Collisions
Elastic and inelastic collisions in one and two dimensions, coefficient of restitution. (Physics › Work, Energy and Power, NEET UG syllabus.)
What is Collisions?
Short interaction in which impulsive internal forces dominate, so total linear momentum of the system is conserved
Key formula / rule: Momentum conservation
Key points
- Classify collisions by kinetic energy and apply momentum conservation with the coefficient of restitution
Common exam trap
Conserving kinetic energy in an inelastic collision
Definitions
- Name
Collision
- Definition
Short interaction in which impulsive internal forces dominate, so total linear momentum of the system is conserved
- Name
Elastic and inelastic
- Definition
Elastic collisions conserve kinetic energy (e = 1); perfectly inelastic bodies move together with maximum energy loss (e = 0)
- Name
Exam insight
- Definition
In a one-dimensional elastic collision between equal masses the velocities are simply exchanged
- Name
Worked example
- Definition
2 kg at 5 m/s sticking to a 3 kg body at rest: v = 10/5 = 2 m/s, kinetic energy falls from 25 J to 10 J
Learning objectives
Classify collisions by kinetic energy and apply momentum conservation with the coefficient of restitution
Formulae
- Name
Momentum conservation
- Expression
m1 u1 + m2 u2 = m1 v1 + m2 v2
- Name
Coefficient of restitution
- Expression
e = (v2 - v1)/(u1 - u2)
Common mistakes
Conserving kinetic energy in an inelastic collision
Ignoring the vector nature of momentum in two dimensions
Keywords
collision
elastic
inelastic
coefficient of restitution
momentum
conservation
kinetic energy
Practice preview
In a perfectly inelastic collision, what happens to the kinetic energy of the system?…
medium
A particle of mass m1 moving with velocity v1 collides with a particle of mass m2 at rest. If the collision is elastic and head-on, the velocity of the first particle after collision is given by:…
hard
A ball of mass m collides head-on with an identical ball at rest. If the collision is perfectly elastic, what is the velocity of the second ball after the collision?…
medium