Page:Elementary Text-book of Physics (Anthony, 1897).djvu/54

40 the collision. These extreme values of e are never exhibited by real bodies, though the value $$e = 0$$ may be closely approached in many instances. No body has a value of $$e$$ that is even appreciably equal to 1, so that there is always a loss of kinetic energy by impact. The energy thus lost is transformed into other forms of energy, principally into heat.

36. Displacement of a Rigid Body.— Under the limitation that we have set, that the points of the body shall move only in parallel planes, it is manifest that the motion of the body is completely given if the motion of its section by any one plane be given. In describing the displacement of a body under these limitations we need only describe the displacement of one of its sections by one of the planes in which the motion occurs. It is furthermore clear that the motion of this section will be completely described if the motion of any two points in it or of the line joining them be given.

When a body is so displaced that each point in it moves in a straight line through the same distance, its displacement is called a translation. When the points of the body describe arcs of circles which have a common centre, its displacement is called a rotation. Any displacement of a body may be effected by a translation combined with a rotation. To show this, let $$AB$$ (Fig. 11) represent the initial position of a line in the body, $$A'B'$$ its final position. The transfer from the initial to the final position may be effected by a translation of the line $$AB$$ to such a position that the point $$C$$, which may be any point in the body, coincides with the corresponding point $$C''$$. Taking this point $$C''$$ as the centre, a rotation through an angle $$\theta$$, which is the same whatever point be chosen for $$C$$, will bring the line into its final position. While the angle of rotation is the same whatever point be chosen for $$C$$, the translation which brings $$C$$ into coincidence with $$C''$$ will differ for different positions of $$C$$.