Foucault's Pendulum

 

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Plan to watch the Foucault pendulum for about 2 hours, noting the exact times when three consecutive pegs are knocked down. Complete the pre-lab, read Crowe, sketch weird people that walk by, sing of the joy in your heart, etc., as you wait between peg knock-downs. Sit on the north side of the pendulum and face south. (When you face south, east is on your left and west is on your right. The entryway doors are on the west side of the of the Science building; the planetarium is on the east side.) All of the questions in the lab pertain only to the south half of the circle of pegs (disregard pegs on north half of circle).

 

Pre-Lab

  1.  
  2. Try the following Yo-Yo experiment on your own:
    Use a yo-yo or tie a small object at one end of a length of string. Swing your pendulum to and fro, holding the end of the string in your fingers. Twist the string in your fingers as you allow it to continue swinging.
    1. Does the yo-yo change its direction of swing? _______
    2. Does the yo-yo twist around with the string? _______

     

  3. Apply the Yo-Yo Model to the Foucault Pendulum:
    1. The inertia of the yo-yo kept it swinging in the same direction. Similarly, the inertia of the heavy pendulum bob keeps it swinging back and forth in the same plane. The pendulum keeps swinging in the same plane while the Earth rotates below it. If the pendulum is like the yo-yo, the rotating Earth is like a merry-go-round rotating underneath it.

       

    2. As with the yo-yo, the twisting of the cable-mount imparts to the pendulum a slow spin about its axis, but this twisting does not alter the direction of the swing of the pendulum (its plane of oscillation).

     

  4. North Pole Thought Experiment:
    • Visualize a Foucault pendulum at the north pole. Imagine that Santa Claus is standing in the exact center of the OBU Pendulum area, and the Earth is rotating beneath his feet. (He does a jolly dance to avoid getting hit by the pendulum as it swings.)
    • In your mind's eye, imagine the pendulum's plane of swing remaining the same with respect to the fixed stars. The pendulum experiences none of the rotational motion of the earth.
    • The Earth silently rotates beneath the pendulum without affecting the pendulum's plane of swing. Imagine the circular row of pegs as the equator, moving counterclockwise around the center as the earth turns on its axis. The rotation of the earth continually pushes one peg after another into the path of the swinging pendulum, causing the pegs to be knocked down. The room rotates around the pendulum; eventually all of the pegs get in its way and are knocked down.
    • Although actually maintaining a constant direction of swing with respect to the fixed stars, the pendulum appears to change its direction with respect to the pegs. Actually, like the pegs, we are sharing in the rotational motion of the floor and the earth, and therefore it is we ourselves that are moving, rather than the pendulum. We believe ourselves to be standing still, instead of rotating with the earth at an eastward speed of many thousands of miles per hour.
    1.  
    2. How long will it take for this north-pole pendulum to knock down all the pegs?

       

       

    3. Why would the pendulum knock down all pegs twice with every 360 degrees of rotation?

       

       

       

    4. How long will it take for the floor to rotate once around (360 degrees) beneath this north-pole pendulum? (Definition: This is the PERIOD of the pendulum.)

     

     

  5. Equator Thought Experiment:
    Set a pendulum swinging north and south at the equator. Beneath a pendulum at the equator, the ground is simply moving from west to east, carrying the pendulum with it, not rotating independently of it. The entire pendulum, and its plane of oscillation, shares in this eastward inertial motion. Note that the pendulum must be independent of the rotational motion of the earth, to some degree, for that motion to be manifest to an observer. Since at the equator the pendulum has no motion independent of the rotation of the earth, it will not knock down any pegs or appear to undergo any change of direction at all.
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    • What would be the period of a Foucault pendulum at the equator?

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Lab

Intermediate-Latitude Observation Exercise

Observe the Foucault pendulum (with explanatory display) in the exhibit area near the entryway to the Wood Science building.

  1.  
  2. When and where did Jean Foucault first perform this experiment?

     

     

     

  3. What did Foucault prove and how did he prove it?

     

     

     

  4. What significance does this have for the acceptance of Copernican astronomy?

     

     

     

     

  5. Rotational Period of the Pendulum's Plane of Oscillation.

    At a latitude intermediate between the equator and pole, such as Shawnee, the ground beneath the pendulum undergoes a combination of motions, both eastward (as at the equator) and rotary (as at the pole). A Foucault pendulum at the Earth's north or south pole would appear to move through a complete revolution of its plane of oscillation in exactly 24 hours.

    As seen from Shawnee, will a complete revolution of the pendulum take longer or shorter than 24 hours? (Answer this before doing the calculations below.) Explain your reasoning.

     

     

     

  6. Discover the period of our Foucault pendulum

     

  7. Data

    Below is a drawing of an ellipse that represents the circle of pegs as viewed at an angle from your sitting or standing position. Label and answer the following on this drawing:

    [ellipse.gif]
    1.  

       

    2. Draw a line to show where the pendulum was swinging when you first arrived. Label the line with your time of arrival.
    3. Count the total number of pegs. ____ pegs
    4. Mark a visible dot on the ellipse for every peg.
    5. Draw a short line through every dot if the corresponding peg has been knocked down.
    6. Record the time beside each peg that is knocked down while you are present. Watch the Foucault pendulum until you observe at least 3 pegs knocked down (consecutive pegs on the same side).
    7. As seen from above, which way does the pendulum appear to be changing its "plane of oscillation"?
      1. ___ clockwise;
      2. ___ counterclockwise
    8. Draw a line to show where the pendulum was swinging when you left. Label the line with your time of departure.

     

  8. Calculations
    1.  
    2. How much time elapses, on average, between peg knock-downs?

      _______ min/peg

       

       

    3. Calculate the time, shortly after the pendulum was first started in the morning, when the first peg on the south side was knocked down.
      Multiply the time between peg knock-downs (min/peg) times the number of pegs already knocked down before you arrived (pegs). Subtract this product (min) from the time you first saw a peg knocked down.

      _______ a.m.

       

       

    4. Calculate the total amount of time required for the pendulum to rotate through 360 degrees.
      Multiply the time between peg knock-downs (min/peg) times the total number of pegs (pegs) to obtain the period in minutes. Then divide by 60 min/hr to obtain the period in hours.

      PERIOD OF THE FOUCAULT PENDULUM:

      _____ minutes

      _____ hours

       

       

    5. Compare your value for the period in hours with the values obtained in the Pre-Lab Thought Experiments for the pendulum at the north pole and at the equator. Does your value for the pendulum's period fall within these upper and lower limits? Is your observed value consistent with the answer you gave in Lab step 4?

     

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For a detailed exposition of the pendulum see Henry Worms, The Earth and Its Mechanism: Being an Account of the Various Proofs of the Rotation of the Earth (London: Longman, Green, 1862), Part I, ch. 6 "On the Apparent Change of the Plane of Oscillation of the Free Pendulum," pp. 84-102.