Wolfgang Demtröder - Mechanics and Thermodynamics

Kaiserslautern, Germany

Wolfgang Demtrder

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The more astronomically oriented observations of ancient Babylonians brought about a better knowledge of the yearly periods of the star sky. The epicycle model of Ptolemy gave a nearly quantitative description of the movements of the planets. However, modern Physics in the present meaning started only much later with Galileo Galilei (15641642, Fig. ), who performed as the first physicist well planned experiments under defined conditions, which could give quantitative answers to open questions. These experiments can be performed at any time under conditions chosen by the experimentalist independent of external influences. This distinguishes them from the observations of natural phenomena, such as thunderstorms, lightening or volcanism, which cannot be influenced. This freedom of choosing the conditions is the great advantage of experiments, because all perturbing external influences can be partly or even completely eliminated (e.g. air friction in experiments on free falling bodies). This facilitates the analysis of the experimental results considerably.

Experiments are aimed questions to nature, which yield under defined conditions definite answers.

The goal of all experiments is to find reasons and causes for all phenomena observed in nature, to see connections between the manifold of observations and to categorize them under a common law. Even more ambitious is the quantitative prediction of future experimental results, if the initial conditions of the experiments are known.

A physical law connects measurable quantities and concepts. Its clear form is a mathematical equation.

Such mathematical descriptions give a clearer insight into the relations between different physical laws. It can reduce the manifold of experimental findings, which might seem at first glance uncorrelated but turn out to be special cases of the same general law that is valid in all fields of physics.

Its range of validity and predictive capability is checked by experiments.

Since the formulation of a theory requires a mathematical description, a profound knowledge of basic mathematics is indispensible for every physicist.

The close relation between theory and experiments is illustrated by the following consideration:

If a free falling body in a vacuum container at the surface of the earth is observed one finds that the fall time over a definite distance is independent of the size or form of the body and also independent of its weight. In contrast to this result is the fall of a body in any fluid, instead of vacuum where the form of the body does play a role because here perturbing influences, such as friction often cannot be neglected. Neglecting these perturbations one can replace the body by the model of a point mass . With other words: In these experiments the falling body behaves like a point mass, because its size does not matter. The theory can now give a complete description of the movement of point masses under the influence of gravitational forces and it can predict the results of corresponding future experiments (see Chap. ).

Now the experimental conditions are changed: For a body falling in water the velocity and fall time do depend on size and weight of the body, because of friction and buoyancy. In this case the model of a point mass is no longer valid and has to be broadened to the model of spatially extended rigid bodies (see Chap. ). This model can predict and quantitatively explain the movements of extended rigid bodies under the influence of external forces.

If we now further extend our experimental condition and let a massive body fall onto a deformable elastic steel plate, our rigid body model is no longer valid but we must include in our model the deformation of the body, This results in the model of extended deformable bodies , which describes the interaction and the forces between different parts of the body and explains elasticity and deformation quantitatively (see Chap. ).