Understanding Inelastic Collisions

An inelastic collision is a type of collision in which kinetic energy is not conserved. In such collisions, some of the initial kinetic energy is transformed into other forms of energy, such as heat, sound, or energy causing deformation of the colliding bodies. An example is when two cars collide and crumple, or when a ball of clay hits a wall and sticks to it.

Conservation Laws in Collisions

Let's look at the fundamental conservation laws that apply during collisions.

• Conservation of Total Energy: In any process, the total energy of a closed system always remains conserved. This means the sum of all forms of energy (kinetic, potential, internal, etc.) before the collision equals the sum of all forms of energy after the collision. However, the question specifically asks about Kinetic Energy and Mechanical Energy.
• Conservation of Linear Momentum: The total linear momentum of a system of bodies remains constant if no external force acts on the system. Linear momentum ($\vec{p}$) is a vector quantity defined as the product of mass ($m$) and velocity ($\vec{v}$), i.e., $\vec{p} = m\vec{v}$. This principle is derived from Newton's laws of motion and applies universally to all types of collisions (elastic and inelastic) as long as the system is isolated from external forces during the collision. For a system of two bodies colliding, the total momentum before collision ($\vec{p}_{1i} + \vec{p}_{2i}$) equals the total momentum after collision ($\vec{p}_{1f} + \vec{p}_{2f}$). Mathematically, $\vec{p}_{system, initial} = \vec{p}_{system, final}$.
• Conservation of Kinetic Energy: Kinetic energy ($KE = \frac{1}{2}mv^2$) is conserved only in elastic collisions. In inelastic collisions, kinetic energy is lost due to work done against internal forces (like friction, deformation). So, the total kinetic energy before an inelastic collision is not equal to the total kinetic energy after the collision ($\sum KE_{initial} \neq \sum KE_{final}$).
• Conservation of Mechanical Energy: Mechanical energy is the sum of kinetic and potential energy. While total energy is always conserved, mechanical energy (kinetic + potential) is only conserved if no non-conservative forces (like friction or forces causing deformation) are doing work within the system. Since inelastic collisions involve loss of kinetic energy due to deformation, heat, etc., mechanical energy is generally not conserved in inelastic collisions.

Which Quantity is Always Conserved?

Based on the principles of physics, the conservation of linear momentum holds true for any isolated system of colliding bodies, regardless of whether the collision is elastic or inelastic. Kinetic energy, however, is not conserved in inelastic collisions. Mechanical energy is also not generally conserved in such cases. Therefore, during an inelastic collision between two bodies, the quantity that always remains conserved is Linear Momentum, provided no external forces act on the system.