Fluids

[Sonyfan08]

A crown, apparently, made of gold is weighed in air, and the weight is 50 N. The crown is weighed again by hanging it from a string and submerging it in water. What reading will the meter give if the crown is true gold? (Au density = 19.3, water is 1.)

I understand how the problem is set up. write all of the forces acting on the crown, so that's: tension, weight, and bouyant force.

What i don't understand is the logic that they used to find the weight of the crown:

(density of Au - density of water)/(density of Au) *mg

Why is it in proportion to the density of gold?

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[plzNOCarribbean]

I agree with the forces.

when I set this up, I got:

ma= Wcrown - (Tension + Fb)

So, Wcrown= ma + (tension + Fb)

That where I got so far. Im not sure how you would solve for tension. Also, I think Fb is affected by how much of the crown is submerged. I think the entire crown is submerged, since P crown/P water = % of the volume submerged.

Not sure how to solve the rest though

 

[AlphaMagnum]

I agree with the forces.

when I set this up, I got:

ma= Wcrown - (Tension + Fb)

So, Wcrown= ma + (tension + Fb)

That where I got so far. Im not sure how you would solve for tension. Also, I think Fb is affected by how much of the crown is submerged. I think the entire crown is submerged, since P crown/P water = % of the volume submerged.

Not sure how to solve the rest though

Here's how I would go about it:

You know that the crown has three forces acting upon it: Buoyant Force and Tension upwards; Weight downwards.

Weight = mg = 50N

Now we can solve for mass, getting m = 5kg.

We know that Buoyant Force = (Density of fluid)(Volume of Object)*g

We also know both the mass of the crown and the density of gold, so if the crown is indeed pure gold then we can determine its volume:

Note: Given density in g/cm3, we need to convert to kg/m3, so we multiply by 1000.

Density = Mass/Volume, so...

V = Mass/Density = 5/19300 = 0.00026 cubic meters, roughly. (Done without calculator: round to 5/20000 and tack on a little extra.)

F(buoyant) = (Density of water)Vg = (1000)(0.00024)(10) = 2.6N.

Thus our Tension must be 50N - 2.6N = 47.4N.

Is that correct?

 

[Sonyfan08]

yes. The answer was 47 N. Thanks!

@plznocarribbean: i think the submerged formula applies only when the item is floating, not completely submerged.

 

[ModelOD]

For this example couldn't you just have done:

Ftension=mg-Fboyant
Ft=mg-(density of water * (mass of gold in ex./gold density)* gravity

Obviously, for the units to cancel one must multiple the gold density by 1000 to put into kg.

I got the write answer but don't know if this is a poor way of completing the problem.

It seems to me that you guys did a couple of unnecessary steps in this question, wouldn't you say?

Let me know what you guys think.

Thanks.

 

[Saint Fu]

For this example couldn't you just have done:

Ftension=mg-Fboyant
Ft=mg-(density of water * (mass of gold in ex./gold density)* gravity

Obviously, for the units to cancel one must multiple the gold density by 1000 to put into kg.

I got the write answer but don't know if this is a poor way of completing the problem.

It seems to me that you guys did a couple of unnecessary steps in this question, wouldn't you say?

Let me know what you guys think.

Thanks.

I think this should work. Also, if you work out the expression posted at the end of the original post,

(density of Au - density of water)/(density of Au) *mg

you will see that it works out to the same expression.

 

[ModelOD]

Definitely. But I just didn't understand why people were deciding to do that extra step and convert more than they had to...

 

[Saint Fu]

Definitely. But I just didn't understand why people were deciding to do that extra step and convert more than they had to...

Unless I'm missing something, I don't think there was any extra steps involved on their part. You just combined all of the mass/volume calculations into one concise expression. The other person spread them out, but ultimately they are the same types of calculations: find mass of gold, use mass and density of gold to find volume, use volume and density of water to calculate buoyancy force, subtract from original weight to get new measured weight.