Find the speed and direction of the balls after collision.

Question

A 1.5 kg ball moving at 2 m/s to the right collides head on with a 1kg ball moving at 3 m/s to the left. The coefficient of restitution is 0.7. Find the speed and direction of the balls after collision.

Answer 1

I have found that the best way to solve this is a combination of conservation of momentum and the relative velocity condition. This system of linear equations can be solved generally:

m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂' and ε(v₁-v₂) = v₂' - v₁'

You can use the second equation to find v₂' in terms of v₁, v₂, and v₁' and substitute into 1st equation to get v₁' in terms of the initial data:

v₁' = (1/(m₁+m₂)((m₁-εm₂)v₁ + (1+ε)m₂v₂)) Note that v₂' is the same equation with all subscripts switched between 1 and 2

Elastic collision is ε=1 and nonelastic is ε=0 (In physics, the terms elastic, inelastic, and perfectly inelastic are used. I prefer the terminology perfectly elastic, partially elastic, and inelastic because perfectly elastic is not seengenerally whereas perfectly inelastic is seen all the time, macroscopically)

You can just substitute in the masses and velocities (note v₂ is -3 m/s if E is taken to be +)

Please consider a tutor. Take care.