Question

In about 1657, Otto von Guericke, inventor of the air pump, evacuated a sphere made of two brass hemispheres (Fig. P14.58). Two teams of eight horses each could pull the hemispheres apart only on some trials and then “with greatest difficulty,” with the resulting sound likened to a cannon firing. Find the force F required to pull the thin-walled evacuated hemispheres apart in terms of R, the radius of the hemispheres; P, the pressure inside the hemispheres; and atmospheric pressure ${\mathit{P}}_{\mathbf{0}}$.

Short answer

The force F required to pull the thin-walled evacuated hemi spheres is $F=2.58\times {10}^4\text{N}$

Step-by-step solution

Given Data

Pressure $P=0.100Pa$

Radius $R=0.300m$

Concept

The pressure P in a fluid is the force per unit area exerted by the fluid on a surface:

$P=\frac{F}{A}$

In the SI system, pressure has units of Newton’s per square meter $(N/m^2)$, and $1N/m^2=1Pascal\left(Pa\right)$.

The pressure at the surface of two hemi sphere is constant at all points and the force on each element of surface area is directed along the radius of the hemi sphere.

$P=(P_0-P)A$

Find the force F

By using concept and the formula, we get

The pressure at the surface of two hemi sphere is constant at all points and the force on each element of surface area is directed along the radius of the hemi sphere.

$$\begin{gathered} F=\left(P_0-P\right)A\left(\because A=\pi R^2\right) \\ F=\left(P_0-P\right)\pi R^2 \\ F=\left(P_0-0.100P_0\right)\times 3.14\times {\left(0.3\right)}^2 \\ F=0.254P_0 \\ F=0.254\times 101325\text{N} \\ F=2.58\times {10}^4\text{N} \end{gathered}$$

Hence, the force F required to pull the thin-walled evacuated hemi spheres is $F=2.58\times {10}^4\text{N}$