My brother lives in Scotland. He recently visited an impressive piece of engineering called the Falkirk Wheel, which is basically an elevator for boats. The wheel connects two canals, one of which is thirty metres higher than the other. It has two huge water-filled troughs, one at the level of each canal. The troughs are opened at one end, so boats can drive in. Then the ends are sealed off and the entire thing rotates, so the bottom trough ends up at the top and vice versa. Then the boats just drive off again.
One of the clever things about the Falkirk wheel is that even if boats of different weight go into the troughs, it stays perfectly balanced. This week we will look at why this happens.
You will need
Two identical plastic cups
Two objects, one heavy and one light, which both float and both fit into the cups.
I used a couple of film containers, with several coins in one of them.
You do not need to use containers the same size or shape.
Water
A set of kitchen scales. They need to be sensitive enough to detect the difference in weight between your two objects.
Ruler
What to do
Place an object into each cup.
Pour water into the cups, so that the water level is the same in both cups.
Make sure it is deep enough for both objects to float in the cups.
You can use the ruler to help make the water levels equal.
Try to predict which cup will have the greatest weight: the cup with the light object in it or the cup with the heavy object in it.
Measure the weight of each cup, with the water and floating object in them. What do you notice about their weight?
Take the objects out and compare the water level in each cup.
What's happening
A lot of people are surprised by this one. If you are reading ahead and haven't tried it yet, go back and try before you look at the answer.
Have you done it? If so, you should have found that the two cups and their contents had almost exactly the same weight. In fact, any difference was either because the plastic cup had a slightly different weight, or the level of the water in the two cups wasn't exactly the same.
If you remove the floating objects from the water and compare the water level, you should find that the cup that held the heavy object had less water in it. They weighed the same when you put them on the scales because the difference in the weight of the objects is cancelled out by the difference in the weight of the water.
So why does it exactly cancel out? When you place something into a liquid, it displaces some of the liquid, or pushes it out of the way. This is why when you climb into a bath, the level of the water goes up. An object will float when the weight of the water it displaces is equal to the weight of the object. If you have a 100 g object that floats, it will displace exactly 100g of water.
Since a heavier object displaces more water, you don't need to pour as much water into the cup to bring it up to a certain water level. For example: Imagine you had cups that weighed 50g and two objects that floated weighing 100g and 10g. If you put the 100g object in one cup and added 150g of water, the object would displace 100g of water, so the water level would be as if you had poured 250g of water into an empty cup. If put the 10g object into the other cup, it will only displace 10g of water, so you would need to pour in 240g of water to have the same depth as the first cup. Now the total weight of one cup would be 50g(cup)+100g(heavy object)+150g(water)=300g, the weight of the other cup would be 50g(cup)+10g(light object)+240g(water)=300g.
To keep the Falkirk Wheel balanced, the engineers need to ensure the weight of the water and boats in the two troughs is equal. As we have seen today, all they need to do is make sure the water level in each trough is the same, then the weight will automatically match.
