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 0.370 m (1.21 feet) with a rubber seal in between are placed together and air pumped out so that the pressure inside is 19.00 millibar. The atmospheric pressure outside is 960 millibar.

[Note: 1 millibar=100 N/m2. One atmosphere is 1013 millibar = 1.013×105 N/m2 ]

(b) Two equal teams of horses, are attached to the hemispheres to pull it apart. If each horse can pull with a force of 1360N (i.e., about 306 lbs), what is the minimum number of horses required?

Explanation / Answer

inside pressure is Pi =19 millibar                               =19 *100 N/m^2 atmospheric pressure is Pa =960 millibar                                          =960*100 N/m^2 radius of each hemisphere is r =0.37m (a) force required to pull the two hemispheres apart is F = pressure difference *circular are of                                                                                     each hemisphere                                                                               =(960-19)*100 *(r^2)                                                                                 =941*100*3.14*(0.37)^2                                                                                 =40450.3906 N ________________________________________________________________________ (b) the pulling force of one horse is f =1360 N the pulling force of each team is F =40450.3906 N let number of required horses for one team are 'n' F =nf n =F/f =40450.3906/1360 =29.7 the required horses for one team is n =30 for both side teams the required number of horses are 60

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