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Foucault Pendulum: How can a pendulum demonstrate the rotation of Earth?

In this experiment you will make a simple Foucault pendulum. When a pendulum is moving freely in air, the air resistance causes the pendulum to slow down and eventually stop. A heavy weight and tall pendulum will reduce the effect of friction. (Foucault's original pendulum consisted of a 62-pound [28-kilogram] iron ball suspended on a 220-foot [67-meter] steel wire.)

You will use a bag of sand as the pendulum's weight, and then note how the sand moves as it trickles from the bag. To observe results from the pendulum it should swing for at least thirty to sixty minutes. After that time, note the apparent change in the direction in which the pendulum is swinging.

To begin this experiment, make an educated guess about the outcome of the experiment based on your knowledge of Earth's rotation. This educated guess, or prediction, is your hypothesis.

A hypothesis should be brief, specific, and measurable. It must be something you can test through further investigation. Your experiment will prove or disprove whether your hypothesis is correct. Here is one possible hypothesis for this experiment: "The lines of sand falling from the Foucault pendulum will shift slightly over time as Earth is continuously rotating."

What Are the Variables

Variables are anything that might affect the results of an experiment. Here are the main variables in this experiment:

  • the length of the pendulum's cord
  • the amount of time the pendulum swings
  • wind

Level of Difficulty

Moderate to Difficult (because of the difficulty in keeping the swing straight).

Materials Needed

  • 13 feet (4 meters) of nylon cord or strong string
  • cloth or canvas sack
  • ladder at least 12 to 15 feet (3.5 to 4.5 meters) high, high swing set, or other tall stable outdoor structure
  • fine, dry sand (available at hardware stores or greenhouses)
  • calm, nonwindy day
  • large garbage bag
  • watch or timer
  • tape
  • sharp nail
  • chair

Approximate Budget

  • $8

Timetable

75 Minutes.

Step-by-Step Instructions

  1. Fill the sack with sand. Make sure there are no leaks in the bag by holding it over a clean surface and moving it gently.
  2. Tie the open end of the sack together with the cord or string, and stand on a chair to hang the bag from the top of the ladder or other stand. You may need an adult's help with this.
  3. Use the nail to punch a small hole in the bottom of the sand bag. The hole should be slightly larger than the tip of a pen, to allow the sand to fall out slowly. Hold the bag up to make sure that sand drops out at a visible rate. When it is flowing properly, seal the hole with a piece of tape.
  4. Lay out the garbage bag on the ground under and around the pendulum.
  5. Make sure the bag of sand hangs straight down and is not tilted. If it is, adjust either the sack or the cord.
  6. Keep the cord tight and pull the bag straight back about 4 feet (1.2 meters) high. Remove the tape and carefully set the pendulum in motion. Make sure you swing in a straight line and do not have an elliptical swing.
  7. Over the next 45 to 60 minutes, carefully give the cord an extra swing when it slows down. Try to keep the pendulum swinging for 60 minutes. Make sure you simply push the swing in the direction it is moving and do not shift the cord at all. This experiment may take more than one attempt.

Summary of Results

Draw the pattern of the sand. Explain the results, including how the Coriolis force influences the direction of the sand lines. For example, a Foucault pendulum set in motion in the northern hemisphere traces out a line that is always shifted toward the right.

How many degrees the pendulum shifts depends on where it is geographically located or its latitude. Latitude identifies the north-to-south position of a point on Earth The equator is 0° latitude; the north and south poles are each 90° latitude. At the equator the pendulum would not shift at all. At either of the poles the pendulum's swing would complete a circle in about twenty-four hours. You can figure out the rate of rotation where you live by finding your latitude and figuring out the following equation through longhand or a calculator. Mathematically, the pendulum's rate of shift is equal to the rate of rotation of Earth multiplied by the sine of the number of degrees of latitude: n = 360 degrees x sine (latitude), where n equals the number of degrees of rotation. The sine of latitude represents the angular distance of a place from the equator.

Troubleshooter's Guide

Here are some problems that may arise during this project, some possible causes, and ways to remedy the problems.

Problem: The bag is moving in a circular, elliptical path.

Possible cause: You may not have pushed the bag in a straight line for the first push or any subsequent pushes. Try practicing a straight-line push with the tape on the bag, and then repeat the experiment.

Problem: There was no shift in the lines of sand.

Possible cause: You may have set the cord slightly off-kilter during one of your pushes, or the pendulum may not have swung long enough. Try practicing a straight-line push with the tape on the bag, and then repeat the experiment, making sure to keep the pendulum swinging for at least sixty minutes.

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