Calculating Volume Using Buoyancy

In summary, the conversation discusses how to find the volume of a wooden sphere using only weight measurements. The suggested method is to find the amount of volume displaced by the wooden and metal spheres in water and subtract it by the volume of just the metal sphere in water. However, the correct equations to use are m1*9.8 + m2*9.8 - (v1 + v2)1000*9.8 = 0.550N and m1*9.8 + m2*9.8 - v2*1000*9.8 = 0.650N. These can be used to solve for the volume of the wooden sphere, but the mass of the wooden sphere cannot be determined
  • #1
BayernBlues
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Homework Statement



http://img524.imageshack.us/img524/1743/buobu1.png

Homework Equations



Vsphere= pi/6(d^3)
W = mg

The Attempt at a Solution



Wc + Wo' = 0.650 N
Wc' + Wo' = 0.550 N

I'm unsure of how to do this because it asks to find the volume ONLY BY USING THE two weight measurements. The simpler way to do it would be to measure how much fluid is displaced but that's not allowed apparently so I'm stuck.
 
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  • #2
So the volume and mass of the metal sphere are unknown?
 
  • #3
I'm supposed to find the volume of the wooden sphere using only the measurements for Wc'+Wo' and Wc+Wo'. I think that what I have to do is find the amount of volume displaced by the wooden and metal spheres in water and subtract it by the volume of just the metal sphere in water.

I'm guessing to find the volume for the metal sphere, I'd need to see the apparent weight of the metal sphere in water (it's 0.650N), find the mass from that (m=W/g), use 1g/cm^3 for the density of water, and find the volume by V=m/D.

Then I'd do the same for the other one and subtract the two volumes.

But the thing is, I'm not sure about what weight value to use for finding the volume of just the metal sphere in Wc+Wo' because this would involve the weight of the cork sphere in the air plus the metal sphere in water and I just want the weight of the metal sphere in water.
 
  • #4
Here's what I've done so far, I know it's wrong because the volume of the cork should be more than the volume of the metal sphere:

In order to find the volume of the cork, the volume of fluid displaced by the metal sphere in water must be found. This amount can be found by using Wc + Wo’.

Wc’ + Wo’ = (0.650 ± 0.010 N)/9.81 m/s² = 0.0662 kg = 66.26 ± 0.10 g
pwater = 1 g/cm³
The volume of the metal sphere will equal the amount of water displaced which is equivalent to mass of water displaced divided by the density of water:
Vcork+sphere = 66.26 g/1g/cm³ = 66.26 ± 0.10 cm³

A similar procedure must be used to find the volume of water displaced by the cork and the metal sphere:

Wc + Wo’ = (0.550 ± 0.010 N)/9.81 m/s² = 0.056 kg = 56.07 ± 0.10 g
pwater = 1 g/cm³
The volume of the metal sphere will equal the amount of water displaced which is equivalent to mass of water displaced divided by the density of water:
Vsphere = 56.07 g/1g/cm³ = 56.07 ± 0.10 cm³

To find the volume of the cork, the value for Vsphere must be subtracted from Vcork+sphere.

Vcork = 66.26 ± 0.10 cm³ - 56.07 ± 0.10 cm³ = 10.19 ± 0.10 cm³
 
  • #5
BayernBlues said:
Here's what I've done so far, I know it's wrong because the volume of the cork should be more than the volume of the metal sphere:

In order to find the volume of the cork, the volume of fluid displaced by the metal sphere in water must be found. This amount can be found by using Wc + Wo’.

Wc’ + Wo’ = (0.650 ± 0.010 N)/9.81 m/s² = 0.0662 kg = 66.26 ± 0.10 g
pwater = 1 g/cm³

yeah, don't think that's right. That measurement isn't the weight of the displaced water...

I believe the equations should be:

m1*9.8 + m2*9.8 - (v1 + v2)1000*9.8 = 0.550N

m1*9.8 + m2*9.8 - v2*1000*9.8 = 0.650N

where m1 is the mass of the cork, and m2 is the mass of the metal sphere. v1 is the volume of the cork... v2 is the volume of the metal sphere...

you can solve for v1 here using these two equations... but I don't see how to get m1...
 
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FAQ: Calculating Volume Using Buoyancy

What is buoyancy and how does it relate to calculating volume?

Buoyancy is the upward force that a fluid exerts on an object that is submerged in it. This force is equal to the weight of the fluid that the object displaces. In order to calculate the volume of an object, we can use the buoyant force and the density of the fluid.

What is the formula for calculating volume using buoyancy?

The formula for calculating volume using buoyancy is V = Fb/ρg, where V is volume, Fb is the buoyant force, ρ is the density of the fluid, and g is the acceleration due to gravity.

How do you determine the buoyant force of an object?

The buoyant force of an object can be determined by multiplying the density of the fluid by the volume of the object that is submerged in the fluid and the acceleration due to gravity. This can be represented by the equation Fb = ρVg.

What is the relationship between the volume of an object and its buoyant force?

The volume of an object and its buoyant force have a direct relationship. This means that as the volume of an object increases, its buoyant force also increases. This is because a larger volume of fluid is displaced by a larger object, resulting in a greater buoyant force.

What are the units of measurement for volume and buoyant force?

The units of measurement for volume are typically cubic meters (m3) or cubic centimeters (cm3), while the units for buoyant force are newtons (N). However, other units of measurement may be used depending on the specific calculation and the units of density and acceleration due to gravity used.

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