# Measuring the average density of a student

##### Class practical

This activity can be a great deal of fun. Students devise their own method and carry out the appropriate measurements and calculation.

#### Apparatus and materials

*For each student group*

Bathroom scales (preferably calibrated in kg and not N)

Paper or card, large sheets (e.g. A1)

String, 1 – 2 m lengths

Ruler, 30 cm

Metre rule

Tape measure OR students can create their own tape measure, using string

#### Health & Safety

The dustbin method needs careful planning. It would be prudent to obtain parental permission, and permission from the school head. Secondly, the bin should be clean, ideally purchased new for the experiment, certainly not previously used for rubbish. The bin needs to be large enough so the student can get right inside with no difficulty. A large tray will be needed for collecting the displaced water, and the student should be careful about tripping as he/she gets in and out.

It would be better to do the experiment near the PE changing rooms so the pupil could easily dry off and get changed back into normal clothes. Some thought needs to be given about emptying the large volume of water left in the bin. If the experiment is done outside on a warm day, the water can simply be poured out on the ground into a nearby drain.

#### Procedure

Ask students to estimate and then measure their own density, using the apparatus provided. Stress that a perfectly accurate value is not expected.

#### Teaching notes

**1** Students will need to have studied density previously and be familiar with the density equation. Examples may have used cm^{3} as the unit of volume and g/cm^{3} as the unit of density, or m^{3} and kg/m^{3}. Either sets of units are generally acceptable, but all length measurements must use the same unit.

**2** The mass measurement is straightforward. Finding the volume of a human being is a difficult thing to do and many different methods are possible. One approach involves looking at limbs, the torso and head as separate solid objects, finding their volumes first and then adding these together to find a total body volume.

The answer should be pretty close to 1000 kg/m^{3}, that of water. If students have studied floating and sinking previously, then they should be able to suggest this as an estimate before they start.

**3** Some students may be sensitive about their mass and care needs to be taken in these situations. You could get them to estimate values for an 'average child'.

**4** A (possibly) more accurate measurement, and certainly more dramatic, can be obtained using a displacement method. Fill a large black dustbin to the brim with water. Have a willing student with a swimming costume and goggles climb into the dustbin and collect the water that is displaced. See the following website for an example!

**5 How Science Works extension:** The ability to estimate a measurement before it is made is a useful skill that sometimes helps to identify errors in measurements. Encourage students to identify the uncertainties in each measurement and to comment on them or quantify them.

*This experiment was safety-checked in January 2007*