In 1656, the Burgmeister (mayor) of the town of Magdeburg, Germany, Otto Von Gue
ID: 2031745 • 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 0.400 m (1.31 feet) with a rubber seal in between are placed together and air pumped out so that the pressure inside is 12.00 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 ]
answer: 4.815×104 N
Two equal teams of horses, are attached to the hemispheres to pull it apart. If each horse can pull with a force of 1450N (i.e., about 326 lbs), what is the minimum number of horses required?
The answer is not 33, or 34, 66, or 67
Explanation / Answer
radius, r = 0.4 m
area of hemisphere, A = (Pi) * r2 = 3.14*0.42 = 0.5024 m2
outside pressure = 960 millibar
inside pressure = 12 millibar
pressure difference ,P = 960 -12 = 948 millibar = 948*100 = 94800 N/m2
Force requried , F= P.A = 94800 * 0.5024 = 47627.52 N
force of each horse = 1450 N
total No of horses = 47627.52 / 1450 = 33
No of horses in each side = 33/2 = 16.5 = 17