# Falling through water

##### Class practical

An object falling through water reaches a constant terminal velocity after falling relatively small distances. This terminal velocity can be seen and measured.

#### Apparatus and materials

For each student group

Gas jars

Chinagraph pencil or water-based pen

Stopwatch or other timer

Other objects and materials (e.g. Plasticine pieces, glass beads and wood)

#### Health & Safety and Technical notes

Unexpanded beads are now classified as a dangerous substance because of the pressure generated when they expand. Teachers must control access to the unexpanded beads and supervise this activity carefully to see that the beads are not removed for unauthorized experiments.

Styrocell beads are the raw material for making expanded polystyrene. There should be enough of them to provide each student group with between thirty and fifty.

They contain an expanding agent, which causes them to expand to forty or sixty times their original volume when heated up. You can expand them by boiling in water for five minutes. If you then allow them to fall freely in air, they will approach a terminal velocity in about 30 cm. They behave like 'slow motion raindrops'. The unexpanded beads should be stored in a cool place, preferably in a sealed polythene bag. Expanded beads should be thrown away.

A drop of a wetting agent in the water will help to prevent beads from clinging to the surface of the water in the gas jar.

Harbutt's original Plasticine is no longer manufactured: modern products have different names.

#### Procedure

a Fill a gas jar, to near the top, with water.

b Use a chinagraph pencil or water-based pen to make marks at regular intervals, such as 2 cm, on the outside of the gas jar. Put the top mark close to the water surface, at the height from which you drop the beads.

c Release a Styrocell bead (unexpanded) on the water surface.

d Find out whether the bead travels at the same speed all the way down. To do this, see if the beads pass the marks with a steady rhythm. You'll probably need to try this more than once.

#### Teaching notes

1 The density of the unexpanded Styrocell is close to that of cold water.

2 Students should find that the motion quickly approaches an almost constant speed, or 'terminal velocity'. They should discuss why, with gravity continuously acting, the beads do not accelerate all the way down. The answer relates to resistive force, which depends on speed.

Initially, when the bead is released and has no speed and there is no resistive force:

Downwards force = weight of bead

Upwards force = upthrust (flotation force)

The weight is slightly larger than the upthrust so the forces are not quite balanced, and there is a small net or unbalanced downwards force. After falling for a short distance, when the bead has acquired speed and experiences resistive force:

Downwards force = weight of bead

Upwards force = upthrust + resistive force

Upwards and downwards forces become balanced as soon as resistive force becomes big enough, and then acceleration is zero.

3 You can use other objects and materials, such as small ball bearings, glass beads, Plasticine pieces of various sizes and loaded pieces of wood. Denser objects need a greater distance before they reach their terminal velocity. The upthrust they experience is less similar to their weight, so they need larger resistive force before they can reach the balanced force condition.

4 How Science Works Extension: This experiment provides opportunities to consider sources of error and how they can be reduced by considering experimental design. Ask your class to suggest how the terminal velocity of a bead can be measured. One approach is to time a bead as it falls between two marked points on the jar. Start a stopclock as the bead passes the first mark, and stop it at the second mark. How far apart should the marks be? The further apart the better, but the upper one must not be in the region where the bead is still accelerating. How should the marks be made? Chinagraph pencil lines have a thickness; it might be better to use coloured adhesive tape and try to start/stop the clock as the bottom of the bead reaches the top edge of the tape.

Now ask an individual student to make repeated measurements of beads falling between two markers. How consistent are the timings? This is a useful way to assess the random error in the measurements, but there may be a systematic error caused by the student’s reactions. (This could be reduced or eliminated by making measurements over different heights.)

Now ask another student to repeat the measurements. Is one experimentalist more consistent than another?

This can lead to a discussion of the desirability of automated measurements (perhaps using light gates), but it is important to stress that these must also be assessed for errors.

This experiment was safety-checked in September 2004