# Hydrostatics question

1. Dec 20, 2008

### uspatange

Somewhere I happen to read that when some floating material is dropped in bucket full of water such that the water does not spill out, the weight of the total system increases.

Well, but i dont understand why this should happen. the body floats as the buoyant force of water balances its weight. due to which the weight appears to be zero and the body floats. why should the weight of the whole system change in spite of addition of a zero?
how to foretell the change in weight that is going to happen in such a case?

2. Dec 20, 2008

### Staff: Mentor

I guess the bucket really wasn't full then. As far as the weight increasing, don't you think it had better? You have a bucket of whatever sitting on a scale. You drop something into it, so wouldn't you think the scale reading should increase?

That's true. But the weight of the bucket + object increases. If the water pushes up on the object (the buoyant force), the object pushes down on the water with an equal force (Newton's 3rd law).

3. Dec 21, 2008

### uspatange

so you mean to say that the increase in weight is equal to the weight of the body dropped!
but doesnt the buyount force of the water affect it in any way?
So even if a non floating body is dropped in the water, the increase will still equal to the weight of the body?

4. Dec 21, 2008

### Staff: Mentor

Of course!
No. Imagine a totally different situation. You have a large block of wood sitting on the scale. You then place a smaller block on top of it. That small block is supported by an upward force from the large block. So, in a sense, it's floating on the large block, just like your dropped object was floating in the bucket of water. Of course the scale reads the total weight of both blocks.

Let's think of it in terms of forces acting on the large block. Before the small block is added, the forces acting on it are: its weight down and the normal force of the scale up. They add to zero, of course, so the scale just reads the weight of the large block. When you add the small block it exerts a second normal force on the large block equal to its weight. So now the forces acting on the large block are: normal force from small block, weight of large block, normal force from scale. Since everything is still in equilibrium, the scale now reads the total weight of both blocks.

Similarly with your object dropped into the bucket of water. The buoyant force is like the normal force between the two blocks. It adds to the force on the water, thus increasing the reading on the scale. (Another thing to realize is that the water level rises when you add the object, which increases the water pressure on the bottom of the pail. That's why I said that the bucket couldn't have been full if no water spilled out.)
Sure! In this case the buoyant force is not enough to support the object, so it just sinks to the bottom of the pail.