Hello everyone in this article we are going to discuss the interesting and important concept of mechanical physics i.e. collision.
Consider the following examples,
- Striking of one marble on another in circle during marble play
- Striking the tennis ball on the wall
- Head on strike of vehicles during accident
All above are the examples of collision. During collision the terms like momentum, velocity and kinetic energy of colliding bodies plays very important role.
Let’s learn the concept of collision in detail……….!
Head-on striking of two objects is known as collision. There are two types of collision viz; 1) Elastic collision 2) Inelastic collision
1) Elastic collision:
The collision between two bodies in which the kinetic energy of collision remains constant before and after collision is known as elastic collision.
∴ Kinetic energy before collision = Kinetic energy after collision
e.g. collisions of gas molecules.
2) Inelastic collision:
The collision between two bodies in which the kinetic energy of collision do not remains constant before and after collision is known as inelastic collision.
∴ Kinetic energy before collision ≠ Kinetic energy after collision
∴ Kinetic energy before collision > Kinetic energy after collision
e.g. ball striking on bat while playing cricket.
Perfectly Inelastic collision:
The inelastic collision between two objects in which colliding bodies stuck in to each other is known as perfectly inelastic collision.
e.g. an arrow remains in fruit like apple in practice of archery.
Let’s discuss the elastic collision in one dimension……!
Suppose that two spheres of masses m1 and m2 moving initial velocities u1 and u2 (u1 > u2 ) along the same line as shown in fig. be
Let the spheres has head on collision in time ‘t’ and gets separated with the velocities v1 and v2.
Initial momentum of sphere before collision = m1 u1 + m2 u2
Final momentum of sphere after collision = m1 v1 + m2 v2
According to law of conservation of linear momentum we have,
Initial momentum before collision = Final momentum after collision
∴ m1 u1 + m2 u2 = m1 v1 + m2 v2 ……………….(1)
∴m1 u1 – m1 v1 = m2 v2 – m2 u2
∴ m1 (u1 – v1) = m2 (v2 – u2 )…………………(A)
Since the collision is perfectly elastic we can write,
∴ Kinetic energy before collision = Kinetic energy after collision
i.e relative speed of approach = relative speed of separation.
∴ relative speed of approach , ua = u1 – u2
∴ relative speed of separation, vs = v2 – v1
The ratio of relative speed of separation to the relative speed of approach is called as coefficient of restitution (e).
∴ e = relative speed of separation/relative speed of approach
If, e = 1 collision is perfectly elastic
If, 1 < e > 1 collision is inelastic
From equation (3) we can write as,
∴ v1 = v2 + u2 – u1…………………………(4)
∴ v2 = u1 + v1 – u2…………………………(5)
Final velocities of object after separation ….!
We have, from equation (4)
∴ v1 = v2 + u2 – u1
On substituting in equation (1) we have
∴m1 u1 + m2 u2 = m1 (v2 + u2 – u1) + m2 v2
∴ m1 u1 + m2 u2 = m1 v2 + m1 u2 – m1 u1 + m2 v2
∴ 2 m1 u1 + m2 u2 – m1 u2 = m1 v2 + m2 v2
∴ (m1 + m2)v2 = 2 m1 u1 + u2 (m2 – m1)