Density, buoyancy, and volume in static fluids

In summary: I found the volume of the rock to be .001and I plugged in that value into the B.F equation for the unknown liquidthen I set that equal to the weight of the rock - the tension and found the density.
  • #1
Notion
10
0

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
 
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  • #2
"When the rock is totally immersed in water ..."
 
  • #3
Bystander said:
"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:

ρliquid * gravity * Vrock = 35.7

Still have 2 unknowns...
 
Last edited:
  • #4
Notion said:
ρliquid * gravity * Vrock = 35.7
Please explain how you obtain that equation from the relevant equations you posted.
 
  • #5
haruspex said:
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:

ρliquid * gravity * Vrock = 19.6
 
  • #6
Notion said:
Sorry I meant to put 19.6 instead of 35.7. So the equation should actually read:

ρliquid * gravity * Vrock = 19.6
No better. Draw a free body diagram of the rock suspended immersed in a fluid. What forces act on it?
 
  • #7
Rock in water/unknown fluid:
Tension & buoyancy pointing up, of force gravity pointing down.

∑forces : Tension + B.F = mg
 
  • #8
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
 
  • #9
Chestermiller said:
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?
 
  • #10
Notion said:
That would be 35.7-25.9=9.8?
Yes. Now apply that to the other liquid.
 
  • #11
Notion said:
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
 
  • #12
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!
 

Related to Density, buoyancy, and volume in static fluids

1. What is density?

Density is a measure of how much mass is contained in a given volume of a substance. It is calculated by dividing the mass of an object by its volume. The units of density are typically grams per cubic centimeter (g/cm3) for solids and liquids, and grams per liter (g/L) for gases.

2. How does density affect buoyancy?

Density is a key factor in determining an object's buoyancy in a fluid. If an object is less dense than the fluid it is placed in, it will float, as the upward force of buoyancy is greater than the downward force of gravity. If an object is more dense than the fluid, it will sink, as the downward force of gravity is greater than the upward force of buoyancy.

3. What is the relationship between volume and density?

Volume and density are inversely related - as the volume of an object increases, its density decreases, and vice versa. This means that if the mass of an object remains constant, but its volume increases, its density will decrease and it will become less dense.

4. How is density affected by temperature?

Density is also affected by temperature - as the temperature of a substance increases, its density typically decreases. This is because at higher temperatures, particles have more energy and move faster, creating more space between them and decreasing the density of the substance.

5. How is density measured?

Density can be measured using various tools and techniques, such as a balance scale to measure mass and a graduated cylinder to measure volume. The density can then be calculated using the formula density = mass/volume. There are also devices called densitometers that can directly measure the density of a substance.

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