Question

Can someone explain this statement to me?

"In conclusion the momentum is conserved in both systems of collision but some energy will be lost in an inelastic system."

Answer 1

Solution:

When no external forces act , the objects involved in a collision are together called a system . Their kinetic energy will be transformed into other forms during the inelastic collision . So it is not conserved.

Inelastic collision is one in which the colliding objects will move with a common velocity after the collision.

When no external forces act , the initial momentum before collision = Final momentum after the collision.

If two objects have masses m₁ and m2 , and initial velocity v1 & v2, after colliding , they will have a common velocity V .

m₁ v₁ + m₂ v₂ = (m₁+m₂) V , according to momentum conservation. Momentum of a system is always conserved as long as No external forces act.

but kinetic energy is not conserved because Energy is converted to other forms

Since each individual mass will have a common final velocity ,which is Lesser than their initial velocities, the total final Kinetic energy is less than the total initial kinetic energy.

Iniital kinetic energy = 1/2 m₁ v₁² + 1/2 m₂ v₂² ..

Final kinetic energy = 1/2 (m₁+m₂) V² . , which is always less than the initial kinetic energy because there will be loss in the form of heat , sound etc. Because there is loss , it is said that kinetic energy is Not conserved in an Inelastic collision.

During an Elastic collision, momentum and kinetic energy of the system are conserved. That implies the momentum of the objects before a collision is equal to the momentum of the objects after the collision. And the kinetic energy before a collision is equal to the kinetic energy after the collision.

If Kinetic energy is not lost during a collision , such a system is said to have undergone an Elastic collision.