How do you find density when given the buoyant force

[BryanC]

Hey

This has stumped me and 2 other people who have also tried to solve this problem. My instructor was about to explain it but just left us with we can get it through the equation of Buoyant force Bf=pgv. Here is the actual question from my book.

An object has a weight of 8.0N in air. However, it apparently weighs only 4.0N when it is completely submerged in water. What is the density of the object?

I have no idea how your supposed to figure this out, my and my friend have been trying to figure this out for over an hour now and we don't know where to start with it, since all your apparently given is the Buoyant force which comes out to be 4N and that leaves you with two unknowns, p and v.

If anyone can help me that would be great because I've got a test coming up on Monday and something this confusing is sure to be on it.

Thanks in Advance
Bryan

 

[franznietzsche]

1) The buoyant force of water is equal to the weight of the water displaced by an object.

You know the density of water, and you know the force that the water is exerting. From there you can get volume.

 

[BryanC]

Thats what I thought, I had solved it using 4N / (1.0x10^3)(9.8m/s)=V but when I got V and plugged it back into the equation I just got 995, because i rounded V...so bascilly i just got the density of water again...so where did i go wrong because that's not the answer is it?

 

[franznietzsche]

$$\vec{F} = mg$$

$$\qquad = \rho V g$$

$$V = \vec{F} \times \frac{1}{g} \times \frac{1}{\rho}$$

The way you have it written is:

$$V = \vec{F} \times g \times \frac{1}{\rho}$$

and I suspect that's how you put it into the calculator.

 

[BryanC]

Isnt that the same exact thing as I wrote though, that is that volume is equal to the force times the inverse density times the inverse gravity is the same as, Volume is equal to force divided by the product of density and gravity. Could you explain more because I don't get what your sayin...cuz I used that already (provided they are the same) and just got the density of water again.

 

[franznietzsche]

Isnt that the same exact thing as I wrote though, that is that volume is equal to the force times the inverse density times the inverse gravity is the same as, Volume is equal to force divided by the product of density and gravity. Could you explain more because I don't get what your sayin...cuz I used that already (provided they are the same) and just got the density of water again.

The density in the bouyancy force equation is the density of water, so of course you'll get that back out (sorry, I misunderstood what you meant by that).
Once you have the volume, you have the weight out of water. Those two will give you the density of the object.