Density

Introduction

Density is simply how heavy something is per unit volume. As an equation it is simply mass divided by volume:

d = mass/volume = m/v

This will usually be expressed in kg per m^3 or sometimes as grams per cubic centimetre (gm/cm^3).

Often density is represented by the Greek letter rho, ‘ρ’. We intuitively know that some things have a greater density than others. We generally expect metal items, especially steel or iron, to be more dense than wood. But how do we get a precise result for the density? We answer this question with this experiment in two ways. If a body is regularly shaped, such as a cube or a sphere, then we can calculate its volume using geometry. If it is irregularly shaped then we need to be more cunning. Here we use the volume of water displaced when the body is submerged. In both cases finding the weight of a body is a simple matter of weighing it, and once we have the volume and the weight, the density is simply derived from the above formula.

The objective

To investigate the density of a variety of objects.

The apparatus

Electronic scales
Glass measurement flask
Two glass beakers;
A regular shaped object;
Selection of irregularly shaped objects.

The variables

There are no independent variable as such however, we have a choice of differently shaped objects for which we can choose to find the density

The Physics

This was stated in the first section as the definition of density;

d= m/v

Where m is the mass and v is the volume.

The method

For the regularly shaped object, such as a cube, measure its weight using the scales. Use a ruler to measure its length and calculate the volume. Calculate the density using the formula for density given above.

For an irregularly shaped object, such as a pointer style knob, measure its weight using the scales. Then use how much water it displaces to determine its volume. This can be done by filling a large beaker with water to the brim and positioning a measuring flask to catch the water that overflows when the object is submerged into the water. The volume can then be read directly from the scale on the side of the measuring flask.

The Video

Watch a video of the Density e-practical here.

This shows how to use it and how to collect the data.

The e-Practical

Pick up the block shaped object by clicking on it. Move it using the coloured handles that appear until it is right over the electronic scales, click again and the block will drop onto the scales. Take a note of the weight as indicated by the scales.

Move the block to the graph paper (to the right of the scales). Use the graph paper to estimate the dimensions of the block.

You can now calculate the volume from the dimensions and with the weight, you can now calculate the density of the block.

Choose one of the other objects and weigh it in the same way you weighed the block.

Fill up the beaker under the tap by putting the mouse over the nearer tap and using the scroll wheel. When the water starts to overflow, turn off the tap. The picture on the right shows the beaker overflowing.

The overflow beaker can now be moved away by placing the mouse pointer over this beaker and using the scroll wheel to move the beaker towards you.

This will allow you to move the measuring cylinder under the overflow to catch the water displaced by the object you are measuring the volume of.

With the overflow beaker out of the way, the measuring cylinder can be moved under the overflow by placing the mouse pointer over the cylinder and using the scroll wheel to move the cylinder to the right.

You can now pick up your object and drop it into the water, this takes a little care, and you may find it necessary to view the apparatus from the side to make sure the object is above the beaker before you drop it.

You can find the volume of the object you dropped by using the measuring cylinder to find the amount of water displaced by the object. Use the scale on the side of the cylinder to read the volume; you may find it useful to move closer to the cylinder and/or use the zoom function (plus key).

You now have the weight and the volume of the object from which you can calculate the density.

Try it yourself

The Results

Where you know the material the object is made from, you can verify your results by searching for the known density on the internet.

Further Discussion

What is fundamentally determining the density of a particular material?

Exam Questions

AQA June 22 Foundation Paper 1

Your description should be of the method used above to find the density of irregularly shaped objects.

2.55 ±10 simply means the maximum is the value plus 10, and the minimum is the value minus 10.

With multiple readings variations in measurement accuracy will tend to average out giving better results.

This section is adapted from material developed by Dr Robert Lucas and is related to the book High School and Undergraduate Physics Practicals, published by CRC Press.