ELASTIC IMPACT

Most of the collisions that have been considered so far have resulted in objects coalescing at impact. Impacts of this type are called inelastic.

If, on the other hand, a bounce occurs at collision, we have an elastic impact the colliding object(s) are said to be elastic.

The simplest example of an elastic impact is a direct impact, i.e. an impact which the direction of motion just before impact is parallel to the impulses that act at the instant of collision e.g.

 

 

 

 

 

 

 

 

NEWTON'S LAW OF RESTITUTION

When two particles approach each other, collide directly and then move apart the speed with which they separate is usually less than the speed at which approached each other.

Experimental evidence suggests that, for two particular colliding particles, the separation speed is always the same fraction of the approach speed. It w from such evidence that Newton formulated a law known as Newton's Law of Restitution, which states that

Separation speed = e x approach speed

Or

relative speed after impact = e x relative speed before impact

The quantity represented by e is called the coefficient of restitution and it is constant for any two particular objects; its value depends upon the material of which the two objects are made.

For colliding particles, a can take any value from zero to 1.

If the particles coalesce the separation speed is zero, i.e. e = 0.

If the relative speeds before and after impact are equal, e = 1, and we say that the particles are perfectly elastic; we shall see later on that in this case there is no loss in kinetic energy because of the impact.

Note that we have been referring only to particles colliding. A particle is regarded as having no measurable size, so its shape cannot be distorted and the time for which the particles are in contact is infinitesimal.

A larger object however, such as a ball, can undergo distortion on impact and the internal changes in its structure may be such that the basic methods for collision are not completely accurate. It is, however, reasonable to model most balls as elastic particles, as the results are accurate enough for most purposes.

Note also that when we refer to the speeds before and after impact, we mean the speeds immediately before and after. If, for instance, a particle falls vertically from a height above a fixed plane, its speed increases as it falls; the speed with which it approaches the plane is understood to be the final speed a split second before the collision with the plane.

Similarly the speed of separation from the plane is the initial speed with which the particle begins to rise again.