Why is the answer 42?

Question

Why does the Foucault Pendulum at Griffith's Observatory in Los Angeles have a cycle time of 42 hours? The docents there can only blabber an attempted explanation, leaving everybody as confused as ever. Person with most convincing explanation for the figure of 42 hours without resorting to a wiki article wins 10 points, because the docents don't go around handing out wiki articles. What should the docents say?

Answer 1

At either pole, the precession time is 23.93 hr. You have to divide that # by the sine of the latitude to get the time for that latitude.

Answer 2

For a start as I understand the problem. If you had a pendulum at the north or south pole then the period would be the rotational speed of the Earth (about 24 hours). If the pendulum was at the Equator it would not rotate at all. So just guessing you take that latitude of Los Angeles and the result might be about 24/sin(lat)

This comes close to 42 hours with the Los Angeles latitude being about 34 degrees.

Answer 3

The situation is more complicated for other latitudes. On the equator, the pendulum would not precess at all - its precession period is infinite. At intermediate latitudes the period has intermediate values. One can calculate that the precession period for an ideal pendulum and support system is 23.93 hours divided by the sine of the latitude (see details). For example, at Sydney's latitude of 34 degrees S, the period is about 43 hours, a precession rate of about one degree every seven minutes.

The same effect that causes a pendulum to appear to veer slightly to the left (in the Southern hemisphere) is also responsible for the apparent motion of the major ocean currents. In the Southern hemisphere these are anticlockwise (they appear to turn to the left) and conversely in the Northern hemisphere.

One might choose to say that the earth was stationary but that a mysterious force makes moving objects turn. Using Newton's laws and the known rotation rate of the earth, one can calculate the size of these "forces", which are called Coriolis forces. Because it is so convenient to measure motion with respect to the surface of the earth, these forces are often used in calculation.

The animation below shows a pendulum swinging above the South pole. At left is the view from a position high above the equator at midday on the equinox---an observer near the sun would see this. The view at right is the view from directly below the South pole. Note how the path, as seen from the Earth, curves always to the left. (To make the details easy to see, the pendulum is depicted as very large and very slow. the amplitude of its motion was chosen equal to the radius of the Earth, and its period 8 hours: these values have no special significance. The animation makes some approximations about the motion.)

Answer 4

The answer to the ultimate question is 42. As you may not be aware the Earth will be distroyed by the Vogons for an Inter Stella Hyper Space Bypass 5 minutes before the ultimate answer to the ultimate question can be anwsered.Alas. So if you realy want to know why the answers is 42 try asking the little withe mice.

Answer 5

The cycle time is longer because of the latitude.

Answer 6

Sorry i thought you meant the answer in The Hitchhikers guide to the Galaxy.