# Conservation of momentum VS friction

#### FelBEach

If you are in a moving train and the train stops instantly would you hit the object ahead of you at the exact same speed the train was traveling or would there be some slight deceleration due to friction? Wouldn't the friction your body experiences with the seat you are sitting on and the air around you cause you to decelerate even at a very minute rate?

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#### Ofey

You are correct in the point that friction acts to slow the passanger down a little (very little).

However, if a train moves and suddenly stops, it loses its momentum (which has to be conserved at all costs), so that momentum is now shared between every "loose" object in the train (people etc.)

For conservation of momentum we have that

m(train+loose objects)*v.initial=m(loose objects)*v.end

The train has a much larger mass than the loose objects, so the end velocity for them has to be a lot larger than when they were moving with the same speed as the train.

Conclusion, friction slows the passenger down a little, but the passengers total velocity is still larger than when moving at the same speed as the train.

#### FelBEach

when I said the train stops I was thinking the train hit some type of immovable object causing an immediate stop. Wouldn't the momentum from the train be just absorbed by the object and your body would only be moving because it was moving to begin with and just hasn't been stopped yet?

#### Doc Al

Mentor
You are correct in the point that friction acts to slow the passanger down a little (very little).

However, if a train moves and suddenly stops, it loses its momentum (which has to be conserved at all costs), so that momentum is now shared between every "loose" object in the train (people etc.)

For conservation of momentum we have that

m(train+loose objects)*v.initial=m(loose objects)*v.end

The train has a much larger mass than the loose objects, so the end velocity for them has to be a lot larger than when they were moving with the same speed as the train.

Conclusion, friction slows the passenger down a little, but the passengers total velocity is still larger than when moving at the same speed as the train.
This is completely incorrect. Momentum of the "train + loose objects" is not conserved--there is an external force acting on the train!

when I said the train stops I was thinking the train hit some type of immovable object causing an immediate stop. Wouldn't the momentum from the train be just absorbed by the object and your body would only be moving because it was moving to begin with and just hasn't been stopped yet?
Perfectly correct. Your body will continue moving in a straight line at constant speed unless acted upon by some force. (This is Newton's 1st law.) The seat friction (hopefully) will slow you down a bit before you collide into something.

#### Ofey

Of course, I am terribly sorry I was just thinking that the train stopped, never thought about the force making it stop, which obviously has to exist.

#### FelBEach

Thanks, you guys helped me a lot. respect

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