Балкански 2008, Теория — Задача 3. Exercise 2

Concours Général de Physiques « Minko Balkanski » — 17 May 2008 · 17 май 2008 г.

Указания

The main problem and the three exercises are completely independent and can be solved in any order.

All the answers must be given in English or French. The clarity and precision will be taken into account for the final note.

The exam is 4 hours long! The calculators are authorized.

Условие

You have a homogenous sphere of mass $m$, radius $R$, and an initial angular speed $\omega$ around a horizontal axe passing by its center. We drop this sphere from a vertical height $h$, without an initial speed. By introducing a coefficient of restitution $e$ (the norm of the final speed divided by the norm of the initial speed):

1.) Formulate the forces acting on the sphere and write the fundamental principle of dynamic applied to the sphere.

2.) By analyzing the following two cases:

a) Rotation with slipping during all the time of the shock.

b) Rotation without slipping during the last part of the shock.

Calculate the bounce angle $\vartheta$, i.e. the angle between the vertical axis and the speed of the center of the masses of the sphere G, just after the impact. Comment.

Решение

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Оригинал в Архива: CGP_2008_en.pdf