A boat full with pieces of heavy rock is floating on the surface of water in a pool.?

Question

A boat full with pieces of heavy rock is floating on the surface of water in a pool. When the pieces are thrown into water, what would happen with the level of water in the pool? Give the arguments in support of your point of view.

Answer 1

The water level _drops_ when you throw the rocks into the water. Here's why:

In both cases, the total buoyant force acting on the boat and the rocks is exactly equal to the _weight_ of the displaced water. That's a fundamental principal of buoyancy. So in general: More buoyant force = greater weight of displaced water = greater volume of displaced water = higher water level.

So let's look at the total buoyant force in each case.

In the first case, the total buoyant force is equal to the weight W1 of the boat, plus the weight W2 of the rocks. We know this is true because the buoyant force is the only force holding the boat & rocks up against gravity. So buoyant force = W1 + W2.

But in the second case, the total buoyant force is _less_ than this. The forces acting on the boat are:

W1 (down) due to weight; and W1 (up) due to buoyancy.

The forces acting on the rocks at the bottom of the pool are:

W2 (down) due to weight:
Fn (up) due to the normal force from the bottom of the pool:
B2 (up) due to buoyancy.

Since the rocks aren't accelerating, it must be that:
W2 = B2 + Fn, or
B2 = W2 - Fn

So in the second case, the total buoyancy is W1 + W2 - Fn. This is _less_ than the total buoyancy in the first case, which was (W1 + W2).

Less buoyant force means lower water level, by above argument. So the water level goes _down_ when you throw the rocks in.

Interestingly, if instead of rocks, you threw in a bunch of _logs_ (or other floaty things) weighing W2, in that case, the water level would NOT drop. It only drops if the stuff you throw overboard is denser than water.

Answer 2

Here's the reasoning:
1. Heavy rock has a higher density than water.
2. So heavy rock weighs more than the same volume of water.
3. When the rock is in the boat, the rock makes the boat sit lower in the water. That forces the water level up higher as water is displaced by the boat.
4. When the rock is thrown out of the boat, the rock isn't weighing down the boat, so the boat should sit higher in the water and the water level would drop. The boat isn't displacing as much water.
5. At the same time, the rocks that were thrown into the water would raise the water level.
6. The question is: do the rocks sitting at the bottom of the pool displace as much water as the same rocks did when they were pressing down on the boat? Since the rocks are denser than water, the answer is no. The rocks displace less water on their own at the bottom of the pool than the same rocks caused to be displaced when they were in the boat -- displacing water by virtue of their weight.
7. That means that throwing the rocks out into the pool actually causes less water to be displaced. The water level would go down. And that's your answer.

Answer 3

I'm guessing the water will lower in the pool because the boat was displacing the rock ,its self and the air in the boat. gravity and air pressure are also pulling,pushing at the rock which also displaced some volume of air in the boat.- with the rocks in the water-- the rocks and boat still displace water but not as much air volume because gravity isn't pulling(air pressure pushing) on the rocks in the boat. i don't think its as much about the rocks being denser than water--you could use plastic bags of water and id bet you get the same results--think its more to do with the atmospheric pressure above the water and gravity.

Answer 4

Nothing will happen. The boat will displace less water, but the water level will not change because you have not taken the rock out of the water. You have only change it's location.
It still has the same and density as it did on board the boat.

Answer 5

The level falls down, because the volume of water displaced (when the rocks are floating) is more than when they are completely immersed inside water.


Let 1000 kg of rock be inside the boat and the area of the pond be A m^2

When the rocks are removed from the boat, the boat rises up and water of volume 1m^3
(Volume of water of mass 1000kg) fill the space created by the rising of boat.


The level of water in the pond FALLS by (1/A)m

And when the rocks are placed inside water,
The volume of water displaced = volume of rock = 0.4m^3
(Taking density of rock to be 2500 kg/m^3)

The level of water in the pond goes UP by (0.4 /A)m

The net FALL in level is (0.6 /A)m.