What it shows
An object put in water seems lighter by exactly the weight of the water it pushes aside. The loss of weight, measured on a balance, equals the weight of the overflowed water.
The science
The upthrust on a body in a fluid equals the weight of the fluid it displaces (Archimedes’ principle). The apparent weight in water is therefore less than the weight in air by that upthrust. So the loss of weight W_air − W_water equals the weight of displaced water, ρ g V. The ratio W_air / (W_air − W_water) is the relative density of the body, which is how a goldsmith can test whether a crown is pure.
Materials
Cost: under Rs 200. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A small spring balance (kitchen hanging scale) or a rubber band with a ruler as a force meter
- An overflow can made from a bottle with a spout cut near the top, or a jar with a side tube
- A small catching cup
- Three solid objects, such as a stone, a metal nut and a steel spoon
- Thread
- A measuring cylinder or a kitchen scale for weighing water
- Water
Safety
For this project: An adult must cut the bottle with a knife or scissors and smooth any sharp edges.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Hang the stone on the balance by the thread and read its weight in air, W_air; if you use a rubber band, mark its stretch on a paper strip.
Fill the overflow can with water until it just stops dripping from the spout and place the empty catching cup under it.
Lower the stone gently into the water while still hanging from the balance, so that it is completely under water but not touching the bottom.
Read the apparent weight W_water and collect the overflow in the cup.
Weigh the overflowed water, remembering that 1 gram of water weighs about 0.01 newton.
Compare the loss of weight with the weight of the displaced water.
Repeat with the other two objects and calculate the relative density W_air / (W_air − W_water) for each.
What you should see
For each object the loss of weight is nearly equal to the weight of the overflow water, within a few percent. The relative density of the stone comes out at about 2.5 and of the steel spoon at about 7.8.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1State Archimedes’ principle.
A body in a fluid feels an upthrust equal to the weight of the fluid it displaces.
2Why does a stone seem lighter in water?
The upthrust of the water acts upward and reduces the pull on the balance.
3What is relative density?
The density of a substance divided by the density of water.
4Why does a steel ship float?
Its hollow shape displaces so much water that the upthrust equals its weight.
Take it further
Use salt water and show that the loss of weight, and so the upthrust, is larger because the liquid is denser.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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