# Buoyant Force Question

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1. Apr 16, 2017

### ztf24

1. The problem statement, all variables and given/known data -

What is the buoyant force that acts on a fully submerged 1-L bottle of water? What is the buoyant force that acts on it if it is full of air, not water, but is still fully submerged? Assume you'd have to hold it under water.

2. Relevant equations - Fb= V x D x G

3. The attempt at a solution -

I know the volume is 1L, and G is 9.8 M/S. I'm unsure with the density therefore I can't get an answer.

2. Apr 16, 2017

### Staff: Mentor

Welcome to the PF.

The density of fresh water is well known. What is the mass of each cc of water?

Assuming that the glass portion of the bottle is negligible, when it is filled with water and is underwater it's just like drawing a box around a piece of water -- that water does not go up or down, so what is the net force on it?

When the bottle is filled with air instead, how much does it weigh?

3. Apr 16, 2017

### ztf24

Densiry of Water is 1g/CM 3 and the liter of water weighs 1KG

4. Apr 16, 2017

### Staff: Mentor

Correct. So how can you use that and the concepts of Buoyancy to answer this set of questions?

https://en.wikipedia.org/wiki/Buoyancy

5. Apr 16, 2017

### ztf24

I guess I'm lost. I don't even know if need an equation for this problem. My guess is the buoyancy force is greater when the bottle is filled with water, and not air.

6. Apr 16, 2017

### Staff: Mentor

I suppose it depends a bit on how your textbook defines "buoyant force". There will always be a buoyant force, but in one case it is counteracted by the weight of the water in the bottle, and in the other case it is not (when the bottle if filled with air). In the first case the bottle has no Net force on it, but in the 2nd case, there is a strong Net force which direction?

EDIT -- fixed a bunch of typos in my post...

7. Apr 16, 2017

### ztf24

There's an upward net force on the bottle

8. Apr 16, 2017

### Staff: Mentor

Read what this link says about Archimedes' principle. That will tell you how to calculate the buoyant force.

9. Apr 17, 2017

### Staff: Mentor

BTW, I missed this before. The mass of 1L of water is 1kg. To get the weight in Newtons, you need to multiply the mass by the acceleration of gravity. Makes sense?