# Force to pull appart hemiphere under vacuum.

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## Homework Statement

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. 14-29

may be considered both the inside and outside radius, show that the force 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 30 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. BOB Answer is 26kN

(c) Explain why one team of horses could have proved the point just as well if the hemispheres were attached to a sturdy wall.

## The Attempt at a Solution

In part a i am not sure what it is asking me to do. My guess is is they are wanting me to state: There is no x or y component in the formula so the the formula provided is the magnitude. The cos(180deg) = -1, therefore the force on the left is equal and opposite to the force on the right.

Part b
$F = \pi 0.30m^2(101325pa - 10132.5pa) = 25774N$

Part c
As a result of Newton's third law, where there is an action their is an equal an opposite reaction, the sturdy wall provides a force equal to the team of horses in the opposite direction. Therefore, one team of horses pulling an object anchored to a sturdy wall is equal to two teams of horses pulling on the object in opposite directions.

In part a i am not sure what it is asking me to do. My guess is is they are wanting me to state: There is no x or y component in the formula so the the formula provided is the magnitude. The cos(180deg) = -1, therefore the force on the left is equal and opposite to the force on the right.
I don't see how that makes any progress towards deriving the required formula.
What is the net force on some small patch dA of one of the hemispheres? What direction does it act in?