Halliday, Resnick & Walker — Fluids: Problem 61

61 In 1654 Otto von Guericke, inventor of the air pump, gave a demonstration before the noblemen of the Holy Roman Empire in which two teams of eight horses could not pull apart two evacuated brass hemispheres. (a) Assuming the hemispheres have (strong) thin walls, so that R in Fig. 14-44 may be considered both the inside and outside radius, show that the force F required to pull apart the hemispheres has magnitude \( F = \pi R^2 \Delta p \), where \( \Delta p \) is the difference between the pressures outside and inside the sphere. (b) Taking R as 40 cm, the inside pressure as 0.10 atm, and the outside pressure as 1.00 atm, find the force magnitude the teams of horses would have had to exert to pull apart the hemispheres. (c) Explain why one team of horses could have proved the point just as well if the hemispheres were attached to a sturdy wall.