# Homework Help: Working with archimedes principle.

1. Dec 25, 2011

### vkash

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

Consider a submarine inside an ocean. It's bottom is flat and upper portion is hemispherical. It is settled at the bottom of the sea. What should direction of Boyant force. Upward or downward? Now by the external agent the submarine is lifted a bit up. Now it is not touching the surface of the sea. What will be direction of boyant force in this case.

2. Relevant equations

upthrust is equal to weight of liquid displaced.
Mainly it is dF=P.dA.

3. The attempt at a solution

I think the direction of boyant force(boyant doesn't seems to be correct word) in first case is in downward and in second case it is upward direction.
Am i correct????????????????????

Last edited: Dec 25, 2011
2. Dec 26, 2011

### JHamm

3. Dec 26, 2011

### vkash

Oh yes i have reasons
In short it is ∫P.dA.
In first case pressure is applied from above the submarine. Since force is perpendicular to surface so should sum up to give net force in downward direction.
In second case it's too long to explain. IT is similar in case when a body is fully inside liquid.

I post this question because it related to a question in my book that is something like this.
There are two immersible liquid of relative density 1.5 and 2.5. There is an object of relative density 2 What is percentage volume inside the liquid of relative density 1.5 & 2.5.

4. Dec 26, 2011

### JHamm

You're correct but I don't see how that problem helps you with your book's question?

5. Dec 26, 2011