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A grandfather clock with a metal pendulum is located on a person's deck. Can you explain why the clock loses time in the summer and gains time in the winter.

If the grandfather clock mechanism is of the relatively inexpensive variety, there is no temperature correction for the pendulum. In the summer when it is warmer, the pendulum expands and is longer. This causes a slightly longer period, hence the clock runs slow (literally). The converse is true in the colder winter weather. The pedulum contracts just a little bit, and has a shorter period.

Precision pendulum clocks have glass enclosed collumns of mercury on the base of the swinging platform of the pendulum. When the pendulum cable would expand, lowering the center of mass, the mercury collumn would also expand, but upward. This upward expansion raises the center of mass just enough to cancel the lowering of the center of mass due to the cable's expansion.

     l ---- cable
l    l    l
l    l    l
l    l    l ---- mercury collumn
l    l    l

e tolman

If you're thinking the different temperature changes the length of the pendulum, and this changes the rate of the clock -- forget it. A pendulum takes the same amount of time to tick-tock whatever its length.

I don't think you have done enough fact-collecting yet to theorize. You clearly suspect the change in temperature is the cause. Test this. Move the clock indoors and see if the change persists. You don't have to do it for a full year: just move it inside for a few days during the summer, when the inside is bound to be cooler, and see if the clock starts speeding up. Or else look at how fast the clock goes during the day and during the night on any day, since the night will typically cooler than the day.

There are certainly a lot of parts in a clock which change shape and size slightly in response to temperature, and these could affect the clock's accuracy. But there are other possibilities, too. It could be humidity, for example, which will change from summer to winter. Perhaps dew condenses on the clock, and is burned off faster by the earlier rising sun in the summer. And so on.

Dr. c. Grayce

This sounds like a homework problem. No sane person would keep such a valuable piece of furniture outside in the weather. Most likely, it would rust in the spring, and never keep time again.

So that you can answer this question yourself, what determines the period of a pendulum? Its length? Its mass? Its kinetic energy? What would temperature changes effect?

Richard Barrans Jr., Ph.D.

The period (or time) of a pendulum swing is related to the mass of the pendulum and the length of the pendulum. The mass will not change during the seasons; however, the length does. In winter, the length shortens and the pendulum swings faster. The opposite occurs in the summer when the pendulum increases in length and the pendulum takes longer to swing. I suggest you go to the library and look in a physics book on the laws governing the period of oscillation of a pendulum (there is an equation that will tell you in mathematical terms what I just mentioned). Galilao is probably the most famous scientist who investigated the laws.
Have fun.

Dr. C. Murphy

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