Estimate of acceleration due to gravity using pulsed water drops

Demonstration

This experiment is one of the most delightful demonstrations in physics and well worth the effort of assembling the equipment.

Apparatus and Materials

• Constant head of pressure apparatus on tall stand
• Bucket

• Xenon stroboscope

• L.T. variable voltage supply (capable of 8A at 12V)
• Screen
• Latex thin walled, small diameter tubing, (not Bunsen tubing)
• Hoffman clip
• Ticker-tape vibrator or vibration generator
• Glass tubing, drawn out to form a stubby jet
• Tubing adaptor to connect to constant head apparatus
• Retort stand, boss, and clamp

Health & Safety and Technical Notes

Avoid setting the frequency of the stroboscope near 8 Hz as the flashing light may induce an epileptic fit.

Read our standard health & safety guidance

Set up the apparatus as shown.

This experiment depends mainly on having a good jet. It is easy to draw a glass tube into a jet by heating it in a strong Bunsen flame. The jet is then cut at a point about 2 mm diameter and the end is smoothed by putting it back into the flame for a few seconds. Take care that you do not seal it up. If the stream breaks up into several streams; or fails to break up into drops then other jets should be tried until a good one is found.

Water from a constant pressure supply flows through a rubber tube to the glass jet. Use a Hoffman clip to reduce the flow to a small stream. At the end of the tube there is a short piece of glass tubing drawn out into a jet. The height of the constant pressure supply should be up to 1 m above the jet. Adjust the Hoffman clip so that if the stream is directed vertically upward it rises to a height of 15 cm to 30 cm above the jet.

To make the stream break up into a regular series of drops, place the latex tubing in the vibrator so that the vibrator squeezes it fifty times a second. The Hoffman clip must be located on the rubber tube just before the vibrator so that the pumping action of the vibrator drives water to the jet.

You may want to adjust the flow rate with a Hoffman clip to a suitable value.

Arrange the stroboscope so that it casts a shadow of the stream on the screen. Viewed without the stroboscope, the stream will appear continuous. When the stroboscope is adjusted to the right flashing rate, the stream is seen to be a series of separate drops, which can be frozen in the air and in the shadow cast on a screen.

Procedure

1. Direct the jet streams in an upward-slanting direction so that one drop in the frozen pattern is exactly at the vertex of the parabola, measurements can be made from that drop, as starting level, downward.
2. On the shadow measure the vertical distances fallen from the vertex drop to the next below it - and the next and the next.
3. Use these distances to estimate g , assuming that the time from drop to drop is 1/50 second.
4. Measure the horizontal separation of the drops.
5. A photograph can also be taken of the pearls and the shadow (see below) and measurements taken from it using a long time exposure. An acetate sheet placed over the photograph enable the horizontal and vertical lines to be drawn and projected. To avoid scaling problems the screen should be moved until the actual size is projected onto it.
6. g = 2s/t ² where s is the distance fallen and t is time.

Teaching Notes

Photograph of pearls in air and their shadow. Photograph courtesy of Brenda Jennison.

• The pulsed stream of water droplets follows a parabolic path. This happens because:
• The horizontal motion of water droplets is at constant velocity.
• The vertical component of motion is a velocity changing at a constant rate due to gravity.
• You can draw horizontal lines every third pearl for convenience (each pearl may be too crowded). If the distance between the first four pearls is called one unit of distance and all the other grid lines are measured from the top in terms of this distance then you should find that the spacing is in the ratio of 1:4:9:16 showing that for equal intervals of time the pearl drops as the square of the time from the beginning of the fall. (s=1/2 at ² )
• For some examples of grids which have been drawn - see below.

This experiment was safety-tested in February 2006