Buoyant Force and air molecules

In summary, the textbook is sitting on a table with a large downward force, while the table has an average distance of .006 mm between the uneven surfaces. There is no net upward force on the book, so it would be rising if there were more air between the book and the table.
  • #1
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Homework Statement


It is hard to imagine that there can be enough air between a book and a table so that there is a net upward (buoyant) force on the book despite the large downward force on the top of the book. About how many air molecules are there between a textbook and a table, if there is an average distance of about 0.006 mm between the uneven surfaces of the book and table?

Additionally, assume the book's area (width x height) to be 138 in^2 (converted suitably to SI units).

Given from previous problems, density of air is 1.3 kg per m^3

Homework Equations



Fbuoy = pVg
where Fbuoy is the buoyant force
p is the density
V is the volume
and g is gravity

The Attempt at a Solution


Converted 138 in^2 to appropriate SI units. Came out to 0.08903208 m^2.
V = (.006*10^-3 m) * (0.08903208 m^2) = 5.3419248*10-7 m^3

Then...
Fbuoy = (1.3 kg/m^3)*(5.3419248*10-7 m^3)*(9.8 m/s^2) = 6.805612195*10-6 N

I'm not sure if I did that right and if I did, I don't have an equation to convert N to number of air molecules.
I'm pretty sure I need Avogadro's number but I don't see how it ties into converting.
 
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  • #2
jtestuer: There is no net upward force on the book; otherwise, the book would be rising. The first sentence in post 1 appears to be a diversion. The problem doesn't ask for buoyancy force; it asks you to compute the number of air molecules. Assume air is an ideal gas. Look for the equation of state for an ideal gas, sometimes called the ideal gas law. Hint: It is a very popular formula, which some people know from memory. Solve it for number of kilogram-moles (kg*mol), n. Hint: Assume standard atmospheric pressure, p = 101 325 Pa. Assume a typical room temperature, in kelvin (K). R = universal gas constant = 8314.472 J/(kg*mol*K). Hint: Multiply n by Na = Avogadro constant = 6.022 141 79e26 molecules/(kg*mol).

By the way, the air density given in post 1 is essentially wrong; perhaps another diversion. For typical indoor temperatures, at standard atmospheric pressure, air density is close to 1.18 or 1.19 kg/m^3, not 1.3.
 
  • #3
Thanks. That helped (even though the assignment was due a couple days ago :P ).

I'll keep this in mind while studying for midterms. :D
 

1. What is buoyant force?

Buoyant force is the upward force exerted on an object immersed in a fluid (liquid or gas) due to the difference in pressure between the top and bottom of the object.

2. How is buoyant force related to air molecules?

Buoyant force is related to air molecules because air is considered a fluid and therefore exerts pressure on objects immersed in it. This pressure is what creates the buoyant force.

3. How do air molecules affect the buoyant force on an object?

The number and density of air molecules in the fluid will affect the buoyant force on an object. The more air molecules, the greater the pressure and therefore the greater the buoyant force.

4. Can buoyant force on an object change with different air molecule densities?

Yes, the buoyant force on an object can change with different air molecule densities. As mentioned before, the greater the density of air molecules, the greater the pressure and therefore the greater the buoyant force.

5. How can buoyant force be calculated with air molecules?

Buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid that the object displaces. This calculation takes into account the density of the fluid, which is affected by the density of air molecules, and the volume of the object.

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