Density, buoyancy, and volume in static fluids

[Notion]

Homework Statement

A rock is suspended by a light string. When the rock is in air, the tension in the string is 35.7N . When the rock is totally immersed in water, the tension is 25.9N . When the rock is totally immersed in an unknown liquid, the tension is 19.6N .

Homework Equations

Density = m/v
buoyant force (b.f.)= density(of fluid) * gravity * Volume(of the part that is immersed in the fluid)

The Attempt at a Solution

Since we're given the tension (T) in the air, we can find the mass of the rock because T = mg in that case. Then after this I'm not sure where to go with it because since I don't know the volume of the rock I can't use the (b.f.) equation to help me at all. What am I missing?

Thanks

 

[Bystander]

"When the rock is totally immersed in water ..."

 

[Notion]

"When the rock is totally immersed in water ..."

I don't see how that helps me though. If I try using that info I come up with the equation:

ρ_liquid * gravity * V_rock = 35.7

Still have 2 unknowns...

 

[haruspex]

ρ_liquid * gravity * V_rock = 35.7

Please explain how you obtain that equation from the relevant equations you posted.

 

[Notion]

Please explain how you obtain that equation from the relevant equations you posted.

Sorry I meant to put 19.6 instead of 35.7. So the equation should actually read:

ρ_liquid * gravity * V_rock = 19.6

 

[haruspex]

Sorry I meant to put 19.6 instead of 35.7. So the equation should actually read:

ρ_liquid * gravity * V_rock = 19.6

No better. Draw a free body diagram of the rock suspended immersed in a fluid. What forces act on it?

 

[Notion]

Rock in water/unknown fluid:
Tension & buoyancy pointing up, of force gravity pointing down.

∑forces : Tension + B.F = mg

 

[Chestermiller]

If the rock weighs 35.7N, and, when it is immersed in water, the tension in the string is 25.9N, what is the upward force exerted on the rock by the surrounding water?

Chet

 

[Notion]

If the rock weighs 35.7N, and, when it is immersed in water, the tension in the string is 25.9N, what is the upward force exerted on the rock by the surrounding water?

Chet

That would be 35.7-25.9=9.8?

 

[haruspex]

That would be 35.7-25.9=9.8?

Yes. Now apply that to the other liquid.

 

[Chestermiller]

That would be 35.7-25.9=9.8?

From Archemides principle, what volume of water would have to be displaced to produce the 9.8 N upward force? How does that relate to the volume of the rock?

Chet

 

[Notion]

Ooh I get it!

I found the volume of the rock to be .001
and I plugged in that value into the B.F equation for the unknown liquid
then I set that equal to the weight of the rock - the tension and found the density.

Thank you very much!