Otto von Guericke's Magdeburg Hemisphere Experiment
The Magdeburg Hemispheres is a classic physics experiment that demonstrates the incredible pressure the atmosphere around us exerts on our bodies and everything else.
The apparatus of the experiment consist of two brass hemispheres that fit together to form an air-tight seal. One hemisphere has a tube that can be attached to a vacuum pump and a stop cock to seal it off. When the air is sucked out from inside the hemispheres, and the valve is closed, the two halves are held firmly together by the air pressure of the surrounding atmosphere. It is nearly impossible to pull the hemispheres apart by any number of hands. Once the air is let back in, the halves fall apart easily. This simple demonstration of the pressure of the atmosphere was first made by German scientist Otto von Guericke in 1654. When the rims were sealed with grease and the air was pumped out, the sphere could not be pulled apart by teams of horses.
Otto von Guericke was born to a patrician family of Magdeburg in 1602. He was privately tutored until the age of fifteen, after which he began studying law and philosophy at the Leipzig University. Thereafter he studied at the Academia Julia in Helmstedt and the universities of Jena and Leiden. It was at Leiden that he first attended courses on mathematics, physics and Military engineering. In 1631, Guericke was appointed as a construction engineer to help rebuild Magdeburg after it was severely damaged during the Thirty Years’ War. In 1646, he was elected as Magdeburg's Burgomeister, the city's chief magistrate or executive, an office that arguably bestowed more power than that of a mayor. He held this position until his retirement in 1678. During four decades in office he undertook numerous diplomatic missions, which took him to many European courts and councils, where he met powerful executives and secretaries and addressed the illustrious elite of dukes, kings and emperors.
Otto von Guericke
Despite his public responsibilities, Von Guericke still found time to pursue his scientific interests, one of which was vacuum. By the time of Von Guericke, water pumps were based on suction but these pumps could only pull water up to a certain height. By experimentation, it was determined that this height was approximately 34 feet. This limit was a concern in irrigation projects, mine drainage, and decorative water fountains planned by the Duke of Tuscany, so the duke commissioned Galileo Galilei to investigate the problem. Galileo incorrectly suggested that a column of water breaks of its own weight when the water was lifted to 34 feet. Gasparo Berti also took up the challenge and managed to produce a vacuum above the water column, but he was not able to explain it. It was Galileo's student Evangelista Torricelli who first wrote a convincing argument that the space at the top was a vacuum. The height of the column was thus limited to the maximum weight that atmospheric pressure could support. This is the limiting height of a suction pump.
Von Guericke made a breakthrough in 1640 by building the first vacuum pump. Von Guericke’s vacuum pump worked with a piston and was capable of pumping entire vessels empty. Von Guericke demonstrated that a ringing bell could not be heard in vacuum, that candles would not burn, and that different species of birds and fish could not survive in very low air pressure. By conducting experiments with a mercury barometer (invented by Evangelista Torricelli) on top of mountains, Von Guericke demonstrated that the Earth traps only a limited amount of air. Therefore he deduced that a vacuum must exist outside our atmosphere.
Engraving showing Otto von Guericke's 'Magdeburg hemispheres' experiment.
In 1654, Von Guericke was invited to Regensburg to demonstrate his experiments on vacuum before the highest dignitaries of the Holy Roman Empire. Von Guericke took two closely fitting hemispheres of copper and, using a vacuum pump, pumped air out of the sphere. He then attached two teams of sixteen horses (eight on each side) but they were unable to pull the evacuated hemispheres apart. The experiment was repeated two years later in his hometown of Magdeburg, where he was mayor. The same demonstration was given again in Berlin in 1661 (or 1663) before Frederick William, Elector of Brandenburg, with twenty-four horses.
Von Guericke’s experiments with vacuum inspired Robert Boyle to conduct his own experiments that eventually led to the formulation of Boyle's law, which states that the volume of a body of an ideal gas is inversely proportional to its pressure.
The Magdeburg Hemisphere experiment became a popular way to illustrate the principles of air pressure. Smaller copies of the hemispheres are used to this day in science classes.
A Magdeburg Hemisphere at 1967 International and Universal Exposition in Montreal, Canada.
References: # Viktor Harsch, Otto von Gericke (1602-1686) and his pioneering vacuum experiments , Aviation, Space, and Environmental Medicine # Wikipedia
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Die Magdeburger Halbkugeln
Schlagwörter: Magdeburger Halbkugel, Experiment , Druck, Otto von Guericke, Luftdruck
Im Jahre 1654 präsentierte Otto von Guericke seinen berühmten Versuch der Magdeburger Halbkugeln. Damit gelang ihm auf spektakuläre Weise der Nachweis des Luftdrucks .
Die Magdeburger Halbkugeln waren aus Kupfer gefertigt. Sie hatten einen Durchmesser von 42 cm .
Die Kugelhälften wurden mit Wachs und Lederstreifen abgedichtet. Dann wurde die Luft aus dem Hohlraum mit einer Pumpe herausgesaugt.
An jede Seite der Kugel wurden 8 Pferde gespannt, die es nicht vermochten die Kugelhälften zu trennen. Erst als von Guericke das Ventil öffnete und Luft in die Kugel strömte, fielen die Kugelhälften auseinander. Damit war es von Guericke gelungen, den Luftdruck nachzuweisen.
Otto von Guericke und dem Versuch der Magdeburger Halbkugeln sind mehrere Münzen und Briefmarken gewidmet.
Erklärung zum Versuch
Vor dem evakuieren der Kugeln ist der Druck im Innenraum gleich dem Druck, der von außen auf die Kugel wirkt ►04(A).
{\large p\,=\,\frac{F}{A}}
Da die Flächen innerhalb und außerhalb der Kugel nahezu gleich sind, können wir A als Konstante betrachten. Es gilt also:
Die Kräfte die auf die Innenseite der Kugelhälften wirken, haben den gleichen Betrag, wie die Kräften, die von außen auf die Kugel wirken. Die Kräfte sind aber entgegengesetzt gerichtet und heben sich auf.
Wenn die Kugel evakuiert wird, dann sinkt der Luftdruck im Innenraum ►04(B). Damit sinkt auch die Kraft, die vom Innenraum auf die Kugelhälften wirkt. Die resultierende Kraft drückt die Kugelhälften zusammen.
Wenn die Kugel vollständig evakuiert ist ►04(C), dann wirken nur nach die äußeren Kräfte.
Wie groß ist die Kraft, die aufgebracht werden müsste, um die vollständig evakuierten Magdeburger Halbkugeln zu trennen?
Zur Vereinfachung gehen wir davon aus, dass Innen- und Außendurchmesser der Kugel gleich sind.
Weiter müssen wir berücksichtigen, dass die Kräfte, die von den Pferden aufgebracht werden, senkrecht zu den Flächen der Halbkugeln wirken. Wir können also nur die senkrechten Kraftkomponenten berücksichtigen (blaue Pfeile). Damit reduziert sich die Kugeloberfläche auf die Kreisfläche der Halbkugeln.
{\large \begin{array}{l}geg.:\,\,d=0,42\,m\,\,\,\,\,\,\,\,\,\,\,\,ges.:\,F\\\,\,\,\,\,\,\,\,\,\,\,\,\,{{p}_{0}}\,=\,101\,kPa\end{array} }
Zunächst berechnen wir die Kreisfläche der Halbkugel.
{\large\begin{array}{l}{{A}_{\,Kreis}}\,=\,\frac{\pi }{4}{{d}^{2}}\\\\{{A}_{\,Kreis}}\,=\,\frac{\pi }{4}\cdot {{0,42}^{2}}\,{{m}^{2}}\\\\{{A}_{\,Kreis}}\,=\,0,14\,{{m}^{2}}\end{array} }
{\large\begin{array}{l}F\,=\,p\cdot \,A\\F\,=\,101\,kPa\,\cdot \,0,14\,{{m}^{2}}\\F\,=\,101\,000\,\frac{N}{{{m}^{2}}}\,\cdot \,0,14\,{{m}^{2}}\\\\F\,=\,14140\,N\,\approx \,14\,kN\end{array} }
Die Kugelhälften werden von außen mit einer Kraft von 14 kN zusammengedrückt.
Wenn wir die Hälften trennen wollen, dann ist eine Kraft von 14 kN erforderlich.
Für die Gewichtskraft F G gilt:
{\large m=\frac{F}{g}\,=\,\frac{14\,000\,N}{10\,\frac{N}{kg}}\,=\,1400\,kg }
An die evakuierten Kugelhälften muss eine Masse von mindestens 1400 kg gehängt werden, damit sie sich trennen.
- zum Luftdruck
- zur Druckmessung
- Experimente zum Luftdruck