In about 1657 Otto von Guericke, inventor of the air pump,...

In about 1657 Otto von Guericke, inventor of the air pump, evacuated a sphere made of two brass hemispheres. 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 (Fig. P15.58). (a) Show that the force $F$ required to pull the evacuated hemispheres apart is $\pi R^{2}\left(P_{0}-P\right)$, where $R$ is the radius of the hemispheres and $P$ is the pressure inside the hemispheres, which is much less than $P_{0}$. (b) Determine the force if $P=0.100 P_{0}$ and $R=0.300 \mathrm{~m} .$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Pressure Difference

The pressure difference is the driving force behind the force required to separate the hemispheres. It is defined as the difference between the external atmospheric pressure and the internal pressure of the evacuated hemisphere. This difference determines how much net force is exerted on the surface of the hemisphere since force is the product of pressure and area.

Projected Area

When calculating the force due to pressure, it is crucial to consider the area over which the pressure difference acts. For a sphere split into two hemispheres, the effective area is not the curved surface area but the projection of the sphere in the direction of the force. This projected area is a circle with radius R, and its area is given by ?R².

Integration Over a Curved Surface

To derive the net force acting to hold the hemispheres together, one must account for the fact that the pressure acts normally to every point on the curved surface, but only a component of this force contributes to the separation. By integrating the pressure contributions over the curved surface and considering the appropriate geometric components, one arrives at the expression for the net force, which simplifies to the pressure difference multiplied by the projected area.

Transcript

Please give Ace some feedback