14.5 : Impact

Impact occurs when two bodies collide, leading to the application of impulsive forces between them. Analyzing impact mechanics involves considering two colliding particles moving along a line known as the line of impact, which passes through their centers and is perpendicular to the contact plane.

When particles with different initial velocities collide, they induce deformation by applying equal and opposite impulses. At the point of maximum deformation, the particles move together with identical velocities. Subsequently, restitution takes place, causing the particles to either return to their original shape or remain permanently deformed. The equal but opposite restitution impulse acts to push the particles apart, with the deformation impulse consistently exceeding the restitution impulse in practical scenarios.

Following separation, the particle with the lower initial velocity experiences an increase in velocity, while the system's overall momentum remains conserved. The principle of impulse and momentum is applicable to individual particles throughout the deformation and restitution phases. Additionally, the coefficient of restitution, representing the ratio of the restitution impulse to the deformation impulse, can be calculated based on the initial and final velocities of the particles. This comprehensive understanding of impact mechanics provides insights into the intricate dynamics of collisions and the subsequent behavior of colliding bodies.