# Time intervals using a heavy pendulum

##### Demonstration

Measurement of regular time intervals.

#### Apparatus and materials

Broom handle

Lengths of wood, about 5 cm x 5 cm x 50 cm, 2

Wooden board, about 20 cm x 8 cm x 2 cm

Nails, 15 cm, 2

Bricks, 6

Cross-beams of wood, 2

Card, about 8 cm x 4 cm

Wooden block, about 6 cm x 4 cm x 12 cm

#### Health & Safety and Technical notes

Drill a broom handle about 3 cm from the end to take a 15 cm nail. Push a wooden platform with a hole in it to take the broom handle over the handle. Secure it in place by a second nail pushed through a hole drilled in the lower end of the handle. This second hole should be about 110 cm below the top hole.

Screw a 25 mm round-headed screw into the bottom of the broom handle so that the head projects about 1 cm. Place two lengths of wood horizontally across two table tops. (Bricks resting on the ends will hold them rigid.) The pendulum is supported from these wood lengths, the 15 cm nail will roll on them. When stable, load the pendulum platform with two bricks, which can be tied into place.

Fasten a piece of thin card to a small block of wood. Position it so that, in swinging through the mid-position, the screw head which protrudes from the pendulum bob strikes the broad side of the card, making an audible click. Alternatively, amplify the sound this way: stick the card to part of a balloon which has been stretched tight and tied over the top of a 1000 ml beaker.

If the pendulum does not make enough swings, add more bricks to the platform.

#### Procedure

a Set the pendulum swinging. Listen to its regular sound.

b Time a number of time intervals – say, 10. (Remember to start counting from zero.)

c Calculate the average time interval.

d The time interval may change slightly as the pendulum swing decreases. Ask: Can this change in time interval be measured?

#### Teaching notes

1 A rigid pendulum of this type has a period of about two seconds so that the audible clicks occur at about one-second intervals. Rigidity is essential, otherwise there will be an unnecessary loss of energy.

2 It is good for students to know that a lack of beautiful shiny apparatus need not stop the progress of science. Where apparatus for modern physics is needed and expensive, an economy like this may be wise.

3 The crude brick pendulum hits a card as it passes through the lowest point each time to give audible signals. The piece of card that is to mark the swings audibly must be placed so that the pendulum hits it sharply and does not slide along its surface. Thus the card must be perpendicular to the plane of the swing. Simple schemes for mounting the card on a beaker or even on a rubber drum to increase the sound may be devised. Even a small bell could be rigged up.

4 The hits which signal the time will, of course, make the amplitude of the pendulum decrease fairly rapidly. However, that will not change the timing appreciably so you can let the amplitude die down without worrying. Since the impacts which lessen the motion occur at the midpoint of the swing, the phase of the motion is not changed in that abrupt decrease of motion. Thus the pendulum continues to keep its true period. Those who have tried this pendulum confirm that students enjoy the ingenuity of it and find it less clumsy and more satisfying than adults do.

This experiment was safety-checked in July 2007