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Buyoancy

The chapter on buoyancy answers a few very important questions on floating and sinking:

  1. When does and object float or sink?
  2. What causes objects to float?
  3. What causes the buoyant force?
  4. What does Archimedes have to do with all of this?

Most of you know that to figure out which objects float or sink you need to know the density of these objects. This is, however, not obvious.  When children first ask about why objects float we are tempted to say that light objects float and heavy objects sink. Can you think of a demo that proofs that this is not true?

How about a small rock and big rock? They both sink. Or how about a small rock and a big, very big, piece of wood. The heavy object floats and the light object sinks. It is easy to see that it is not the mass that determines whether an object floats. But how would you explain this to a six-year old? You need to have a really good understanding as to what density is to be able to do this.

In the tutorial we figured out that objects that have a density that is bigger than the density of the liquid sinks and f they have a density that is smaller they float. This is the first key concept and answers the first question.

In the second tutorial we looked into what happens to floating and sinking objects. From the definition of volume we already know that we can find the volume by submerging an object in water (but it does not have to be water, any liquid will do). Therefore objects that sink will always displace their volume.  Objects that float will not. Look at the cylinder in the picture. Some of it is outside the water and therefore cannot displace any water. In class you figured out that objects that float displace their weight (or mass). We did this three different ways: first you calculated how much water gets displaced by a floating piece of wood and then compared that to the mass of the wood. You found that the mass of the wood is equal to the mass of the water that gets displaced. The second experiment involved the graduated cylinder filed to the brim with water. You measured the mass of the cylinder before and after the wood was placed in it and found them to be the same. Some time later we did a third experiment. From these experiments is was evident that floating objects displace their weight (or mass). This is the first step to answering the second question.

If you look at a free-body diagram of a floating boat it will be clear that the weight force will have to be cancelled out by an upward force by the water. This is because of Newton’s Second Law. The upward force has to be bigger the bigger the floating object is. Consider a tanker being filled with oil. It will always float, empty or filled, but it will float differently. When it is filled it will float lower in the water, displacing more water.

Floating objects displace their weight and if their weight increases they need to displace ore water. Boats can only do this by sinking lower into the water. Therefore the more water gets a floating ship displaces the more the water can push up. This upward push force by the water has a special name. It is called the buoyant force. The buoyant force therefore depends on how much water gets displaced. That leads to the seemingly paradox situation in which a big heavy object that sinks has a greater buoyant force then the same size floating object. The sinking object displaces more water and therefore has to have a greater buoyant force.

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To sum up: the weight force of a floating object is equal to the upward buoyant force (Newton’s Second Law) – Wobject = Fbuoy  .  We now also know that the buoyant force is equal to the weight of the water that gets displaced - Fbuoy = Wwater displ  . The latter statement is also called Archimedes’ Principle.

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Putting this all together we get:

Wobject = Fbuoy = Wwater displ

The first half of the equation is only true for floating objects while the second half is always true, for both sinking and floating objects.

At this point you will need to go over all the key concepts, because these are used to solve all of the problems we will encounter in class and on the test. There are a lot of problems in the workbook and you should be able to do all of them by just applying the key concepts.

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