# Collisions (elastic vs inelastic)?

If i take two objects...like two toy cars and roll one at the second one(at rest)

In an elastic collision, is the loss momentum in the first one equal to the gain of momentum in the second one (at rest)?

and imagining the same situation, say that the collision is inelastic..

Is the loss in momentum of car 1 equal to the gain in momentum in car 2?

I don't know if im over thinking this

Relevance
• Jim
Lv 7

Conservation of Momentum:

total momentum in = total momentum out

In the elastic collison:

m1 = mass of toy car #1

v11 = initial velocity of toy car # 1 (prior to collision)

v12 = velocity of toy car # 2 (just after collision)

m2 = mass of toy car # 2

v22 = initial velocity of toy car # 2 (just after collision)

applying conservation of momentum:

m1v11 = m1v12 + m2v22 (vector equation)

---------------

In the perfectly inelastic collision:

m1 = mass of toy car # 1

v11 = velocity of toy car # 1 (prior to collision)

vf = velocity after collision

m2 = mass of toy car # 2

applying conservation of momentum:

m1v11 = (m1 + m2)vf (vector equation)

the answer to the first question is yes, however much momentum is lost from car 1 is equal to the momentum gain in car 2 assuming it is a perfectly elastic collision.

assuming it is a perfectly inelastic collision for scenario two, then the momentum of car 1 before the impact is now equal to the momentum of car 1+ car 2 after the impact.

in any scenario where the collision is either not perfectly inelastic or elastic, then some much more complex math relying on many variables comes into play, just worry about perfectly elastic and inelastic.

Source(s): physics class.