Читать книгу Fundamentals of Numerical Mathematics for Physicists and Engineers - Alvaro Meseguer - Страница 19

A small point‐like object of mass initially at rest is released from the highest point of the surface A of height , as shown in the following figure. The object slowly starts to slide under the effects of gravity until it reaches point B at which it loses contact with the surface. The goal of this practical is to determine the abscissa of that point.

First, assuming there are no friction forces, show that the speed of the object at , i.e. still in contact with the surface, is

Then show that the horizontal velocity is given by the expression in the figure on the left. Imposing that there is no horizontal acceleration at point B (i.e. ) show that (excluding points where )

at the point where contact is lost.

Consider the family of surfaces shown in the figure on the right. Releasing the object from point , find the abscissas for , and 0.9.