# Buoyant forces problem

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1. Dec 24, 2014

### BrainMan

1. The problem statement, all variables and given/known data
A man decides to make some measurements on a bar of gold before buying it at a cut-rate price. He find that the bar weighs 2000 N in air and 1600 N when submerged in water. Is the bar gold?

2. Relevant equations
B = density* V* g

3. The attempt at a solution
I tried to use the equation B = density *V*g and use 400 N for the buoyant force to solve for the density and compare it to the density of gold. I wanted to use 400 N because that is the difference in the two weights and would be the force of the water pushing up. However, this problem doesn't give the volume so I am not sure how to solve this problem. The answer the book gives is 5.00 x 10^3 kg/m^3 as the density and says that it is clearly not gold.

2. Dec 24, 2014

### haruspex

What quantity did you calculate from the 400N using the equation? I don't just mean the number, I mean what does that number represent?
If you don't understand what I'm asking, state exactly what each of the terms in your equation stands for when you apply it to this question.

3. Dec 24, 2014

### Maged Saeed

Try to use two equation :
One is of the actual weight {give the mass in terms of the density times volume} equate it by the actual weight.
The other is of the buoyant force {give also the mass in term of the Density times volume} equate it by the difference.
And solve for your two unknown

4. Dec 24, 2014

### BrainMan

The equation means the buoyant force is equal to the density times the volume times the acceleration due to gravity. I used the 400 Newtons as the buoyant force because it is the difference in weights meaning the water has to be pushing up 400 N to decrease the weight of the block from 2000 N to 1600 N.

5. Dec 24, 2014

### haruspex

Right, but the density of what?

6. Dec 24, 2014

### BrainMan

The density should be the density of the block right?

7. Dec 24, 2014

### haruspex

What does Archimedes' principle state?

8. Dec 24, 2014

### BrainMan

OK so the density is actually the density of the fluid not the density of the block. So how do I find the density of the block using this equation?

9. Dec 24, 2014

### haruspex

One step at a time.
You know the density of water, so what do you calculate from the 400N?

10. Dec 24, 2014

### BrainMan

I'm not entirely sure. Is it the pressure?

11. Dec 24, 2014

### haruspex

No.
You are applying the equation B = density* V* g with B = 400N. You now understand that the density is that of water. What quantity does the equation then give you?

12. Dec 24, 2014

### BrainMan

The volume of the water displaced

13. Dec 24, 2014

### haruspex

Right. And what will that also equal here?

14. Dec 24, 2014

### BrainMan

Would it equal the volume of the bar?

15. Dec 24, 2014

### haruspex

Yes. You are told it is completely submerged.

16. Dec 24, 2014

### BrainMan

OK I figured it out. I just found the volume of the metal bar and divided the mass by the volume. Thanks a lot!