ahead a grandfather clock gets after a period of time

• Nathan B
In summary, the conversation discusses how a change in temperature can affect the length and period of a pendulum. The equations for calculating the period and change in length due to temperature are provided. The conversation also mentions the accuracy of a grandfather clock and the attempt to calculate the exact amount of time off in 24 hours. Despite some initial discrepancies, it is ultimately determined that the calculations were correct.
Nathan B

## Homework Statement

A pendulum shortens due to a change in temperature, decreasing the length L and therefore period T. How many seconds ahead does the clock get in 24 hours? We assume that the grandfather clock is completely accurate at a normal pendulum length.
Li = 1.3 m
ΔT = -10°C

## Homework Equations

Equation for the period of a pendulum, T = 2π√(L/G)
Equation for change in length due to temperature. ΔL = αLiΔT

## The Attempt at a Solution

The new and old periods are relatively easy to calculate.

I've gotten all sorts of approximate values for time off, but I need to be exact. One of several methods that I've tried:

T2 / T1 = time given by the shortened pendulum/actual time

If we want to examine the results of 24 hours of time passing, we take the number of seconds in 24 hours to be our actual time = 84600 seconds.

Time given by shortened pendulum = 84600*T2 / T1

subtract actual time and we know how far off we are:

Time off in seconds = 84600*T2 / T1 - 84600

This seems like it should work, but it's always a little bit off.

What can I do to make this more accurate?

Nathan B said:
This seems like it should work, but it's always a little bit off.
What values are you using for g and α, what answer do you get, and what do you think is a more accurate answer?

Turns out it was correct, I had a mistake elsewhere in the problem. Thanks for the willingness to help!

## 1. How do you calculate the amount of time a grandfather clock gains?

The amount of time a grandfather clock gains can be calculated by measuring the time difference between the clock's time and the actual time, and then converting that into seconds. Then, divide the seconds by the number of seconds in a day (86,400) to get the number of days the clock has gained.

## 2. What factors can affect the amount of time a grandfather clock gains?

The main factor that can affect the amount of time a grandfather clock gains is the clock's pendulum length. If the pendulum is too long or too short, it can cause the clock to gain or lose time. Other factors that can affect the clock's accuracy include temperature, humidity, and the clock's location.

## 3. How often should a grandfather clock be adjusted to maintain its accuracy?

Typically, a grandfather clock should be adjusted every 7-10 days to maintain its accuracy. However, this may vary depending on the clock's construction and environmental factors.

## 4. Can a grandfather clock be adjusted to gain or lose time intentionally?

Yes, a grandfather clock can be adjusted to gain or lose time intentionally by adjusting the length of the pendulum. However, this should only be done by a trained professional to avoid damaging the clock's mechanism.

## 5. How does the accuracy of a grandfather clock compare to other types of clocks?

Grandfather clocks are known for their accuracy and can maintain their precision for centuries if properly maintained. They are often more accurate than other types of clocks, such as digital clocks, which can lose or gain time due to power outages or technical malfunctions.

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