What is an impact, and what are direct, oblique and central impacts and the phases of collision?

In one line

An impact is a collision of two bodies over a very short time with very large forces; it is classified by the line of impact and the direction of the velocities.

Explained simply

Two billiard balls hitting each other is an impact. If they hit head-on along the line joining their centres, it is direct; if one strikes the other at an angle, it is oblique.

Technically, the line of impact is the common normal to the contact surfaces at the point of contact. If the mass centres of both bodies lie on it, the impact is central; otherwise eccentric. If the velocities are along the line of impact, it is direct; if not, oblique.

How it works

1. Direct central impact: velocities along the line joining the centres (head-on balls).
2. Oblique central impact: centres on the line of impact, but one or both velocities at an angle to it.
3. Period of deformation: bodies press into each other until they momentarily share a common velocity along the line of impact.
4. Period of restitution: bodies regain shape partly or fully and separate.
5. The ratio of restitution impulse to deformation impulse is the coefficient of restitution e.
6. Types by e: perfectly elastic (e = 1, no KE loss), perfectly plastic (e = 0, bodies move together), real (0 < e < 1).

Key formula

\( e = \dfrac{\int R\,dt}{\int D\,dt} \) (impulse of restitution / impulse of deformation), dimensionless, \( 0 \le e \le 1 \).

Quick example

A car rear-ending another on a straight road is close to a direct central impact. A carrom striker hitting a coin at an angle is an oblique central impact. A bullet that embeds in a wooden block is perfectly plastic (e = 0).

Common mistakes

• Defining the line of impact as the direction of the velocity; it is the common normal at contact.
• Calling every angled hit 'eccentric'; if centres lie on the common normal it is still central.
• Thinking the bodies stop during the deformation phase; they reach a common velocity, not necessarily zero.

How MU asks it

A 3 to 4-mark theory part: 'Explain direct central and oblique central impact with sketches' or 'Explain the periods of deformation and restitution'. Draw two spheres with the line of impact marked for each case.