Impact

During deformation, two colliding particles exert equal and opposite impulses on each other, causing material compression at the contact plane. The particles move along the line of impact, perpendicular to the contact surface. At maximum deformation, both particles momentarily move with the same velocity before restitution begins, even though the deformation impulse is always greater than the restitution impulse in practical scenarios.

The coefficient of restitution is the ratio of the restitution impulse to the deformation impulse during collision. It quantifies how much the particles separate after impact based on their initial and final velocities. This dimensionless value indicates whether particles undergo elastic recovery, partial recovery, or permanent deformation following the collision.

During impact, the restitution impulse pushes the particles apart with equal but opposite forces. The particle with lower initial velocity experiences a greater relative change in velocity because it receives the same impulse magnitude as the faster particle. However, the system's overall momentum remains conserved throughout both deformation and restitution phases.

The line of impact is an imaginary line passing through the centers of two colliding particles, perpendicular to the contact plane. It defines the direction along which impulsive forces act during collision. Analyzing motion along this line simplifies impact mechanics by isolating the primary collision effects from other motion components.

The deformation impulse occurs first, compressing the particles together and reducing their relative velocity until they move at the same speed. The restitution impulse follows, pushing them apart and increasing their relative separation. Practically, the deformation impulse always exceeds the restitution impulse, meaning particles never fully return to their pre-collision state.

The principle of linear impulse and momentum applies to individual particles during both deformation and restitution phases of impact. By analyzing impulses and velocity changes for each particle separately, engineers can determine post-collision velocities and verify momentum conservation. This approach enables systematic calculation of impact outcomes using impulse-momentum relationships.

Yes, the system's total momentum remains conserved throughout impact, even though individual particles experience significant velocity changes. Equal and opposite impulses act on each particle during both deformation and restitution phases. This conservation principle holds regardless of whether particles undergo elastic recovery or permanent deformation.