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Weighing Buoyancy

Does a glass get heavier if you put your finger in the water? Find out in this experiment.

What you need

	2 plastic glasses		A stick
	String

What to Do

Water scales The idea is to build some scales, with a glass of water on each side. So first you want a way of attaching the cups to some string.

One way of doing this is by cutting two holes in each cup, slightly below the rim.

Then tie the cups to the stick, and attach a piece of string to the centre of the stick.

Now fill the two glasses almost full.

Add water so that the stick balances when hung from the centre piece of string.

Put your finger in one cup, without touching the sides. What happens?

What may Happen

You should find that the cup you put your finger into, moves downwards.

What is going on?

One way of thinking about this, is that if you put anything in water - a boat, a rubber duck or just your finger, it will feel an upthrust force pushing up on it. This is the force which makes boats float, and is equal to the weight of water that is displaced by the object.

Issac Newton worked out that if you apply a force to something, you will feel an equal and opposite force (every action has an equal and opposite reaction). So if the water is applying an upwards, upthrust force to your finger, your finger must be applying a downward force to the water.

Another way of thinking of it is that when you put your finger in the water, it will increase the level of water in the cup. This means that there is more water pressure at the bottom of the cup, acting on the same area, so there is a greater force.

Written by Dave Ansell

Your Comments

We received this question

Hi Chris,

I just listened to the podcast about how putting a finger in a cup of water causes the scale to register a higher value. I've got two questions on this:
- instead of using a finger, what about if you suspended an object from a scale into the water. Would the two scales cancel out, ie. would the suspended scale register less and the ground scale register exactly more?
- If the liquid is pushing against the liquid, then does the value of the register increase as the surface area of the object is increased?

I didn't understand the explanation whereby increasing the water level increases the force. That would mean that two long skinny cup would weigh more than a short fat cup even though they have the same amount of water.

Really like your show!
Barry

- daveshorts - 11th Dec 09

The force on the bottom of the cup is the pressure times the area of the bottom of the cup.

If you halve the area of the cup, you will also double its depth and therefore the water pressure at the bottom. So the overall foce stays the same.

However if you put your finger in the cup, you will increase the depth without changing the area so the overall force will increase.

- daveshorts - 11th Dec 09

Here was my reasoning, before seeing the results: I will push down, or actually hold my finger up less, exactly the same amount as the buoyancy the water provides. Thus there will be the equivalent weight pushing down. Here is how I would test this - set up the same experiment, but use an inanimate object *placed on the floor* (or other surface). It would have to be an inverted U of some kind, or held in a clamp for example. I suspect that as it will *not* compensate for the up thrust from the water, there will be no increased down thrust (weight). The 'water is higher => more pressure => more weight' idea does not seem possible to me, or a taller container would have an effect, which obviously it would not (assuming an equal weight of the two containers).

- Jerome - 3rd Jan 10

Galileo came up against these forces when under house arrest on the instructions of the Vatican.
He was asked to advise as to why the form work for a bell casting had failed
.
It is a strange link between fluid pressure,force and gravity.
in the experiment where you put your finger in the liquid your finger actually weighs less by the same amount that the scales measuring the weight of the beaker increase. action/reaction

Another experient that you can do in your kitchen is get two seal-able lightweight plastic containers one slightly larger so the smaller one can fit inside the larger place the larger one on a set of scales and add a small amount of water in it then try putting the smaller container in and put on the lid.

You will notice the reading on the scales increase as you force the smaller container down in the water as also the level of the water rises in the large container due to displacement.
In fact the reading on the scale should exceed the total sum of the weight of the articles actually on the scales.

But when you place the seal-able lid on the larger container trapping in the smaller one and observe the reading on the scales you will find they only read the exact amount as the combined weight of the two containers and the water.

even though you had actually felt a greater force pushing up against you than the sum of the parts you also have to pair it with the increased reading on the scales.
It is a good example of newtons law, for every action there must be a equal and opposite reaction.
But that's not to say that just by putting on the lid these forces have disappeared,they are applying force to the containers at a pressure equal to the height of the fluid.

So height of the fluid metal in the bell casting was causing a pressure force greater than the weight of the metal, fortunately gallio was up to solving the dynamics of the forces involved and advised a revision of the design of the form work to counter these forces

ding dong

- gem - 4th Feb 10

You feel the upthrust because your finger is less dense than water. If your finger was made of iron, you would feel no upthrust. The extra weight shown on the scale is the weight of the water displaced by the part of the finger that is under water.q76pqv

- Al - 25th Apr 10

If your finger was made of iron, there would still be an upthrust. The way I visualise displacement is to think of the volume of water that is being displaced being 'lifted' at the top of the container. To lift the displaced fluid takes a force, and this is the bouyancy that is felt. That is why the bouyancy of a non-floating object is related to the volume, not the mass or weight.

- Ian - 15th Nov 11

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Listen to this as part of the show: 6th Sep 2009 - Can you run faster on the moon?
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