Elastic Collision in Two Dimensions (Oblique Collision)

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If the colliding bodies do not move along the same straight line path, then the collision is said to be an oblique collision.

A typical oblique collision in two dimensions

A body of mass m₁ is moving with a velocity along X-axis. Let it suffer elastic collision with a stationary body of mass m₂. The distance b, between the initial line of motion and a line parallel to it through the centre of the target body is called the impact parameter. This is a measure of the directness of the collision. It may be defined as the distance by which the collision misses being head-on.

Clearly, for a head-on collision, b = 0.

After collision, let body of mass m₁ be deflected at angle q₁ with the initial direction. The body of mass m₂ is deflected at angle q₂ with the initial direction.

Let  be the velocities of bodies of masses m₁ and m₂ respectively, after the collision.

Applying the law of conservation of momentum to the X-component of motion, we get

For Y - component of motion,

The collision is elastic. So kinetic energy will be conserved.

In the equations (1), (2) and (3) v_1f and v_2f can be resolved_, if m₁, m₂, v_1f, v_2f, q₁ and q₂ are known.

Coefficient of restitution

According to Newton's experimental law of impact, the ratio of relative speed of separation after collision and the relative speed of approach before collision is constant. This constant is called coefficient of restitution or coefficient of resilience. It is denoted by e. It is a measure of the degree of elasticity of a collision. Its value depends upon the nature of the colliding bodies.

For a perfectly elastic collision, the value of e is 1. If 0 < e < 1, then the collision is inelastic. For a perfectly inelastic collision, e = 0. If e > 1, then the collision is a super-elastic collision. (An example of super elastic collision is that of a cracker which is forcefully struck against the ground.)