# Fun with Archimedes’ Principle

**Manish Yadav, **in ** i wonder…**, presents how a group of Science teachers explored Archimedes’ Principle, and related concepts, with well-loved fables like the Thirsty Crow, and a series of simple, open-ended experiments with readily available materials.

Although most teachers agree on the need for experiments in the teaching and learning of physics, experimentation in schools often consists of students being asked to follow a series of instructions so as to arrive at a predetermined result or verify a previously stated law.

This approach is aimed more at getting predictable results rather than encouraging students to use experiments to explore questions. This is perhaps one of the reasons why teachers see very little value in conducting experiments in their classrooms. How do we rethink the kind of experiments we use to teach physics in school?

We explore this question by using an experiment-based approach to understand Archimedes’ Principle. Each of these experiments may be demonstrated by the teacher, or performed by students as group activities. Ask students to predict what they expect to see before the experiment is performed.

Draw them into discussion to help them recognise the prior experiences and assumptions that form the basis of their predictions. Once their predictions have been tested through experimentation, ask students to reflect upon and discuss their observations with each other. This approach will allow students to **arrive **at an understanding of the principle, on their own, through deeper inquiry.

### Can the thirsty crow story be true?

Many of us have heard the story of the thirsty crow that used pebbles to get to the water in a clay pot. But how many of us have attempted to verify this story?

We designed this experiment to help begin an exploration of Archimedes’ principle (see **Activity** **Sheet** **I**).

Start by reading out the story. Then encourage your students to experiment with a variety of materials to bring water to the brim of a pot. This will get them to think more deeply about the floating and sinking properties of objects in water.

### Factors that cause sinking or floating

We designed this experiment to help students think more deeply about the floating and sinking properties of objects, and their relationship with properties of the liquids into which they are dropped (see **Activity** **Sheet** **II**).

For simplicity, you can even start this experiment with one liquid — water.

Ask students a variety of questions to get them to identify factors that influence floatation. Students at the school level will most likely answer these questions by mentioning concepts like mass, volume, density, area, etc.

You may also get responses like colour or length. Selecting objects that vary widely in colour and length can be used to demonstrate that these properties have no connection with floatation (see **Box 1**).

Box 1. What kind of objects can we use for this experiment?There is no rule about the set of objects chosen for this experiment. They’ve been chosen because they display different conditions of floatation in different liquids.

Teachers can choose to have an entirely different set of objects that fulfil this same broad condition.

### The volume of objects and the liquid they displace

We designed this experiment to explore the relationship between the volume of objects and that of the liquid they displace (see **Activity Sheet III**).

To do this, we test the floatation of cuboids and spheres made of wood, metal, and glass in water.

Start this experiment by asking students to calculate the volume of the cuboids and spheres by making necessary measurements and using appropriate mathematical formulae.

Once they finish water displaced in each case. Encourage your students to compare these values with the volumes calculated at the beginning of this experiment. Can they identify any broad patterns?

These are some observations that are typical of this experiment:

- The volume of an object that sinks is equal to the volume of the liquid it displaces.
- The volume of an object that floats is greater than the volume of the liquid it displaces.

These observations can be expressed mathematically:

V_{object} = V liquid displaced when object sinks.

V_{object }> V liquid displaced when object floats.

### Mass and density in floatation and sinking

We designed this experiment to explore the relationship between the mass and volume of objects and that of the liquids they displace with their floatation (see **Activity Sheet IV**).

This activity has two stages. In the first stage, ask students to measure the mass of cuboids made of wood, iron or soap, and calculate their volume and density.

Then ask them to dip the cuboids one- by-one in water, and record the mass and volume of displaced water in each case.

Given the fact that objects of the same volume can show different floatation properties (one floats while the other may sink), encourage students to use these observations to explore the relationship between the mass, volume, and density of an object with its tendency to sink or float.

You can also ask them to test this relationship with objects of irregular shape (see **Box** **2**).

Box 2.Does the shape of an object have any role to play in its tendency to sink or float?Give students some clay or aluminum foil and a tub of water. Encourage them to use the clay or foil to carve out differently shaped objects of the same mass, drop them in water and record the volume, mass, and density of water they displace.

Since differently shaped objects have different contact areas, they may displace different volumes of water.

Does the shape of a boat help it float?What makes it sink?

This can lead to a discussion about how the shape of boats and ships are designed for floating despite being made of material that has a much higher density than seawater.

This will help them arrive at a relationship like this:

Volume Relation | Mass Relation | Density Relation (Mass / Volume) | |
---|---|---|---|

Sink | Vo = Vw | Mo > Mw | Do > Dw |

Float | Vo > Vw | Mo = Mw | Do < Dw |

Here,

- Vo stands for the volume of the object.
- Vw for the volume of water displaced by it.
- Mo stands for the mass of the object.
- Mw stands for the mass of the water displaced by it.
- Do stands for the density of the object.
- Dw stands for the density of the water displaced by it.

In the second stage, you can extend this exploration to other liquids, like alcohol, citric acid, salt solution, and sugar solution (see Box 3).

Box 3.Will an object’s tendencyto float or sink change if it is dropped in a liquid with the same density?We know that objects float on the surface of liquids of higher density, or below the surface of liquids of equal density. We also know that objects sink in liquids with a density lower than their own.

You can help students arrive at this understanding with an egg, some tap water, and some table salt.

Ask students to predict if the egg would float or sink if dropped into water. Once they have made their predictions, drop the egg into the water, and allow students to watch it sink.

Then, start adding salt to the water, gradually adding enough to cause the egg to start floating. Ask students what they think the salt does to the water to cause the egg to float.

Ask students to think of factors that cause an object to float (partially or fully) in one liquid and sink in another. This will help establish the fact that floating and sinking do NOT depend upon object properties alone.

### Conclusion

These are just some ideas for experiments that can be used to explore a concept in physics in more engaging ways. This kind of approach provides students with the opportunity to **explore **and **discover **these concepts for themselves.

Through such experiences, they begin to construct their own knowledge. Wouldn’t you want to try these experiments out too?

#### Key takeaways

- Students can develop a strong understanding of Archimedes’ principle through a series of simple, enjoyable, and open-ended experiments with readily available materials.

- An experiment-based approach that encourages students to predict, test, reflect, and discuss observations can help them ‘arrive’ at an understanding of core concepts and principles, on their own, through deeper inquiry.

### Acknowledgements

** **I would like to thank my colleagues Rakesh Tewary and Ganesh Jeeva (co-developer of the module ‘Let’s do physics’). I would also like to thank Azim Premji Foundation Jaipur state and Tonk teams for their help in organising the training workshop ‘Let’s do Physics’ with 35 Government teachers at Nawai, Rajasthan in December 2012.