02 Feb, 2013
PRESENTATION: Two plungers or suckers are adjusted to obtain good coupling and create a partial vacuum between them. The force needed to separate them is proportional to the cross-section and the atmospheric pressure surrounding them.
- Improved Vacuum Bazooka, John Cockman, Phys. Teach. 41, 246 (2003)
- Simple vacuum experiments, R. D. Edge, Phys. Teach. 25, 523 (1987)
INTRODUCTION: Two hemispheres are joined and an attempt is made to pull them apart. If a vacuum is formed within the sphere, it will not be possible to separate them without a great effort because the force exerted by the pressure inside disappears and the atmospheric pressure is not compensated for. The experiment was thought up by Otto von Guericke, Burgomaster of Magdeburg. In 1654 it was tried with two hemispheres measuring 55 cm in radius in the presence of Emperor Ferdinand III. Those present were amazed to see that Guericke needed a great effort by 16 horses to separate the hemispheres.
OBJECTIVE: To verify Guericke’s experiment with two hemispheres with a smaller radius, and to calculate the force needed to separate them.
MATERIALS: Two hemispheres, in this case, two identical plungers (of radius 7.5 cm), a vacuum pump (optional).
SETUP: The two hemispheres are joined so that a seal is created at the contact surface that is hermetic, i.e., one which does not let air get in. Later, a vacuum will be produced in the space between the hemispheres. In this case the two hemispheres are two plungers, which will be taken as being semi-spheres for the mathematical calculations that will be done, and, despite not being a highly efficient system, we will interpret the vacuum achieved when forcing the plungers together as being total (even though there is no vacuum as such). Later a force will be applied in an attempt to separate the two hemispheres.
EXPLANATION: Each hemisphere is found to be subjected to a force F₀ due to atmospheric pressure P₀, and an internal force F due to internal pressure P. Therefore, and taking into account the relationship between the force and the pressure exerted on a surface: F= P·S (as the force is exerted perpendicular to the plane of the joint of the hemispheres, then that surface will be a circle of radius R), the resultant force on each hemisphere will be aimed inwards and will be given by: FR=F₀ – F
When the vacuum is formed, P≃0, and the only force acting is that exerted by atmospheric pressure. Thus, for our hemispheres of R=0.075 m (and assuming a total vacuum inside) the force required to separate them would be: F= P₀·(3.1415·0.075²)=1,790.56 N
CONCEPTS: pressure, atmospheric pressure, force.
- Tipler P.A. Física. Barcelona: Reverté, 2010.
- De Juana J.M., Física General, Pearson, 2009.
- Serway R.A y J.W.Jewett. Física, Thomson-Paraninfo, 2010.
STUDENTS 2012-2013: Manuel Otero Jorge, Óscar Penas García, Julián Pérez Tavernier
LINK pdf STUDENTS (in Spanish):