3.2 Required practical: density

Aim

To find the density of regular solids, irregular solids and liquids by measuring their mass and volume.

The density of each substance is found using

\rho = \frac{m}{V}

Method 1: a regular solid

1. Measure the mass of the object on a top-pan balance.
2. Measure the length, width and height with a ruler (or the diameter and length for a cylinder).
3. Calculate the volume: for a cuboid, volume = length × width × height.
4. Calculate the density using \rho = \frac{m}{V}.

Method 2: an irregular solid

1. Measure the mass of the object on a balance.
2. Fill a eureka can with water until it just starts to overflow from the spout, and wait until the dripping stops.
3. Place a measuring cylinder under the spout.
4. Lower the object gently into the can using a thread. It must be fully submerged.
5. Collect all of the water that flows out. The volume of this water equals the volume of the object.
6. Calculate the density.

Method 3: a liquid

1. Place an empty measuring cylinder on the balance and record its mass (or press the tare button to reset the balance to zero).
2. Pour in some of the liquid, and read the volume at eye level from the bottom of the meniscus.
3. Measure the mass of the cylinder and liquid together.
4. The mass of the liquid is the difference between the two readings.
5. Calculate the density.

Precautions and sources of error

• Read the balance when the reading is steady, and check it reads zero before you start.
• Read the measuring cylinder at eye level, so the reading is not affected by parallax.
• In the eureka can, wait for dripping to stop, and make sure no water is left behind in the spout or lost when the object is lowered in.
• Take several measurements of each length with a ruler and find a mean. Use the smallest measuring cylinder that holds the water, so the scale gives the most precise reading.

Example results

Regular solid. A metal cuboid has a mass of 135.0 g. Its dimensions are 5.0 cm, 2.0 cm and 5.0 cm.

• Volume = 5.0 \times 2.0 \times 5.0 = 50 cm³
• Density = \frac{135.0}{50} = 2.7 g/cm³

Irregular solid. A stone has a mass of 81 g and displaces 30 cm³ of water.

• Density = \frac{81}{30} = 2.7 g/cm³

Liquid. An empty measuring cylinder has a mass of 85 g. With 40 cm³ of a liquid in it, the mass is 117 g.

• Mass of the liquid = 117 - 85 = 32 g
• Density = \frac{32}{40} = 0.80 g/cm³

You can check your answer by comparing it with the known values of the density of common materials. Both solids above have a density of 2.7 g/cm³, which is the density of aluminium.

Reducing the uncertainty

Every measurement has an uncertainty. A ruler with 1 mm divisions can be read to about ± 0.5 mm. The percentage uncertainty is the uncertainty divided by the measurement, multiplied by 100.

• For a length of 10 mm: \frac{0.5}{10} \times 100 = 5\%
• For a length of 50 mm: \frac{0.5}{50} \times 100 = 1\%

The volume of a cuboid is found from three lengths, so these percentages add up: about 15% for a small cube, and about 3% for a large one. To get the best result, use the largest object that you can, or a more precise instrument, such as a micrometer or vernier callipers, for small objects.

Other tips

• Objects that float: an object such as a piece of wood floats, so you cannot use a eureka can to find its volume. You can tie a heavy object (a sinker) to it, to hold it under the water, and subtract the volume of the sinker.
• Using a measuring cylinder for an irregular solid: record the volume of water before, put in the object, and record the volume after. The difference is the volume of the object.
• Take readings of mass using a balance with a reading of 0.1 g, and make sure it is zeroed first.
• Repeat the measurements and take a mean, to reduce the effect of random errors.