# Confused with the Archimedes' Principle

1. Apr 4, 2012

### Natko

Archimedes' Principle states: "Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object."

If this is true, why then, when you take a bowling ball and submerge it in water, and take a rubber ball of the same size and submerge it in water, the bowling sinks and the rubber ball floats if they are the same size and thus displace the same volume of water?

Can anyone explain? (I'm a grade 8 student so be simple, please).

2. Apr 4, 2012

### HallsofIvy

Staff Emeritus
For exactly the reason you state. A bowling ball has density greater than that of water. Even if it is completely immersed, "force equal to the weight of the fluid displaced by the object" is less than the weight of the bowling ball so it keeps descending. The rubber ball has density less than that of water so in order that the force be equal to its weight, it only has to displace a volume of water less than its own- It only sinks part way into the water.

3. Apr 4, 2012

### Natko

Shouldn't it be the opposite way around? Since the rubber ball is displacing less water but is buoyed more, and the bowling ball is displacing more water but has no buoyant force acting upon it.

Also, the two balls start off submerged in the water, so they displace the same volume of water.

4. Apr 4, 2012

### davenn

its NOT just about volume displacement of the object but also of the density of the object

in your case the 2 same sized balls but VERY different densities

Dave

5. Apr 4, 2012

### DrewD

Let me expand what HallsofIvy said. Perhaps more details will help.
First just consider when two balls are fully submerged. Don't worry about them moving, just take a snapshot in time. Since they are fully submerged and have the same volume, both have the same force pushing them up which is equal to the weight of the fluid displaced. But, the bowling ball has a larger force pulling it down so it will sink. It does have a buoyant force acting on it too, but the force of gravity on it is greater.

The rubber ball is the opposite (assuming it is less dense than the water). The weight of the water displaced is greater than the weight of the ball, so the quasi-equation

$\uparrow$Weight of water + $\downarrow$Weight of ball

is more up than down. So the total force will be up.

If that makes sense, then we can consider the point when the ball is floating on the surface. If that doesn't make sense yet, think about it for a bit (and ask questions) before worrying too much about the second part.

Now remember that force makes things change their velocity. So if the ball is floating on the surface, that means the total force must be zero. Lets work back from there. We know that the weight of water taking up the total volume of the ball is more than the weight of the ball, but we expect that

$\uparrow$Weight of water + $\downarrow$Weight of ball

should equal zero in this case. That is (weight of water) = (weight of ball). For this to be true, the ball would have to be displacing a volume of water that is less than the volume of the total ball... which is exactly what happens when the ball is floating. It only displaces a volume of water that is equal to the submerged part of the ball.

6. Apr 5, 2012

### davenn

hey Drew

Thanks for putting into words what I knew and understood, but couldnt verbalise to be able to explain to Natko

appreciated :)
Dave

7. Apr 6, 2012

### Natko

1. The gravitational force on the bowling ball is greater than the buoyant force and the gravitational force on the rubber ball is less than the buoyant force. Gravity and Buoyant Force work together to conclude whether an object sinks/floats (buoyancy). So the bowling ball has more buoyant force than the rubber ball, yet it still sinks because the gravity is greater.

2. If the volume of the ball is greater than the volume of the water displaced, it sinks, and if the volume of the ball is less than the volume of the water displaced, it floats.

3. The partial mass and partial volume of the rubber ball floating on the surface and the volume of water displaced is equal.

Is buoyant force and buoyancy the same thing?

Last edited: Apr 6, 2012
8. Apr 8, 2012

### dragoljub

mg-gravitational force
ρfVg -Buoyancy = weight of displaced fluid
Fnet=mg-ρfVg
if mg>ρfVg (or ρof) -object falls
if mg<ρfVg (or ρof) -object floats

9. Apr 8, 2012

### DrewD

If they are both fully submerged (and the same volume), the buoyant force is the same, but the second part is correct.

This is not correct. I'm not sure where your confusing is coming in. If the ball is fully submerged, both volumes are the same. Did you mean mass of the ball is greater than the mass of the water displaced?

The mass of the rubber ball is equal to the mass of the water displaced when it is floating.