In 1656, the Burgmeister (mayor) of the town of Magdeburg, Germany, Otto Von Gue
ID: 2027052 • Letter: I
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 0.450 m (1.48 feet) with a rubber seal in between are placed together and air pumped out so that the pressure inside is 15.00 millibar. The atmospheric pressure outside is 970 millibar. Calculate the force required to pull the two hemispheres apart.
[Note: 1 millibar=100 N/m2. One atmosphere is 1013 millibar = 1.013×105 N/m2 ]
Two equal teams of horses, are attached to the hemispheres to pull it apart. If each horse can pull with a force of 1390N (i.e., about 312 lbs), what is the minimum number of horses required?
Please show all work and answer in sig-figures
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 = (970 - 15 mB)( * (0.45 m)2) = 60754 N on each side.
So each side needs a minimum of 44 horses [44 * 1390 = 61160 N]