Collision of Bodies and Its Types

Collision of Bodies: In the realm of engineering mechanics, the study of collisions holds immense importance in understanding the behavior and interactions of bodies in motion. Whether it's analysing the impact of vehicles in accidents, predicting the effects of machinery collisions, or assessing the resilience of structures against impacts, a comprehensive understanding of collision mechanics is essential for engineers.

A collision can be defined as “ an event that occurs when two or more bodies interact by physically coming into contact for a very short period of time and exert very large force on each other, resulting in the exchange of energy and/or momentum between them ”. During collisions, energy and momentum exchange, resulting in a change in the objects' velocities and trajectories. In physics, collision is also referred to as "impact."

In our daily lives, we often observe collisions between bodies. Examples include the collision between a leg and a football, the collision between two coins in carrom, the collision between a bat and a ball, and the collision between a dropped object and the floor. These instances highlight the dynamic exchange of energy and momentum that occurs during each collision.

Type of Collision of Bodies

Collision of bodies can be classified based on the direction of motion of colliding bodies relative to the line of impact. Here is the classification:

Central (Direct) Impact

Oblique Impact

1. Perfectly Elastic Collision

• Momentum is conserved.
• Kinetic energy is conserved.

2. Inelastic Collisions

(i) Perfectly Inelastic Collision

• Momentum is conserved.
• Kinetic energy is not conserved.

(ii) Partially Inelastic Collision

• Momentum is conserved.
• Kinetic energy is not conserved.

Laws used in Collision of Bodies

Principle of Conservation of Momentum

Initial momentum of system = Final momentum of system

m ₁ u ₁ + m ₂ u ₂ = m ₁ v ₁ + m ₂ v ₂

Note: Assign the correct sign to the velocity values in the formula above, by designating one direction as positive

Newton’s Law of Restitution

For a given pair of bodies in collision, the ratio of relative velocity after collision and relative velocity before collision is always same.

• This ratio is known as coefficient of restitution ( e ). Its value depends on the material and it is the measure of the elasticity of a collision. Value of e lies in between zero and 1.

• The coefficient of restitution helps determine the degree of energy loss or preservation during a collision, aiding in the selection of materials, designing impact-absorbing structures, and optimizing machinery performance.

e = greater than zero and less than one for inelastic collision (0 < e <1)

e = 1 for perfectly elastic collision

e = 0 for perfectly plastic collision

Principle of Conservation of Kinetic Energy

• For perfectly elastic collision, kinetic energy of the system is conserved.

• If e < 1, some kinetic energy is lost.

Special Case: Case 1

Special Case: Case 2

Some Practical Applications of Collision Studies in Engineering

• Vehicle Crash Safety: Understanding collision mechanics is vital in automotive engineering for designing vehicles with enhanced crash safety
• Structural Analysis and Design: In civil and structural engineering, collision analysis is crucial for assessing the resilience of structures against impacts such as earthquakes, explosions, or accidental collisions
• Machinery Safety and Reliability: Collision studies play a significant role in machinery design and safety. Engineers analyze collisions to prevent failures, minimize downtime, and optimize machine performance