In 1656, the Burgmeister (mayor) of the town of Magdeburg, Germany, Otto Von Gue

Question

In 1656, the Burgmeister (mayor) of the town of Magdeburg, Germany, Otto Von Guericke, carried out a dramatic demonstration of the effect resulting from evacuating air from a container. It is the basis for this problem. Two steel hemispheres of radius 0.430 m (1.41 feet) with a rubber seal in between are placed together and air pumped out so that the pressure inside is 18.00 millibar. The atmospheric pressure outside is 960 millibar. Calculate the force required to pull the two hemispheres apart.

Explanation / Answer

The pressure differential acts on the hemisphere to create a normal force all over the surface, but we are only interested in the component that acts horizontally, since the vertical components all cancel. That can be calculated by treating the hermispheres as flat circular plates with the same radius as the hemisphere pressed together. So force = pressure times area = (960 - 18 mB)(p * (0.43 m)^2) = 54717.3 N on each side.

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