Collision
Category : JEE Main & Advanced
Collision is an isolated event in which a strong force acts between two or more bodies for a short time as a result of which the energy and momentum of the interacting particle change.
In collision particles may or may not come in real touch e.g. in collision between two billiard balls or a ball and bat, there is physical contact while in collision of alpha particle by a nucleus (i.e. Rutherford scattering experiment) there is no physical contact.
(1) Stages of collision : There are three distinct identifiable stages in collision, namely, before, during and after. In the before and after stage the interaction forces are zero. Between these two stages, the interaction forces are very large and often the dominating forces governing the motion of bodies. The magnitude of the interacting force is often unknown, therefore, Newton?s second law cannot be used, the law of conservation of momentum is useful in relating the initial and final velocities.
(2) Momentum and energy conservation in collision
(i) Momentum conservation : In a collision, the effect of external forces such as gravity or friction are not taken into account as due to small duration of collision \[(\Delta t)\] average impulsive force responsible for collision is much larger than external force acting on the system and since this impulsive force is 'Internal' therefore the total momentum of system always remains conserved.
(ii) Energy conservation : In a collision 'total energy' is also always conserved. Here total energy includes all forms of energy such as mechanical energy, internal energy, excitation energy, radiant energy or even mass energy.
These laws are the fundamental laws of physics and applicable for any type of collision but this is not true for conservation of kinetic energy.
(3) Types of collision : (i) On the basis of conservation of kinetic energy.
| Perfectly elastic collision | Inelastic collision | Perfectly inelastic collision |
| If in a collision, kinetic energy after collision is equal to kinetic energy before collision, the collision is said to be perfectly elastic. | If in a collision kinetic energy after collision is not equal to kinetic energy before collision, the collision is said to inelastic. | If in a collision two bodies stick together or move with same velocity after the collision, the collision is said to be perfectly inelastic. |
| Coefficient of restitution e = 1 | Coefficient of restitution 0 < e < 1 | Coefficient of restitution e = 0 |
| \[{{(KE)}_{\text{final}}}={{(KE)}_{\text{initial}}}\] | Here kinetic energy appears in other forms. In some cases \[{{(KE)}_{\text{final}}}<{{(KE)}_{\text{initial}}}\] such as when initial KE is converted into internal energy of the product (as heat, elastic or excitation) while in other cases \[{{(KE)}_{\text{final}}}>{{(KE)}_{\text{initial}}}\] such as when internal energy stored in the colliding particles is released | The term 'perfectly inelastic' does not necessarily mean that all the initial kinetic energy is lost, it implies that the loss in kinetic energy is as large as it can be. (Consistent with momentum conservation). |
| Examples : (1) Collision between atomic particles (2) Bouncing of ball with same velocity after the collision with earth. | Examples : (1) Collision between two billiard balls. (2) Collision between two automobile on a road. In fact all majority of collision belong to this category. | Example : Collision between a bullet and a block of wood into which it is fired. When the bullet remains embedded in the block. |
(ii) On the basis of the direction of colliding bodies
| Head on or one dimensional collision | Oblique collision |
| In a collision if the motion of colliding particles before and after the collision is along the same line, the collision is said to be head on or one dimensional. | If two particle collision is ?glancing? i.e. such that their directions of motion after collision are not along the initial line of motion, the collision is called oblique. If in oblique collision the particles before and after collision are in same plane, the collision is called 2-dimensional otherwise 3-dimensional. |
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Impact parameter b is zero for this type of collision.
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Impact parameter b lies between 0 and \[({{r}_{1}}+{{r}_{2}})\] i.e. 0 < b < \[({{r}_{1}}+{{r}_{2}})\] where \[{{r}_{1}}\] and \[{{r}_{2}}\] are radii of colliding bodies.
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| Example : collision of two gliders on an air track. | Example : Collision of billiard balls. |
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