Is the Bar of Gold Real? Using Buoyancy to Determine Density

[BrainMan]

Homework Statement

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?

Homework Equations

B = density* V* g

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. [/B]

 

[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.

 

[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

 

[BrainMan]

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.

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.

 

[haruspex]

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.

Right, but the density of what?

 

[BrainMan]

Right, but the density of what?

The density should be the density of the block right?

 

[haruspex]

The density should be the density of the block right?

What does Archimedes' principle state?

 

[BrainMan]

What does Archimedes' principle state?

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?

 

[haruspex]

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?

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

 

[BrainMan]

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

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

 

[haruspex]

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

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?

 

[BrainMan]

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?

The volume of the water displaced

 

[haruspex]

The volume of the water displaced

Right. And what will that also equal here?

 

[BrainMan]

Right. And what will that also equal here?

Would it equal the volume of the bar?

 

[haruspex]

Would it equal the volume of the bar?

Yes. You are told it is completely submerged.

 

[BrainMan]

Yes. You are told it is completely submerged.

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