Galileo, or Stopped, Pendulum

Description: The length of a pendulum is shortened in mid swing by the string hitting a peg placed below the support. The bob swings to the height from which it was released.

from Galileo Galilei "Dialogues Concerning Two New Sciences" (Leyden, 1638) trans Henry Crew and Alfonso de Salvio (Dover 1954)

"Imagine this page to represent a vertical wall, with a nail driven into it; and from the nail let there be suspended a lead bullet of one or two ounces by means of a fine vertical thread, AB, say from four to six feet long, on this wall draw a horizontal line, DC, at right angles to the vertical thread AB, which hangs about two finger-breadths in front of the wall. Now bring the thread AB with the attached ball into the position AC and set it free; first it will be observed to descend along the arc CBD, to pass the point B, and to travel alongthe arc BD, till it almost reaches the horizontal CD, a slight shortage being caused by the resistance of the air and the string; from this we may rightly infer that the ball in its descent through the arc CB acquired a momentum [impeto] on reaching B, which was just sufficient to carry it through a similar arc BD to the same height. Having repeated this experiment many times, let us now drive a nail into the wall close to the perpendicular AB, say at E or F, so that it projects out some five or six finger-breadths in order that the thread, again carrying the bullet through the arc CB, may strike upon the nail E when the bullet reaches B, and thus compel it to traverse the arc BG, described about E as center. From this we can see what can be done by the same momentum [impeto] which previously starting atthe same point B carried the same body through the arc BD to the horizontal CD. Now, gentlemen, you will observe with pleasure that the ball swings to the point G in the horizontal, and you would see the same thing happen if the obstacle were placed at some lower point, say at F, about which the ball would describe the arc BI, the rise of the ball always terminating exactly on the line CD. But when the nail is placed so low that the remainder of the thread below it will not reach to the height CD (which would happen if the nail were placed nearer B than to the intersection of AB with the horizontal CD) then the thread leaps over the nail and twists itself about it."
A 1.5 inch diameter wooden ball is suspended by a string from a bar attached to a magnet which sticks to the blackboard. The maximum length of the string possible with our blackboards is 90 cm. Mark the starting position of the bob on the blackboard. Release the pendulum and note that it rises to (essentially) the same height on the other side. Place the stop at some position below the pendulum support. Release the pendulum and note the height it now reaches on the other side.

The bob may be made to loop the stop if the heights of release and the stop are chosen appropriately.

Cautions: Practice is required to release the bob so that it swings free of the blackboard. Do not use the heavy bob. It may pull the mount off the blackboard if swung too vigorously.

Concepts demonstrated: Conservation of mechanical energy

Equipment: Magnetic pendulum mount, wooden bob on string, stop on magnetic mount, meter stick, chalk

Setup Time: Short

Difficulty/Commitment: Straightforward

Visibility: Visible

Related demonstrations:

References: PIRA 1M40.15
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Sutton M-132;DHP Mr-3; DaR M-414; JSMiller p102

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