# How is it that momentum is being preserved in a non elastic collision?

xWaldorf
How is it that momentum is being preserved in a non elastic collision?
for example let's say that two balls are colliding head-on, not elastically and heat is produced, does that not reduce the momentum of the system?

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Summary:: conservation of momentum in a non-elastic collision

How is it that momentum is being preserved in a non elastic collision?
for example let's say that two balls are colliding head-on, not elastically and heat is produced, does that not reduce the momentum of the system?
No. It reduces the mechanical energy.

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Summary:: conservation of momentum in a non-elastic collision

How is it that momentum is being preserved in a non elastic collision?
for example let's say that two balls are colliding head-on, not elastically and heat is produced, does that not reduce the momentum of the system?
Momentum is a vector. The momentum of that system, in the CoM (centre of momentum) frame, before and the collision, would be zero.

PS Newton's third law implies conservation of momentum in a collision.

• vanhees71
How is it that momentum is being preserved in a non elastic collision?
for example let's say that two balls are colliding head-on, not elastically and heat is produced, does that not reduce the momentum of the system?

Thought I might add, total energy is conserved since the decrease in mechanical energy is accounted for by the increase in internal energy of the balls. They'll get hot!

During the collision, ball 1 exerts a force ##\vec{F}_{21}## on ball 2, and likewise ball 2 exerts ##\vec{F}_{12}## on ball 1. These are necessarily related by ##\vec{F}_{21} = - \vec{F}_{12}##, and are some functions of time.

The impulse on ball 1, ##\Delta\vec{p}_{1} = \int_{t_1}^{t_2} \vec{F}_{12} dt = - \int_{t_1}^{t_2} \vec{F}_{21} dt = -\Delta \vec{p}_{2}##. The total change in momentum of the system ##\Delta\vec{p}_{1} + \Delta\vec{p}_{2} = \vec{0}##.

There's nothing here @kuruman and @PeroK haven't already said, but I often find it helpful to scribble some stuff out and see if it works out!

• vanhees71