In 1656, the Burgmeister (mayor) of the town of Magdeburg, Germany, Otto Von Gue
ID: 2089576 • 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 0.430 m (1.41 feet) with a rubber seal in between are placed together and air pumped out so that the pressure inside is 11.00 millibar. The atmospheric pressure outside is 970 millibar. Calculate the force required to pull the two hemispheres apart.Two equal teams of horses, are attached to the hemispheres to pull it apart. If each horse can pull with a force of 1420N (i.e., about 319 lbs), what is the minimum number of horses required?
Explanation / Answer
Net pressure on sphere = 970 - 11 = 959 mb 1mb = 100 Pascal So pressure P = 9.59 * 10E4 Pascal = 9.59 * 10E4 N/m^2 F = P * A = 9.59 * 10E4 * pi * .43^2 = 5.57 * 10E4 N 5.57 * 10E4 / 1420 = 39.2 teams of horses required So you would need 2 teams of 40 horses = 80 horses Note that net force on the hemisphere is the same as that which would be exerted on the flat surface of an enclosed hemisphere - if it weren't the such an enclosed hemisphere would experience a net force in air. Check: atmospheric air pressure is about 15 lbs/ft^2 P = 15 * pi * 1.41^2 * 144 (using 144 sq in / sq ft) P = 1.35 * 10E4 lbs 1.35 * 10E4 / 319 = 42.2 (atmospheric pressure is somewhat less than 15 lb/in^2)