Pulling the Magdeburg hemispheres apart turned out to be much harder than anyone

Question

Pulling the Magdeburg hemispheres apart turned out to be much harder than anyone thought. Let's make some estimates to see what we can learn. In case you missed the demo, this is two iron hemispheres with a gasket on their open sided and a rope on their closed side. When the two hemispheres are put together and the air inside pumped out, they are extremely difficult to pull apart. Let's see what this tells us.

A. The original hemispheres (in 1656) were about the size of a basketball. Calculating the force of the air on a sphere is a little tricky because some forces cancel. What a vector calculus calculation shows is the result for the sphere is ½ the result for the cylinder of the same radius R, and a height equal to the sphere's diameter. If all the air has been pulled out of the cylinder, estimate the force that would be needed by the people pulling on the rope on each side to separate the two halves.

____ N

Explain your reasoning.

B. From the mass density of the air and the average molecular weight of its components, we can estimate the number density of molecules in the air. From the pressure that the air exerts, estimate the average speed of a molecule in the air. (We actually know a lot about the air. We know that it is mostly nitrogen and oxygen—an average molecular weight of about 30 Daltons.)

_____ m/s

Explain your reasoning.

Explanation / Answer

To open the ballon, the applied force should overcome the force due to atmosphere

so

F = Po A

Po = atmospheric pressure

A = cross sectional area of sphere.

A = pi R2

=> F = Po (pi)R2

B)

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